use mod.prelude.widgets_internal.*
use mod.sdf.Cap

// Milled dark panels lit from inside. One blue-black material at three
// heights -- the ground, the slabs standing on it, the wells punched into
// the slabs -- and one orange light, thin and hot and close to an edge.
// Every control is a face set into a bezel that is part of its own box, so
// nothing a control draws reaches a neighbour: only the slab's short
// shadow (gone within 4 points) falls outside the box, onto the ground,
// and the soft light a chosen cell spills (gone within about 8).
// Every face is drawn in true points; `px` is one device pixel.

// ---------------------------------------------------------------- helpers

let lm_px = fn(dpi: float) -> float {
    return 1.0 / max(dpi, 0.5)
}

// An edge rounded to a whole device pixel in window space, handed back in
// box space: a hairline on it lands on one pixel row.
let lm_snap = fn(v: float, o: float, px: float) -> float {
    return Finish.snap(o + v, px) - o
}

// Distance from p to the segment a..b, in points.
let lm_seg = fn(p: vec2, a: vec2, b: vec2) -> float {
    let pa = p - a
    let ba = b - a
    let t = clamp(dot(pa, ba) / max(dot(ba, ba), 0.0001), 0.0, 1.0)
    return length(pa - ba * t)
}

// Which way the outline of a rounded box faces at p.
let lm_normal = fn(p: vec2, c: vec2, h: vec2, r: float) -> vec2 {
    let s = vec2(step(0.0, p.x - c.x) * 2.0 - 1.0, step(0.0, p.y - c.y) * 2.0 - 1.0)
    let q = abs(p - c) - (h - vec2(r, r))
    let qc = max(q, vec2(0.0, 0.0))
    var n = vec2(0.0, s.y)
    if q.x > q.y {
        n = vec2(s.x, 0.0)
    }
    if q.x > 0.0 && q.y > 0.0 {
        n = qc / max(length(qc), 0.0001) * s
    }
    return n
}

// Anything drawn in a grown quad fades out over its last points, so a
// shadow never ends on a hard edge where the quad stops.
let lm_fade = fn(pos: vec2, size: vec2, m: float) -> float {
    let q = pos * (size + vec2(2.0 * m, 2.0 * m))
    let e = min(min(q.x, q.y), min(size.x + 2.0 * m - q.x, size.y + 2.0 * m - q.y))
    return smoothstep(0.0, min(m, 4.0), e)
}

// The palette. The ground, and the light: body, deep, pale core, glow.
let lm_ground = fn() -> vec3 {
    return vec3(0.067, 0.086, 0.106)
}
let lm_orange = fn() -> vec3 {
    return vec3(1.0, 0.416, 0.118)
}
let lm_deep = fn() -> vec3 {
    return vec3(0.722, 0.204, 0.039)
}
let lm_core = fn() -> vec3 {
    return vec3(1.0, 0.776, 0.565)
}
let lm_glowc = fn() -> vec3 {
    return vec3(1.0, 0.353, 0.078)
}

// ---------------------------------------------------------------- heights

// A SLAB: a bezel or a panel standing on the ground. #1b1f25 with a quiet
// fall, a one-pixel lighter line along its top (#363c44), a dark line along
// its foot (#0a0c0f), the sides between; its short soft shadow falls on the
// ground under it (1.2 down, gone within 4 points). `sh` scales the shadow.
let lm_slab = fn(p: vec2, lo: vec2, hi: vec2, r: float, px: float, sh: float, hover: float, dis: float) -> vec4 {
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let n = lm_normal(p, c, h, r)
    let s = Finish.drop(p, c, h, r, vec2(0.0, 1.2), 1.3) * 0.62 * sh * (1.0 - a) * (1.0 - 0.5 * dis)
    let res = vec4(0.0, 0.0, 0.0, s)
    let t = clamp((p.y - lo.y) / max(hi.y - lo.y, 1.0), 0.0, 1.0)
    var col = mix(vec3(0.118, 0.133, 0.157), vec3(0.094, 0.110, 0.133), t)
    let ring = Finish.band(d, 0.0, px, px)
    let up = smoothstep(-0.25, 0.75, -n.y)
    let dn = smoothstep(-0.25, 0.75, n.y)
    col = mix(col, vec3(0.141, 0.157, 0.184) + vec3(0.05, 0.052, 0.055) * hover, ring * (1.0 - up) * (1.0 - dn))
    col = mix(col, vec3(0.212, 0.235, 0.267) + vec3(0.1, 0.105, 0.11) * hover, ring * up)
    col = mix(col, vec3(0.039, 0.047, 0.059), ring * dn)
    col = mix(col, lm_ground(), 0.35 * dis)
    return Finish.over(res, vec4(col * a, a))
}

// A WELL punched into a slab: floor #0b0d10, an inner shadow under its top
// edge that fades over about 5 points, a near-black top line and a faint
// light line along its lower inner edge. `deep` scales the inner shadow.
let lm_well = fn(p: vec2, lo: vec2, hi: vec2, r: float, px: float, deep: float, dis: float) -> vec4 {
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let n = lm_normal(p, c, h, r)
    let t = clamp((p.y - lo.y) / max(hi.y - lo.y, 1.0), 0.0, 1.0)
    var col = vec3(0.043, 0.051, 0.063) + vec3(0.012, 0.013, 0.016) * t
    let ins = Finish.inset(p, c, h, r, vec2(0.0, 1.8), 2.2)
    col = mix(col, vec3(0.0, 0.0, 0.0), clamp(0.8 * ins * deep, 0.0, 0.9))
    let ring = Finish.band(d, 0.0, px, px)
    let up = smoothstep(-0.25, 0.75, -n.y)
    let dn = smoothstep(-0.1, 0.8, n.y)
    col = mix(col, vec3(0.012, 0.014, 0.017), ring * up)
    col = mix(col, vec3(0.165, 0.184, 0.208), ring * dn * 0.85)
    col = mix(col, vec3(0.075, 0.086, 0.1), 0.45 * dis)
    return vec4(col * a, a)
}

// A TRACK: a long well a segmented group's answers stand in. Its floor a
// little lighter than a well's, an inner shadow under its upper wall, and
// its lower wall a 1.3 point band facing up, lit a shade from above.
let lm_track = fn(p: vec2, lo: vec2, hi: vec2, r: float, px: float) -> vec4 {
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let n = lm_normal(p, c, h, r)
    let t = clamp((p.y - lo.y) / max(hi.y - lo.y, 1.0), 0.0, 1.0)
    var col = mix(vec3(0.058, 0.067, 0.08), vec3(0.068, 0.078, 0.092), t)
    let ins = Finish.inset(p, c, h, r, vec2(0.0, 1.8), 2.0)
    col = mix(col, vec3(0.0, 0.0, 0.0), clamp(0.75 * ins, 0.0, 0.85))
    let x = max(-d, 0.0)
    let dn = smoothstep(0.2, 0.9, n.y)
    col = mix(col, vec3(0.098, 0.11, 0.128), (1.0 - smoothstep(0.9, 1.4, x)) * dn)
    let ring = Finish.band(d, 0.0, px, px)
    col = mix(col, vec3(0.012, 0.014, 0.017), ring * smoothstep(-0.25, 0.75, -n.y))
    col = mix(col, vec3(0.17, 0.188, 0.212), ring * dn * 0.8)
    return vec4(col * a, a)
}

// A FACE set into its bezel: a dark key (#202428 falling to #15181d) with a
// one-pixel outline (#3a4048) lighter on top (#4d545d). Round it a dark cut
// seats it in the slab; a raised face throws a short shadow into the cut
// under its foot. Hover brightens the outline; held, the face sinks: darker,
// a shade under its top edge, the top line gone.
let lm_face = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, hover: float, down: float, dis: float, raise: float) -> vec4 {
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let hh = hi.y - lo.y
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let n = lm_normal(p, c, h, r)
    let live = 1.0 - dis
    let up = raise * (1.0 - down * live)
    let seat = Finish.ring_out(d, 0.0, px, px) * (0.5 + 0.4 * smoothstep(0.0, 0.9, n.y))
    let sh = Finish.drop(p, c, h, r, vec2(0.0, 1.1 * up), 0.8 + 0.4 * up) * (0.3 + 0.4 * up) * (1.0 - a)
    var res = Finish.over(dst, vec4(0.0, 0.0, 0.0, max(seat, sh) * (1.0 - 0.5 * dis)))
    let t = clamp((p.y - lo.y) / max(hh, 1.0), 0.0, 1.0)
    var col = mix(vec3(0.125, 0.141, 0.161), vec3(0.082, 0.094, 0.114), t)
    col = col + vec3(0.018, 0.02, 0.022) * hover * live * (1.0 - down)
    let ins = Finish.inset(p, c, h, r, vec2(0.0, 1.6), 1.8)
    col = mix(col, col * 0.7, down * live)
    col = mix(col, vec3(0.0, 0.0, 0.0), clamp(ins * 0.7, 0.0, 0.8) * down * live)
    let upper = smoothstep(-0.3, 0.7, -n.y)
    // A faint light just under the top line of a raised face.
    col = col + vec3(0.028, 0.03, 0.034) * Finish.band(d, px, px * 2.0, px) * upper * up
    let ring = Finish.band(d, 0.0, px, px)
    var oc = mix(vec3(0.227, 0.251, 0.282), vec3(0.302, 0.329, 0.365), upper)
    oc = oc + vec3(0.1, 0.105, 0.11) * hover * live * (1.0 - down)
    oc = mix(oc, mix(vec3(0.36, 0.39, 0.425), vec3(0.47, 0.5, 0.54), upper), down * live)
    oc = mix(oc, col, 0.55 * dis)
    col = mix(col, oc, ring)
    col = mix(col, vec3(0.09, 0.1, 0.115), 0.45 * dis)
    return Finish.over(res, vec4(col * a, a))
}

// The outline of a well or a face brightened: what an unlit control shows
// under the hand (a little) and held (more). One device pixel, lighter on top.
let lm_edge = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, amt: float) -> vec4 {
    if amt < 0.001 {
        return dst
    }
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let n = lm_normal(p, c, h, r)
    let e = Finish.band(d, 0.0, px, px) * min(amt, 1.0)
    let col = mix(vec3(0.35, 0.384, 0.42), vec3(0.52, 0.553, 0.592), smoothstep(-0.3, 0.7, -n.y))
    return Finish.over(dst, vec4(col * e, e))
}

// ---------------------------------------------------------------- light

// 1. THE LIT FRAME: a line 1.5 to 2 points wide just inside the face's
// edge, orange with a pale core; the face turns near black with a dark
// orange-brown rim (#3a1a0c) that falls off within 6 to 9 points; a hot
// spill just inside the line; outward on the bezel about 0.4 of the line
// one device pixel out, gone to a tenth by 2.5 points. `s` 1 is lit; up to
// 1.5 is brighter (hover, held); under 1 a partial light.
let lm_frame = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, s: float) -> vec4 {
    if s < 0.001 {
        return dst
    }
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let hh = min(hi.y - lo.y, hi.x - lo.x)
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let x = max(-d, 0.0)
    let lw = clamp(0.085 * hh, 1.2, 2.0)
    let k = clamp(0.13 * hh, 1.0, 3.0)
    let sv = min(s, 1.0)
    let hot = clamp((s - 1.0) * 2.0, 0.0, 1.0)
    var res = Finish.over(dst, vec4(0.0, 0.0, 0.0, 0.3 * sv * a))
    let bleed = exp(-max(x - lw, 0.0) / k) * a * sv * 0.62
    res = Finish.over(res, vec4(vec3(0.36, 0.13, 0.04) * bleed, bleed))
    let inl = Finish.band(d, 0.0, lw, px)
    let spill = exp(-max(x - lw, 0.0) / 0.7) * a * (0.3 + 0.15 * hot) * sv * (1.0 - inl)
    res = Finish.over(res, vec4(lm_glowc() * spill, spill * 0.35))
    let od = max(d, 0.0)
    let g = (0.42 + 0.1 * hot) * exp(-(od * od) / (2.0 * 1.45 * 1.45)) * (1.0 - a) * sv
    res = Finish.over(res, vec4(lm_glowc() * g, g * 0.45))
    let lc = mix(lm_orange(), mix(lm_orange(), lm_core(), 0.35), hot)
    let line = inl * sv
    res = Finish.over(res, vec4(lc * line, line))
    let core = Finish.band(d, lw * 0.3, lw * 0.7, px) * sv * (0.8 + 0.2 * hot)
    return Finish.over(res, vec4(lm_core() * core, core))
}

// FOCUS on a control that is not lit: a lit line round the OUTSIDE of the
// whole control -- its bezel's edge -- with a pale core and a close halo
// (gone within 3 points), the face left as it stands (still raised, not
// darkened). Chosen is lit inside the face; focus rings the bezel: the two
// never read alike.
let lm_focus = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, s: float) -> vec4 {
    if s < 0.001 {
        return dst
    }
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let x = max(-d, 0.0)
    let lw = clamp(0.06 * min(hi.y - lo.y, hi.x - lo.x), 1.0, 1.4)
    let od = max(d, 0.0)
    let g = 0.4 * exp(-(od * od) / (2.0 * 1.2 * 1.2)) * (1.0 - a) * s
    var res = Finish.over(dst, vec4(lm_glowc() * g, g * 0.45))
    let inl = Finish.band(d, 0.0, lw, px)
    let spill = 0.22 * exp(-max(x - lw, 0.0) / 0.8) * a * s * (1.0 - inl)
    res = Finish.over(res, vec4(lm_glowc() * spill, spill * 0.3))
    let line = inl * s
    res = Finish.over(res, vec4(lm_orange() * line, line))
    let core = Finish.band(d, lw * 0.3, lw * 0.7, px) * s * 0.6
    return Finish.over(res, vec4(lm_core() * core, core))
}

// 2. THE UNDER-LIGHT: a raised key throws a thin line of light at its foot,
// a pool on the bezel's rim below it, and the pool runs on past the bezel's
// foot onto the ground for about 3 points, gone by 4 (half the 8 point gap
// to a row below). `foot` is where the bezel ends under the face.
let lm_under = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, s: float, foot: float) -> vec4 {
    if s < 0.001 {
        return dst
    }
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let w = hi.x - lo.x
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let dx = (p.x - c.x) / max(0.34 * w, 2.0)
    let along = exp(-dx * dx)
    // On the rim: bright under the face, a little less at the bezel's foot.
    let rimy = clamp((p.y - hi.y) / max(foot - hi.y, 0.5), 0.0, 1.0)
    let past = max(p.y - foot, 0.0) / 1.9
    let fy = step(hi.y, p.y) * (1.0 - 0.35 * rimy) * exp(-past * past)
    // Across, it keeps to the face's width: full in the middle, gone at
    // the face's ends, so it never runs past the bezel toward a neighbour.
    let ax = abs(p.x - c.x) / max(h.x, 1.0)
    let pool = (1.0 - smoothstep(0.3, 1.0, ax)) * fy * (1.0 - a) * 0.72 * s
    var res = Finish.over(dst, vec4(lm_glowc() * pool, pool * 0.6))
    let low = smoothstep(0.35, 0.95, (p.y - c.y) / max(h.y, 0.01))
    let foot = Finish.band(d, 0.0, px * 1.5, px) * low * along * min(s, 1.0)
    let fc = mix(lm_orange(), lm_core(), smoothstep(0.55, 1.0, along) * 0.75)
    res = Finish.over(res, vec4(fc * foot, foot))
    // The light also warms the face just above its foot.
    let warm = exp(-max(-d, 0.0) / 1.2) * low * along * a * 0.18 * min(s, 1.0)
    return Finish.over(res, vec4(lm_glowc() * warm, warm * 0.3))
}

// 2b. THE LIT CELL: the chosen cell, the tab in use and the chosen radio
// tab. The face stays DARK: a deep red-brown glass (#3c140b), darkest in
// its upper middle. The light is a thin line just inside the edge, 1.15
// points on top and sides, 1.6 along the foot, orange with a pale hot core
// that is brightest along the foot. From the line a red glow bleeds inward:
// a point or so under the top, about 3 at the sides, and from the foot a
// deep red that rises over the lower third. A faint gloss lies over the
// upper part. Outward the light spills red on the bezel and the track for a
// few points, a little more under the foot. The label is lit orange on it.
// `s` 1 is lit, more under the hand, less held.
let lm_lit = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, s: float, dis: float) -> vec4 {
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let x = max(-d, 0.0)
    let od = max(d, 0.0)
    let live = 1.0 - dis
    let sv = clamp(s, 0.0, 1.3) * live
    // Where p lies: -1 at the top edge, 1 at the foot. The weights are
    // taken from position, not from the outline's normal, so no seam runs
    // in from a corner.
    let vy = (p.y - c.y) / max(h.y, 0.5)
    let foot = smoothstep(0.25, 0.95, vy)
    // The spill outside: red, strongest against the line, gone by 7.
    let near = 0.5 * exp(-od / 0.7) + 0.36 * exp(-(od * od) / (2.0 * 2.8 * 2.8))
    let g = near * (0.75 + 0.6 * foot) * (1.0 - a) * sv * (1.0 - smoothstep(5.0, 8.0, od))
    let gc = mix(vec3(0.8, 0.2, 0.05), vec3(0.42, 0.05, 0.015), smoothstep(0.3, 3.0, od))
    var res = Finish.over(dst, vec4(gc * g, g * 0.55))
    // The face: dark maroon glass.
    let t = clamp((p.y - lo.y) / max(hi.y - lo.y, 1.0), 0.0, 1.0)
    let lv = min(sv, 1.0)
    var col = vec3(0.235, 0.078, 0.042)
    // The deep red rising from the foot over the lower part.
    let rise = smoothstep(0.3, 1.0, t)
    col = mix(col, vec3(0.64, 0.05, 0.0), rise * rise * 0.88 * lv)
    // The glow the line bleeds inward from each edge: short under the
    // top, longer from the sides, strong over the foot.
    let lwt = 1.15
    let lwb = 1.6
    let dtop = max(p.y - lo.y - lwt, 0.0)
    let dbot = max(hi.y - p.y - lwb, 0.0)
    let dsid = max(min(p.x - lo.x, hi.x - p.x) - lwt, 0.0)
    let gt = 0.5 * exp(-dtop / 1.1)
    let gs = 0.5 * exp(-dsid / 2.2)
    let gb = 0.85 * exp(-dbot / 1.8)
    let ig = (1.0 - (1.0 - gt) * (1.0 - gs) * (1.0 - gb)) * lv
    col = mix(col, vec3(0.86, 0.2, 0.02), ig)
    // A faint gloss over the upper part.
    let gl = (1.0 - smoothstep(0.12, 0.5, t)) * smoothstep(0.8, 2.6, x)
    col = col + vec3(0.035, 0.022, 0.018) * gl
    col = col * (1.0 + Finish.grain(p / px, 0.02))
    // The line, orange; its pale core brightest along the foot.
    let lw = mix(lwt, lwb, foot)
    let inl = Finish.band(d, 0.0, lw, px) * min(sv, 1.15)
    let lc = mix(vec3(0.88, 0.48, 0.3), vec3(1.0, 0.56, 0.24), foot)
    col = mix(col, lc, clamp(inl, 0.0, 1.0))
    let core = Finish.band(d, lw * 0.3, lw * 0.72, px) * mix(0.18, 1.0, foot) * min(sv, 1.15)
    col = mix(col, vec3(1.0, 0.87, 0.64), clamp(core, 0.0, 1.0))
    col = mix(col, vec3(0.2, 0.2, 0.215), 0.75 * dis)
    return Finish.over(res, vec4(col * a, a))
}

// 2c. THE LIT ROW: the lit cell drawn for a chosen row of a list, a face
// taller than a key. The same thin line with its pale core brightest along
// the foot; the face a darker, browner glass (#2d1914) the light bleeds into
// over fixed points, not over a share of the height: about 4 under the top,
// 5 in from the sides and 6 up from the foot. Outward its red light reaches
// `room` points and is gone there.
let lm_litrow = fn(dst: vec4, p: vec2, lo: vec2, hi: vec2, r: float, px: float, s: float, room: float) -> vec4 {
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let d = Material.sd_box(p, c, h, r)
    let a = Finish.cover(d, px)
    let x = max(-d, 0.0)
    let od = max(d, 0.0)
    let sv = clamp(s, 0.0, 1.3)
    let lv = min(sv, 1.0)
    let vy = (p.y - c.y) / max(h.y, 0.5)
    let foot = smoothstep(0.25, 0.95, vy)
    let near = 0.5 * exp(-od / 0.9) + 0.34 * exp(-(od * od) / (2.0 * 2.3 * 2.3))
    let g = near * (0.75 + 0.5 * foot) * (1.0 - a) * sv * (1.0 - smoothstep(room * 0.45, room, od))
    let gc = mix(vec3(0.8, 0.2, 0.05), vec3(0.42, 0.05, 0.015), smoothstep(0.3, 3.0, od))
    var res = Finish.over(dst, vec4(gc * g, g * 0.55))
    var col = vec3(0.176, 0.098, 0.078)
    let lwt = 1.15
    let lwb = 1.6
    let dtop = max(p.y - lo.y - lwt, 0.0)
    let dbot = max(hi.y - p.y - lwb, 0.0)
    let dsid = max(min(p.x - lo.x, hi.x - p.x) - lwt, 0.0)
    let gt = 0.5 * exp(-dtop / 1.6)
    let gs = 0.55 * exp(-dsid / 3.5)
    let gb = 0.62 * exp(-dbot / 2.6)
    let ig = (1.0 - (1.0 - gt) * (1.0 - gs) * (1.0 - gb)) * lv
    col = mix(col, vec3(0.62, 0.14, 0.02), ig)
    let t = clamp((p.y - lo.y) / max(hi.y - lo.y, 1.0), 0.0, 1.0)
    let gl = (1.0 - smoothstep(0.1, 0.45, t)) * smoothstep(0.8, 2.6, x)
    col = col + vec3(0.03, 0.02, 0.016) * gl
    col = col * (1.0 + Finish.grain(p / px, 0.02))
    let lw = mix(lwt, lwb, foot)
    let inl = Finish.band(d, 0.0, lw, px) * min(sv, 1.15)
    let lc = mix(vec3(0.88, 0.48, 0.3), vec3(1.0, 0.56, 0.24), foot)
    col = mix(col, lc, clamp(inl, 0.0, 1.0))
    let core = Finish.band(d, lw * 0.3, lw * 0.72, px) * mix(0.75, 1.0, foot) * min(sv, 1.15)
    col = mix(col, vec3(1.0, 0.87, 0.64), clamp(core, 0.0, 1.0))
    return Finish.over(res, vec4(col * a, a))
}

// 6. A LAMP: a dot `r` across the middle, orange with a pale centre and a
// halo of 2 to 3 points; off, a dark lens in a dark ring.
let lm_lamp = fn(dst: vec4, p: vec2, c: vec2, r: float, px: float, lit: float, dis: float) -> vec4 {
    let d = length(p - c) - r
    let a = Finish.cover(d, px)
    let od = max(d, 0.0)
    let li = lit * (1.0 - 0.7 * dis)
    let g = 0.45 * exp(-(od * od) / (2.0 * 1.1 * 1.1)) * (1.0 - a) * li
    var res = Finish.over(dst, vec4(lm_glowc() * g, g * 0.5))
    let rr = length(p - c) / max(r, 0.5)
    let body = mix(lm_orange(), lm_core(), (1.0 - smoothstep(0.0, 0.75, rr)) * 0.8)
    let off = mix(vec3(0.078, 0.086, 0.098), vec3(0.2, 0.216, 0.24), Finish.band(d, 0.0, px, px))
    var col = mix(off, body, li)
    col = mix(col, vec3(0.3, 0.2, 0.15), dis * lit * 0.6)
    return Finish.over(res, vec4(col * a, a))
}

// 4. A LIT TUBE in a groove: a thin line `tw` points across, lying along
// the middle of the well `wlo`..`whi` (corner `wr`) from `u0` to `u1` along
// it (x, or y where `vert` is 1). The line is orange (#f7873b) with a pale
// core (#ffb066). Its light turns the well's floor a dark red (#450300)
// over the lit stretch, orange right against the line and gone to the red
// within 2 points; it burns the well's rim a pale orange-brown (#944832)
// there and warms the slab round the well, gone within 4 points. Past the
// lit stretch the groove stays black.
let lm_tube = fn(dst: vec4, p: vec2, u0: float, u1: float, tw: float, px: float, dis: float, hot: float, wlo: vec2, whi: vec2, wr: float, vert: float) -> vec4 {
    let live = 1.0 - dis
    let wc = (wlo + whi) * 0.5
    let u = mix(p.x, p.y, vert)
    let v = mix(p.y - wc.y, p.x - wc.x, vert)
    let len = u1 - u0
    let on = step(0.3, len)
    let tr = max(min(tw * 0.5, len * 0.5), 0.01)
    let hl = max(len * 0.5 - tr, 0.0)
    let d = length(vec2(max(abs(u - (u0 + u1) * 0.5) - hl, 0.0), v)) - tr
    let a = Finish.cover(d, px) * on
    let od = max(d, 0.0)
    let hk = 1.0 + 0.25 * hot
    // Along the lit stretch, soft at its two ends.
    let am = smoothstep(u0 - 1.2, u0 + 1.2, u) * (1.0 - smoothstep(u1 - 1.2, u1 + 1.2, u)) * on * live
    let dw = Material.sd_box(p, wc, (whi - wlo) * 0.5, wr)
    let inw = Finish.cover(dw, px)
    // The floor: dark red over the stretch, orange against the line.
    let fl = 0.85 * am * inw
    var res = Finish.over(dst, vec4(vec3(0.27, 0.012, 0.0) * fl, fl))
    let near = exp(-od / 0.7) * inw * (1.0 - a) * on * live * hk
    res = Finish.over(res, vec4(vec3(1.0, 0.4, 0.08) * near, near * 0.3))
    // The rim of the well, lit along the stretch, the lower lip brighter.
    let rim = Finish.band(dw, 0.0, px, px) * am
    let rc = mix(vec3(0.58, 0.282, 0.196), vec3(0.65, 0.337, 0.24), step(0.0, v)) * hk
    res = Finish.over(res, vec4(rc * rim, rim))
    // The warm light on the slab past the rim.
    let ow = max(dw, 0.0)
    let wide = smoothstep(u0 - 3.0, u0 + 1.0, u) * (1.0 - smoothstep(u1 - 1.0, u1 + 3.0, u)) * on * live
    let og = 0.42 * exp(-ow / 1.5) * (1.0 - smoothstep(3.0, 4.5, ow)) * (1.0 - inw) * wide * hk
    res = Finish.over(res, vec4(vec3(0.47, 0.1, 0.012) * og, og))
    // The tube: a flat bright body, its pale core along the middle.
    let q = abs(v) / tr
    var col = mix(vec3(0.97, 0.53, 0.2), vec3(1.0, 0.69, 0.4), exp(-q * q * 4.0) * (0.85 + 0.15 * hot))
    col = mix(col, vec3(0.24, 0.22, 0.21), dis)
    return Finish.over(res, vec4(col * a, a))
}

// The three-quarter arc a waiting button turns in place of its label.
let lm_spinner = fn(dst: vec4, p: vec2, c: vec2, rad: float, t: float, amt: float, stroke: float, ink: vec3) -> vec4 {
    let sdf = Sdf2d.viewport(p)
    let a0 = t * 2.0 * PI
    sdf.arc_round_caps(c.x, c.y, rad, a0, a0 + 1.5 * PI, stroke)
    sdf.fill(vec4(ink, amt))
    return Finish.over(dst, sdf.result)
}

// A screw head in a slab's corner, 6 points across: a dark counterbore
// with a light lip on its lower edge, a domed head lit from the top left
// with a bright rim above, and a slot across it.
let lm_screw = fn(dst: vec4, p: vec2, c: vec2, px: float) -> vec4 {
    let q = p - c
    let d0 = length(q) - 3.0
    let a0 = Finish.cover(d0, px)
    var res = Finish.over(dst, vec4(vec3(0.016, 0.02, 0.024) * a0, a0))
    // The counterbore's lower lip catches the light.
    let lip = Finish.band(d0, 0.0, px, px) * smoothstep(0.0, 0.8, q.y / 3.0)
    res = Finish.over(res, vec4(vec3(0.25, 0.27, 0.3) * lip * 0.8, lip * 0.8))
    let d1 = length(q) - 2.3
    let a1 = Finish.cover(d1, px)
    let lit = clamp(0.55 - 0.65 * (q.x * 0.45 + q.y * 0.9) / 2.3, 0.0, 1.0)
    var col = mix(vec3(0.12, 0.13, 0.15), vec3(0.38, 0.4, 0.43), lit)
    let rim = Finish.band(d1, 0.0, px, px) * smoothstep(0.2, -0.8, q.y / 2.3)
    col = mix(col, vec3(0.5, 0.53, 0.57), rim * 0.8)
    let sl = abs((q.x - q.y) * 0.7071) - 0.4
    col = mix(col, vec3(0.03, 0.035, 0.04), Finish.cover(sl, px) * step(length(q), 1.9))
    return Finish.over(res, vec4(col * a1, a1))
}

// ---------------------------------------------------------------- buttons

// Every button is a face set into its own bezel: a slab 28 points tall
// with a 7 point corner, the face 3 points in. Padding 14 each side (the
// bezel's 3 and 11 of room), the label on a 12 point line.
mod.widgets.ButtonFlat.padding = mod.turtle.Inset{left: 14.0 right: 14.0 top: 4.0 bottom: 4.0}
mod.widgets.ButtonFlat.min_height = 28.0
mod.widgets.ButtonFlat.icon_walk.width = 14.0
mod.widgets.ButtonIcon.padding = mod.turtle.Inset{left: 7.0 right: 7.0 top: 4.0 bottom: 4.0}
mod.widgets.ButtonFlatIcon.padding = mod.turtle.Inset{left: 7.0 right: 7.0 top: 4.0 bottom: 4.0}
mod.widgets.ButtonFlatterIcon.padding = mod.turtle.Inset{left: 7.0 right: 7.0 top: 4.0 bottom: 4.0}
mod.widgets.ButtonXs.min_height = 20.0
mod.widgets.ButtonSm.min_height = 24.0
mod.widgets.ButtonLg.min_height = 32.0
mod.widgets.ButtonXl.min_height = 36.0
mod.widgets.ButtonFlat.draw_bg.border_radius = uniform(3.5)
mod.widgets.ButtonFlat.draw_bg.border_size = uniform(0.34)
mod.widgets.ButtonFlat.clip_x = false
mod.widgets.ButtonFlat.clip_y = false
mod.widgets.ButtonFlat.draw_bg.vertex = fn() {
    let m = 6.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}

// The bezel and its face for a box lo..hi: the rim, the corner of each.
let lm_rim = fn(hh: float) -> float {
    return clamp(0.125 * hh, 3.2, 4.0)
}

// The button and its variants share one face; `kind` picks it:
// 0 flat plate seated in its bezel, 1 raised key, 2 lit key (the lit
// frame and the light under it), 3 raised key with the light under it,
// 4 raised key with a lit legend, 5 danger, 6 outline (an empty bezel),
// 7 flatter (a face only under the hand).
let lm_button = fn(pos: vec2, size: vec2, o: vec2, dpi: float, hover: float, down: float, dis: float, focus: float, loading: float, anim: float, kind: float, dash: float) -> vec4 {
    let m = 6.0
    let px = lm_px(dpi)
    let p = pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    let hh = hi.y - lo.y
    let rim = lm_rim(hh)
    let flo = vec2(lm_snap(rim, o.x, px), lm_snap(rim, o.y, px))
    let fhi = vec2(lm_snap(size.x - rim, o.x, px), lm_snap(size.y - rim, o.y, px))
    let rb = min(7.0, 0.3 * hh)
    let rf = max(rb - rim + 0.5, 2.0)
    let live = 1.0 - dis
    var res = vec4(0.0, 0.0, 0.0, 0.0)
    var ink = vec3(0.788, 0.808, 0.831)
    if kind > 5.5 {
        let d = Material.sd_box(p, (lo + hi) * 0.5, (hi - lo) * 0.5, rb)
        let a = Finish.cover(d, px)
        let n = lm_normal(p, (lo + hi) * 0.5, (hi - lo) * 0.5, rb)
        if kind < 6.5 {
            // Outline: the bezel's edge alone, one device pixel, lighter on top.
            var ring = Finish.band(d, 0.0, px, px)
            if dash > 0.0 {
                ring = ring * step(0.5, fract((p.x + p.y) / (dash * 2.0)))
            }
            let col = mix(vec3(0.227, 0.251, 0.282), vec3(0.33, 0.357, 0.392), smoothstep(-0.3, 0.7, -n.y)) + vec3(0.1, 0.105, 0.11) * hover * live
            let ra = ring * mix(1.0, 0.45, dis)
            res = vec4(col * ra, ra)
            let wash = (0.05 * hover + 0.08 * down) * live * a * (1.0 - ring)
            res = Finish.over(res, vec4(vec3(0.0, 0.0, 0.0), wash * 2.0))
            res = Finish.over(res, vec4(vec3(0.788, 0.808, 0.831) * wash * 0.3, wash * 0.3))
        } else {
            // Flatter: a face comes up under the hand and sinks when held.
            let show = max(hover, down) * live
            if show > 0.001 {
                res = lm_face(res, p, flo, fhi, rf, px, 0.0, down, dis, 0.0) * show
            }
        }
        res = lm_focus(res, p, lo, hi, rb, px, focus * live)
    } else {
        res = lm_slab(p, lo, hi, rb, px, 1.0, hover * live, dis)
        var raise = 1.0
        if kind < 0.5 {
            raise = 0.0
        }
        res = lm_face(res, p, flo, fhi, rf, px, hover, down, dis, raise)
        // The light under a raised key: at rest on the lit and the
        // secondary key, a trace of it under the hand on any raised key,
        // none while held (the key is down in its bezel).
        var under = 0.32 * hover * raise
        if kind > 1.5 && kind < 3.5 {
            under = 0.85 + 0.15 * hover
        }
        under = under * live * (1.0 - 0.85 * down)
        res = lm_under(res, p, flo, fhi, rf, px, under, hi.y)
        // The lit frame on the lit key, brighter under the hand, held and
        // focused; any other key shows focus as the frame's line alone.
        if kind > 1.5 && kind < 2.5 {
            res = lm_frame(res, p, flo, fhi, rf, px, (1.0 + 0.2 * hover + 0.4 * down + 0.25 * focus) * live)
        } else {
            res = lm_focus(res, p, lo, hi, rb, px, focus * live)
        }
    }
    if loading > 0.001 {
        let c = (lo + hi) * 0.5
        let rad = max(min(hh, size.x) * 0.5 - rim - 5.0, 2.0)
        res = lm_spinner(res, p, c, rad, anim, loading, 1.5, vec3(1.0, 0.541, 0.235))
    }
    return res * lm_fade(pos, size, m)
}

mod.widgets.ButtonFlat.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 0.0, 0.0), 6.0)
}
mod.widgets.Button.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 1.0, 0.0), 6.0)
}
mod.widgets.ButtonPrimary.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 2.0, 0.0), 6.0)
}
mod.widgets.ButtonSecondary.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 3.0, 0.0), 6.0)
}
mod.widgets.ButtonTertiary.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 4.0, 0.0), 6.0)
}
mod.widgets.ButtonDanger.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 5.0, 0.0), 6.0)
}
mod.widgets.ButtonOutline.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 6.0, self.border_dash), 6.0)
}
mod.widgets.ButtonFlatter.draw_bg.pixel = fn() {
    return self.host_over(lm_button(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.disabled, self.focus, self.loading, self.anim_time, 7.0, 0.0), 6.0)
}

// Label ink: grey-white on an unlit face, orange on a lit one or a lit
// legend, red-orange for danger (the meaning kept by the word).
mod.widgets.ButtonFlat.draw_text.color = #c9ced4
mod.widgets.ButtonFlat.draw_text.color_hover = #e4e8ec
mod.widgets.ButtonFlat.draw_text.color_down = #b9bfc6
mod.widgets.ButtonFlat.draw_text.color_focus = #e4e8ec
mod.widgets.ButtonFlat.draw_text.color_disabled = #5b636d
mod.widgets.ButtonFlat.draw_icon.color = #c9ced4
mod.widgets.ButtonPrimary.draw_text.color = #ff8a3c
mod.widgets.ButtonPrimary.draw_text.color_hover = #ffa060
mod.widgets.ButtonPrimary.draw_text.color_down = #ffb27a
mod.widgets.ButtonPrimary.draw_text.color_focus = #ffa060
mod.widgets.ButtonPrimary.draw_text.color_disabled = #5b636d
mod.widgets.ButtonPrimary.draw_icon.color = #ff8a3c
mod.widgets.ButtonSecondary.draw_text.color = #e8ebee
mod.widgets.ButtonSecondary.draw_text.color_hover = #f4f6f8
mod.widgets.ButtonSecondary.draw_text.color_down = #d0d5db
mod.widgets.ButtonSecondary.draw_text.color_focus = #f4f6f8
mod.widgets.ButtonSecondary.draw_text.color_disabled = #5b636d
mod.widgets.ButtonSecondary.draw_icon.color = #e8ebee
mod.widgets.ButtonTertiary.draw_text.color = #ff8a3c
mod.widgets.ButtonTertiary.draw_text.color_hover = #ffa060
mod.widgets.ButtonTertiary.draw_text.color_down = #ff8a3c
mod.widgets.ButtonTertiary.draw_text.color_focus = #ffa060
mod.widgets.ButtonTertiary.draw_text.color_disabled = #5b636d
mod.widgets.ButtonTertiary.draw_icon.color = #ff8a3c
mod.widgets.ButtonDanger.draw_text.color = #ff5a3c
mod.widgets.ButtonDanger.draw_text.color_hover = #ff7458
mod.widgets.ButtonDanger.draw_text.color_down = #ff5a3c
mod.widgets.ButtonDanger.draw_text.color_focus = #ff7458
mod.widgets.ButtonDanger.draw_text.color_disabled = #5b636d
mod.widgets.ButtonDanger.draw_icon.color = #ff5a3c
mod.widgets.ButtonOutline.draw_text.color = #c9ced4
mod.widgets.ButtonOutline.draw_text.color_hover = #e4e8ec
mod.widgets.ButtonOutline.draw_text.color_down = #c9ced4
mod.widgets.ButtonOutline.draw_text.color_focus = #e4e8ec
mod.widgets.ButtonOutline.draw_text.color_disabled = #5b636d
mod.widgets.ButtonOutline.draw_icon.color = #c9ced4
mod.widgets.ButtonFlatter.draw_text.color = #c9ced4
mod.widgets.ButtonFlatter.draw_text.color_hover = #e4e8ec
mod.widgets.ButtonFlatter.draw_text.color_down = #c9ced4
mod.widgets.ButtonFlatter.draw_text.color_focus = #e4e8ec
mod.widgets.ButtonFlatter.draw_text.color_disabled = #5b636d
mod.widgets.ButtonFlatter.draw_icon.color = #c9ced4
mod.widgets.ButtonFlat.draw_description.color = #8b95a1
mod.widgets.ButtonSecondary.draw_description.color = #9aa3ae
mod.widgets.ButtonOutline.draw_description.color = #9aa3ae
mod.widgets.ButtonFlatter.draw_description.color = #9aa3ae
// A link is words on the ground, lighting orange under the hand.
mod.widgets.LinkLabel.draw_text.color = #c9ced4
mod.widgets.LinkLabel.draw_text.color_hover = #ff8a3c
mod.widgets.LinkLabel.draw_text.color_down = #ff6a1e
mod.widgets.LinkLabel.draw_text.color_focus = #ffa060
mod.widgets.LinkLabel.draw_text.color_disabled = #5b636d
mod.widgets.CloseButton.draw_bg.cross_color = #c9ced4

// ---------------------------------------------------------------- selection

// The small controls keep their bezel inside their box; the quad grows only
// for the slab's short shadow.
mod.widgets.CheckBoxFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.CheckBoxFlat.clip_x = false
mod.widgets.CheckBoxFlat.clip_y = false
mod.widgets.CheckBoxFlat.padding = mod.turtle.Inset{left: 8.0 right: 8.0 top: 4.0 bottom: 4.0}
mod.widgets.CheckBoxFlat.draw_bg.size = uniform(16.0)
mod.widgets.CheckBoxFlat.draw_bg.border_radius = uniform(2.0)
mod.widgets.CheckBoxFlat.label_walk.margin.left = 16.0

// The check box: a 16 point bezel with a 12 point well punched in it. On,
// the well's frame is lit and an orange check burns in it; mixed, a dash.
mod.widgets.CheckBoxFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let sz = self.size
    let x0 = (self.rect_size.x - sz) * self.mark_at_end
    let y0 = self.rect_size.y * 0.5 - sz * 0.5
    let lo = vec2(lm_snap(x0, o.x, px), lm_snap(y0, o.y, px))
    let hi = vec2(lm_snap(x0 + sz, o.x, px), lm_snap(y0 + sz, o.y, px))
    let wlo = vec2(lm_snap(x0 + 2.0, o.x, px), lm_snap(y0 + 2.0, o.y, px))
    let whi = vec2(lm_snap(x0 + sz - 2.0, o.x, px), lm_snap(y0 + sz - 2.0, o.y, px))
    let c = (wlo + whi) * 0.5
    let held = max(self.down, self.pressed)
    let on = max(self.active, self.mixed)
    let live = 1.0 - self.disabled
    // CheckBoxCircle asks for its corners rounded all the way: a round
    // bezel and a round well.
    let round = step(20.0, self.border_radius)
    let rb = mix(4.5, (hi.x - lo.x) * 0.5, round)
    let rw = mix(2.5, (whi.x - wlo.x) * 0.5, round)
    var res = lm_slab(p, lo, hi, rb, px, 1.0, self.hover * live, self.disabled)
    // Held, the bezel dims round a well pushed deeper.
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, 0.3 * held * live * res.w))
    res = Finish.over(res, lm_well(p, wlo, whi, rw, px, 1.0 + 1.4 * held * live, self.disabled))
    // The frame: lit when on; focus lights its line; under the hand the
    // well's edge brightens, held it brightens more and warms.
    res = lm_edge(res, p, wlo, whi, rw, px, (0.45 * self.hover + held) * live * (1.0 - on))
    res = lm_frame(res, p, wlo, whi, rw, px, max(on * (1.0 + 0.25 * self.hover + 0.3 * held), 0.35 * held) * live)
    res = lm_focus(res, p, lo, hi, rb, px, self.focus * live * (1.0 - on))
    // The error: the bezel's edge turns red-orange.
    let bd = Material.sd_box(p, (lo + hi) * 0.5, (hi - lo) * 0.5, rb)
    let er = Finish.band(bd, 0.0, px, px) * self.error * live
    res = Finish.over(res, vec4(vec3(1.0, 0.29, 0.16) * er, er))
    // The mark: a check 7 points across in a 1.6 point stroke, or a dash;
    // orange with a pale middle and a close halo on the floor.
    let dm = min(lm_seg(p, vec2(c.x - 3.0, c.y + 0.1), vec2(c.x - 1.0, c.y + 2.2)), lm_seg(p, vec2(c.x - 1.0, c.y + 2.2), vec2(c.x + 3.0, c.y - 2.3)))
    let dd = lm_seg(p, vec2(c.x - 2.8, c.y), vec2(c.x + 2.8, c.y))
    let dk = mix(dm, dd, self.mixed) - 0.85
    let halo = 0.35 * exp(-max(dk, 0.0) / 0.9) * (1.0 - Finish.cover(dk, px)) * on * live
    res = Finish.over(res, vec4(lm_glowc() * halo, halo * 0.4))
    let mk = Finish.cover(dk, px) * on
    var ink = mix(lm_orange(), lm_core(), (1.0 - smoothstep(-0.8, -0.2, dk)) * 0.6)
    ink = mix(ink, vec3(0.36, 0.39, 0.43), self.disabled)
    res = Finish.over(res, vec4(ink * mk, mk))
    return res * lm_fade(self.pos, self.rect_size, m)
}

// The toggle: a 34 x 18 point bezel with a pill well punched in it. Off,
// a dark domed thumb sits at the left; on, the thumb is a lit orange ball at
// the right, its light on the floor of the track.
// Size and aspect stay uniforms: the widget reads them back to find the
// knob (a plain value here left the knob icons standing in the row).
mod.widgets.ToggleFlat.draw_bg.size = uniform(18.0)
mod.widgets.ToggleFlat.draw_bg.pill_aspect = uniform(1.9)
// The knob stands centred in the track's height at both ends, 4 points in
// from the bezel's edge (the 0.5 border and 3.5 of inset); told so, the
// widget rides a knob icon on it at the knob's own size and drags it the
// same travel.
mod.widgets.ToggleFlat.draw_bg.knob_centred = uniform(1.0)
mod.widgets.ToggleFlat.draw_bg.knob_inset = uniform(3.5)
mod.widgets.ToggleFlat.label_walk.margin.left = 34.0
mod.widgets.ToggleFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let tw = self.size * self.pill_aspect
    let th = self.size
    let x0 = (self.rect_size.x - tw) * self.mark_at_end
    let y0 = self.rect_size.y * 0.5 - th * 0.5
    let lo = vec2(lm_snap(x0, o.x, px), lm_snap(y0, o.y, px))
    let hi = vec2(lm_snap(x0 + tw, o.x, px), lm_snap(y0 + th, o.y, px))
    let wlo = vec2(lm_snap(x0 + 2.5, o.x, px), lm_snap(y0 + 2.5, o.y, px))
    let whi = vec2(lm_snap(x0 + tw - 2.5, o.x, px), lm_snap(y0 + th - 2.5, o.y, px))
    let held = max(self.pressed, self.down)
    let live = 1.0 - self.disabled
    let on = self.active
    var res = lm_slab(p, lo, hi, th * 0.5, px, 1.0, self.hover * live, self.disabled)
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, 0.25 * held * live * res.w))
    let wr = (whi.y - wlo.y) * 0.5
    res = Finish.over(res, lm_well(p, wlo, whi, wr, px, 1.0 + 1.0 * held, self.disabled))
    // The thumb follows the value, or the pointer while it is dragged.
    let kt = mix(on, self.drag_pos, self.drag)
    let kr = wr - 1.5
    let kc = vec2(wlo.x + 1.5 + kr + (whi.x - wlo.x - 3.0 - kr * 2.0) * kt, (wlo.y + whi.y) * 0.5)
    // Its light on the floor of the track, reaching toward the left.
    let fl = exp(-max(length((p - kc) * vec2(0.45, 1.0)) - kr, 0.0) / 3.0) * 0.28 * on * live
    let win = Finish.cover(Material.sd_box(p, (wlo + whi) * 0.5, (whi - wlo) * 0.5, wr), px)
    res = Finish.over(res, vec4(lm_glowc() * fl * win, fl * win * 0.4))
    // Under the hand and held the track's edge brightens; focus lights it.
    res = lm_edge(res, p, wlo, whi, wr, px, (0.45 * self.hover + held) * live)
    res = lm_focus(res, p, lo, hi, th * 0.5, px, self.focus * live)
    // The dark thumb, off: a domed cap with a thin light ring.
    let kd = length(p - kc) - kr
    let ka = Finish.cover(kd, px)
    let ksh = Finish.drop(p, kc + vec2(0.0, 0.8), vec2(kr, kr), kr, vec2(0.0, 0.0), 1.0) * 0.6 * (1.0 - ka)
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, ksh * (1.0 - on)))
    let kq = (p - kc) / max(kr, 1.0)
    var kcol = mix(vec3(0.21, 0.227, 0.255), vec3(0.086, 0.098, 0.114), smoothstep(-1.0, 1.0, kq.y))
    kcol = kcol + vec3(0.03, 0.032, 0.035) * self.hover * live - vec3(0.03, 0.03, 0.03) * held
    let kring = Finish.band(kd, 0.0, px, px)
    kcol = mix(kcol, mix(vec3(0.22, 0.24, 0.27), vec3(0.4, 0.43, 0.47), smoothstep(0.3, -0.6, kq.y)) + vec3(0.08, 0.08, 0.08) * self.hover * live, kring)
    kcol = mix(kcol, vec3(0.1, 0.11, 0.125), 0.5 * self.disabled)
    res = Finish.over(res, vec4(kcol * ka * (1.0 - on), ka * (1.0 - on)))
    // The lit ball, on.
    res = lm_lamp(res, p, kc, kr, px, on * (1.0 - 0.25 * held), self.disabled)
    // The error: the bezel's edge turns red-orange.
    let bd = Material.sd_box(p, (lo + hi) * 0.5, (hi - lo) * 0.5, th * 0.5)
    let er = Finish.band(bd, 0.0, px, px) * self.error * live
    res = Finish.over(res, vec4(vec3(1.0, 0.29, 0.16) * er, er))
    return res * lm_fade(self.pos, self.rect_size, m)
}

// The radio: a 16 point round bezel with a round well; chosen, a lamp 6
// points across burns in it; off, the well is a dark ring.
mod.widgets.RadioButtonFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.RadioButtonFlat.clip_x = false
mod.widgets.RadioButtonFlat.clip_y = false
mod.widgets.RadioButtonFlat.draw_bg.size = uniform(16.0)
mod.widgets.RadioButtonFlat.padding = mod.turtle.Inset{left: 8.0 right: 8.0 top: 4.0 bottom: 4.0}
mod.widgets.RadioButtonFlat.label_walk.margin.left = 16.0
mod.widgets.RadioButtonFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let sz = self.size
    let y0 = self.rect_size.y * 0.5 - sz * 0.5
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(y0, o.y, px))
    let hi = vec2(lm_snap(sz, o.x, px), lm_snap(y0 + sz, o.y, px))
    let c = (lo + hi) * 0.5
    let live = 1.0 - self.disabled
    var res = lm_slab(p, lo, hi, sz * 0.5, px, 1.0, self.hover * live, self.disabled)
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, 0.3 * self.down * live * res.w))
    let wr = sz * 0.5 - 2.0
    res = Finish.over(res, lm_well(p, c - vec2(wr, wr), c + vec2(wr, wr), wr, px, 1.0 + 1.4 * self.down * live, self.disabled))
    res = lm_edge(res, p, c - vec2(wr, wr), c + vec2(wr, wr), wr, px, (0.45 * self.hover + self.down) * live)
    res = lm_frame(res, p, c - vec2(wr, wr), c + vec2(wr, wr), wr, px, 0.35 * self.down * live * (1.0 - self.active))
    res = lm_focus(res, p, lo, hi, sz * 0.5, px, self.focus * live)
    return lm_lamp(res, p, c, 3.0, px, self.active * (1.0 + 0.0 * self.hover), self.disabled) * lm_fade(self.pos, self.rect_size, m)
}

// The radio tab: a raised key in its bezel; chosen, the face is lit from
// within, dark glass behind a lit line, its word lit orange.
mod.widgets.RadioButtonTabFlat.draw_bg.vertex = fn() {
    let m = 5.0
    let mb = 12.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, m + mb))
}
mod.widgets.RadioButtonTabFlat.clip_x = false
mod.widgets.RadioButtonTabFlat.clip_y = false
// The label is laid at the top of its box: 2.5 more on top and 2.5 less
// below stand its capitals in the middle of the face.
mod.widgets.RadioButtonTabFlat.padding = mod.turtle.Inset{left: 2.0 right: 14.0 top: 6.5 bottom: 1.5}
mod.widgets.RadioButtonTabFlat.min_height = 28.0
mod.widgets.RadioButtonTabFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let mb = 12.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let size = self.rect_size
    let p = self.pos * (size + vec2(2.0 * m, m + mb)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    let hh = hi.y - lo.y
    let rim = lm_rim(hh)
    let flo = vec2(lm_snap(rim, o.x, px), lm_snap(rim, o.y, px))
    let fhi = vec2(lm_snap(size.x - rim, o.x, px), lm_snap(size.y - rim, o.y, px))
    let rb = min(7.0, 0.3 * hh)
    let rf = max(rb - rim + 0.5, 2.0)
    let live = 1.0 - self.disabled
    let sel = self.active
    var res = lm_slab(p, lo, hi, rb, px, 1.0, self.hover * live, self.disabled)
    if sel > 0.5 {
        // Chosen: the face lit from within, its light spilling on the
        // bezel round it.
        res = lm_lit(res, p, flo, fhi, rf, px, 1.0 + 0.12 * self.hover - 0.3 * self.down, self.disabled)
    } else {
        res = lm_face(res, p, flo, fhi, rf, px, self.hover, self.down, self.disabled, 1.0)
        res = lm_under(res, p, flo, fhi, rf, px, 0.28 * self.hover * live * (1.0 - self.down), hi.y)
        res = lm_focus(res, p, lo, hi, rb, px, self.focus * live)
    }
    // The old 5 point fade on every side for the quiet states; the chosen
    // one has 12 below for its light.
    let e = min(min(p.x + m, p.y + m), min(size.x + m - p.x, size.y + mix(m, mb, step(0.5, sel)) - p.y))
    return res * smoothstep(0.0, 4.0, e)
}
mod.widgets.RadioButtonTabFlat.draw_text.color = #aab2bc
mod.widgets.RadioButtonTabFlat.draw_text.color_hover = #e4e8ec
mod.widgets.RadioButtonTabFlat.draw_text.color_active = #ffb47c
mod.widgets.RadioButtonTabFlat.draw_text.color_disabled = #5b636d

// ---------------------------------------------------------------- sliders

// A slider thumb: a dark round cap with a thin light ring; under the hand
// the ring brightens, dragged or focused it is lit.
let lm_thumb = fn(dst: vec4, p: vec2, c: vec2, rad: float, px: float, hover: float, drag: float, focus: float, dis: float) -> vec4 {
    let live = 1.0 - dis
    let d = length(p - c) - rad
    let a = Finish.cover(d, px)
    let sh = Finish.drop(p, c, vec2(rad, rad), rad, vec2(0.0, 1.2), 1.3) * 0.7 * (1.0 - a)
    var res = Finish.over(dst, vec4(0.0, 0.0, 0.0, sh))
    let q = (p - c) / max(rad, 1.0)
    var col = mix(vec3(0.12, 0.14, 0.165), vec3(0.035, 0.047, 0.06), smoothstep(-1.0, 0.8, q.y))
    col = col + vec3(0.04, 0.045, 0.05) * exp(-dot(q - vec2(-0.25, -0.45), q - vec2(-0.25, -0.45)) * 5.0)
    col = col - vec3(0.03, 0.03, 0.03) * drag * live
    // A small dimple in the middle.
    col = mix(col, vec3(0.05, 0.055, 0.065), Finish.cover(length(p - c) - 1.4, px))
    // Its thin ring: pale on top, lit orange-brown underneath and on the
    // side the lit tube comes from.
    let ring = Finish.band(d, 0.0, px, px)
    let warm = clamp(smoothstep(-0.5, 0.6, q.y) + smoothstep(-0.2, -0.95, q.x) * 0.8, 0.0, 1.0) * live
    var rc = mix(vec3(0.46, 0.47, 0.48), vec3(0.76, 0.74, 0.7), smoothstep(0.0, -0.9, q.y))
    rc = mix(rc, vec3(0.86, 0.5, 0.27), warm) + vec3(0.15, 0.15, 0.15) * hover * live
    rc = mix(rc, vec3(0.16, 0.17, 0.19), 0.6 * dis)
    col = mix(col, rc, ring)
    col = mix(col, vec3(0.09, 0.1, 0.115), 0.5 * dis)
    res = Finish.over(res, vec4(col * a, a))
    // Lit: an orange ring with its pale core and a close halo.
    let lit = drag * live
    if lit > 0.001 {
        let od = max(d, 0.0)
        let g = 0.4 * exp(-(od * od) / (2.0 * 1.2 * 1.2)) * (1.0 - a) * lit
        res = Finish.over(res, vec4(lm_glowc() * g, g * 0.45))
        let lr = Finish.band(d, 0.0, 1.4, px) * lit
        res = Finish.over(res, vec4(lm_orange() * lr, lr))
        let lcr = Finish.band(d, 0.45, 0.95, px) * lit * 0.85
        res = Finish.over(res, vec4(lm_core() * lcr, lcr))
    }
    return res
}

// The groove every bar slider shares: a slab 12 points tall, a well 6
// points tall punched along it, the lit fill in the well.
let lm_groove = fn(p: vec2, x0: float, x1: float, cy: float, o: vec2, px: float, bh: float, wh: float, dis: float, hover: float) -> vec4 {
    let lo = vec2(lm_snap(x0, o.x, px), cy - bh * 0.5)
    let hi = vec2(lm_snap(x1, o.x, px), cy + bh * 0.5)
    var res = lm_slab(p, lo, hi, bh * 0.5, px, 1.0, hover * (1.0 - dis), dis)
    let inset = (bh - wh) * 0.5
    let wlo = vec2(lo.x + inset, cy - wh * 0.5)
    let whi = vec2(hi.x - inset, cy + wh * 0.5)
    return Finish.over(res, lm_well(p, wlo, whi, wh * 0.5, px, 1.0, dis))
}

mod.widgets.SliderFlat.clip_x = false
mod.widgets.SliderFlat.clip_y = false
mod.widgets.SliderFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.SliderFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let rad = 7.0
    let cy = lm_snap(20.0 + (self.rect_size.y - 20.0) * 0.5, o.y, px)
    let live = 1.0 - self.disabled
    var res = lm_groove(p, 0.0, self.rect_size.x, cy, o, px, 12.0, 9.333, self.disabled, self.hover)
    let wlo = vec2(lm_snap(0.0, o.x, px) + 1.333, cy - 4.667)
    let whi = vec2(lm_snap(self.rect_size.x, o.x, px) - 1.333, cy + 4.667)
    let span = self.rect_size.x - rad * 2.0
    let hx = rad + self.slide_pos * span
    let ox = rad + self.origin_pos * span
    let f0 = mix(wlo.x + 1.5, min(ox, hx), self.arc_origin)
    let f1 = mix(hx, max(ox, hx), self.arc_origin)
    // Focus lights the groove's line, laid under the fill so the fill keeps
    // its own light.
    res = lm_focus(res, p, vec2(lm_snap(0.0, o.x, px), cy - 6.0), vec2(lm_snap(self.rect_size.x, o.x, px), cy + 6.0), 6.0, px, self.focus * live)
    res = lm_tube(res, p, f0, f1, 2.667, px, self.disabled, max(max(self.hover, self.drag), self.focus), wlo, whi, 4.667, 0.0)
    return lm_thumb(res, p, vec2(hx, cy), rad, px, self.hover, self.drag, self.focus, self.disabled) * lm_fade(self.pos, self.rect_size, m)
}

// The minimal slider: a slim slab with its slot and the lit value; a small
// dark cap with a lit line shows under the hand.
// Its box ends close under the value, so the groove sits at the box's foot
// and runs a point past it (the quad grows 4 for that and the short shadow;
// the next row stands 8 below): the value stands 3 points clear above it.
mod.widgets.SliderMinimal.clip_x = false
mod.widgets.SliderMinimal.clip_y = false
mod.widgets.SliderMinimal.draw_bg.vertex = fn() {
    let m = 4.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.SliderMinimal.draw_bg.pixel = fn() {
    let m = 4.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let cy = lm_snap(self.rect_size.y - 2.5, o.y, px)
    var res = lm_groove(p, 0.0, self.rect_size.x, cy, o, px, 7.0, 4.0, self.disabled, self.hover)
    let wlo = vec2(lm_snap(0.0, o.x, px) + 1.5, cy - 2.0)
    let whi = vec2(lm_snap(self.rect_size.x, o.x, px) - 1.5, cy + 2.0)
    let lo2 = min(self.origin_pos, self.slide_pos)
    let hi2 = max(self.origin_pos, self.slide_pos)
    let f0 = mix(0.0, lo2, self.arc_origin) * self.rect_size.x
    let f1 = mix(self.slide_pos, hi2, self.arc_origin) * self.rect_size.x
    res = lm_tube(res, p, max(f0, wlo.x + 1.0), min(f1, whi.x - 1.0), 1.333, px, self.disabled, max(self.hover, self.drag), wlo, whi, 2.0, 0.0)
    let hx = clamp(self.slide_pos * self.rect_size.x, 4.0, self.rect_size.x - 4.0)
    let show = max(self.hover, self.drag)
    if show > 0.001 {
        let cap = lm_face(vec4(0.0, 0.0, 0.0, 0.0), p, vec2(hx - 3.5, cy - 5.5), vec2(hx + 3.5, cy + 5.5), 2.0, px, 0.0, 0.0, self.disabled, 1.0)
        var cl = Finish.over(res, cap)
        let ln = Finish.cover(abs(p.x - hx) - 0.5, px) * step(abs(p.y - cy), 3.5)
        cl = Finish.over(cl, vec4(lm_orange() * ln, ln))
        res = mix(res, cl, show)
    }
    return res * lm_fade(self.pos, self.rect_size, m)
}

// The round slider: a label column, then the bar slider's groove, fill and
// thumb; the groove ends short of the right edge so the value stands clear.
mod.widgets.SliderRoundFlat.clip_x = false
mod.widgets.SliderRoundFlat.clip_y = false
mod.widgets.SliderRoundFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.SliderRoundFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let rad = 7.0
    let cy = lm_snap(self.rect_size.y * 0.5, o.y, px)
    let x0 = self.label_size
    let x1 = self.rect_size.x - 37.0
    var res = lm_groove(p, x0, x1, cy, o, px, 12.0, 9.333, self.disabled, self.hover)
    let wlo = vec2(lm_snap(x0, o.x, px) + 1.333, cy - 4.667)
    let whi = vec2(lm_snap(x1, o.x, px) - 1.333, cy + 4.667)
    let span = whi.x - wlo.x - rad * 2.0 + 2.667
    let hx = wlo.x - 1.333 + rad + self.slide_pos * span
    res = lm_focus(res, p, vec2(lm_snap(x0, o.x, px), cy - 6.0), vec2(lm_snap(x1, o.x, px), cy + 6.0), 6.0, px, self.focus * (1.0 - self.disabled))
    res = lm_tube(res, p, wlo.x + 1.5, hx, 2.667, px, self.disabled, max(max(self.hover, self.drag), self.focus), wlo, whi, 4.667, 0.0)
    return lm_thumb(res, p, vec2(hx, cy), rad, px, self.hover, self.drag, self.focus, self.disabled) * lm_fade(self.pos, self.rect_size, m)
}

// The fader: his cove cap with a white line across it (the slider bench's
// "Cove cap, white line", a wedge), drawn by the cap engine (mod.sdf.Cap):
// a narrow flat ridge carrying the line, concave coves sweeping down to the
// foot along the travel and straight sides across it, the ridge brought
// toward the eye by its height. It runs a 5 point slot lit orange from its
// foot to the cap, the light's halo round the lit stretch beside the cap,
// and it throws a soft shadow down and to the right. The shape, the
// material and the inks are his bench preset number for number; the ground
// under them is this sheet's (#11161b, not the bench's #2e3034). His cap
// throws its shadow and its fill's halo farther than this sheet's own faces
// do (see lm_fader_room). Under the hand the light runs a little hotter, as
// the old lit tube did, and the cap's face a shade lighter, as every face
// here; held, the cap sinks half a point; disabled, the light goes out (the
// fill a dark bar), the face dims toward the disabled face, the line greys
// and the shadows halve. The old fader drew no focus ring; neither does this.
mod.widgets.SliderFader.cap_size = 26.0
mod.widgets.SliderFader.track_inset = 8.0
mod.widgets.SliderFader.draw_bg.track_size = uniform(5.0)
mod.widgets.SliderFader.draw_bg.cap_cross = uniform(0.44)
mod.widgets.SliderFader.clip_x = false
mod.widgets.SliderFader.clip_y = false
// The material, tunable live: the key light (x right, y down, z toward the
// viewer) and its intensity; the highlight, its roughness and the sheen; the
// rim toward grazing; the occlusion and how far up the walls it reaches; the
// plain sky's reflection and how near the eye is over the cap; metal, spun
// grain and glow (none); the exposure in EV and the highlight roll-off; the
// cast shadow's strength and blur, the contact shadow and the slot's inner
// shadow.
mod.widgets.SliderFader.draw_bg.cap_light = uniform(vec3(-0.22, -0.72, 0.66))
mod.widgets.SliderFader.draw_bg.cap_light_intensity = uniform(0.95)
mod.widgets.SliderFader.draw_bg.cap_specular = uniform(0.12)
mod.widgets.SliderFader.draw_bg.cap_roughness = uniform(0.84)
mod.widgets.SliderFader.draw_bg.cap_gloss = uniform(0.16)
mod.widgets.SliderFader.draw_bg.cap_rim = uniform(0.35)
mod.widgets.SliderFader.draw_bg.cap_ao = uniform(0.45)
mod.widgets.SliderFader.draw_bg.cap_ao_reach = uniform(1.2)
mod.widgets.SliderFader.draw_bg.cap_reflection = uniform(0.12)
mod.widgets.SliderFader.draw_bg.cap_reflection_perspective = uniform(0.35)
mod.widgets.SliderFader.draw_bg.cap_metal = uniform(0.0)
mod.widgets.SliderFader.draw_bg.cap_spun = uniform(0.0)
mod.widgets.SliderFader.draw_bg.cap_glow = uniform(0.0)
mod.widgets.SliderFader.draw_bg.cap_exposure = uniform(-0.35)
mod.widgets.SliderFader.draw_bg.cap_rolloff = uniform(0.6)
mod.widgets.SliderFader.draw_bg.cap_shadow = uniform(0.7)
mod.widgets.SliderFader.draw_bg.cap_shadow_blur = uniform(6.0)
mod.widgets.SliderFader.draw_bg.cap_contact = uniform(0.5)
mod.widgets.SliderFader.draw_bg.cap_inner = uniform(0.7)
// His inks: the cap's charcoal body, the white line, the slot's black, the
// orange fill, the light's warm white and the shade's grey. None of them is
// a token of this sheet (its handle and material tokens carry other colours
// and dress other widgets), so they stand here as he chose them. The ground
// is this sheet's window ground; disabled, the sheet's own disabled face,
// mark and value colours.
mod.widgets.SliderFader.draw_bg.ground_color = uniform(theme.color_bg_app)
mod.widgets.SliderFader.draw_bg.handle_color = uniform(#1f1f22)
mod.widgets.SliderFader.draw_bg.handle_color_disabled = uniform(theme.color_outset_disabled)
mod.widgets.SliderFader.draw_bg.mark_color = uniform(#f2f0ea)
mod.widgets.SliderFader.draw_bg.mark_color_disabled = uniform(theme.color_mark_disabled)
mod.widgets.SliderFader.draw_bg.track_color = uniform(#111214)
mod.widgets.SliderFader.draw_bg.fill_color = uniform(#bd5b00)
mod.widgets.SliderFader.draw_bg.fill_color_disabled = uniform(theme.color_val_disabled)
mod.widgets.SliderFader.draw_bg.light_color = uniform(#f4f2ee)
mod.widgets.SliderFader.draw_bg.shadow_color = uniform(#46474c)

// How far the fader's quad reaches past its rect, in points: the throw of
// the cap's cast shadow from its 14 point height along the key light, the
// blur at the shadow's tip (the engine holds it between 0.35 and 1 times the
// height), two points for the contact shadow's tail, and the glow's reach
// when the cap emits. The cap itself stays well inside that: never wider
// than the fader, stopped at the track's ends, its ridge magnified by the
// perspective by at most 16% of its half width. The lit fill's long faint
// halo is cut there (see lm_fader_fade).
let lm_fader_room = fn(lgt: vec3, blur: float, glo: float) -> float {
    let ln = normalize(lgt)
    return 14.0 * 0.7 * length(ln.xy) / max(ln.z, 0.25) + clamp(blur, 4.9, 14.0) + 24.0 * step(0.001, glo) + 2.0
}

// The grown quad fades out over the outer half of its margin, where the
// cap's shadow never reaches, by how far `p` lies outside the rect, rather
// than over the last 4 points of the quad as lm_fade fades the sheet's
// faces: the lit fill's halo still carries a few levels of orange out
// there, and ended by the quad's edge it drew each fader's quad on the
// ground as a faint square box. Faded by the distance from the rect, the
// halo dies out round a rounded outline, as light does.
let lm_fader_fade = fn(p: vec2, size: vec2, m: float) -> float {
    let d = length(max(abs(p - size * 0.5) - size * 0.5, vec2(0.0, 0.0)))
    return 1.0 - smoothstep(m * 0.5, m, d)
}

// The fader laid over the ground without painting it: the share of the
// ground it darkens away and the light it puts back, premultiplied, so bare
// ground comes out clear and the window's own ground (its vignette and
// grain) shows through. Exact for any colour. Cap.on_ground adds only what
// each channel has above the ground and takes the ground away by the
// darkest channel's share, so a colour below the ground in one channel
// loses the ground's own share in the others: the orange fill, which has no
// blue, came out 17 levels short in red and 22 in green on this ground.
let lm_on_ground = fn(col: vec3, gnd: vec3) -> vec4 {
    let dk = max(gnd - col, vec3(0.0, 0.0, 0.0)) / max(gnd, vec3(0.01, 0.01, 0.01))
    let k = clamp(max(dk.x, max(dk.y, dk.z)), 0.0, 1.0)
    return vec4(max(col - gnd * (1.0 - k), vec3(0.0, 0.0, 0.0)), k)
}

// The cove cap's solid at `w` (cap-local points in the fader's frame), his
// curves read as the bench reads them: the along curve symmetric, from its
// centre to one end, mirrored; the across curve over the half width; the
// edge over the edge width, 0.1 of the smaller half, in from the footprint
// `fp`. No ribs and no cut; a painted line leaves the solid as it is.
let lm_cove = fn(w: vec2, hs: vec2, fp: vec3, shape: vec4, mark: vec4, mark_at: vec4) -> vec4 {
    let c_along = Cap.mirror(Cap.curve(abs(w.x) / hs.x, 8.0, vec2(0.0, 1.0), vec2(0.0533, 0.0), vec2(0.0, 0.0), vec2(0.16, 1.0), vec2(0.0, 0.0), vec2(-0.01, 0.0386), vec2(0.19, 0.86), vec2(0.01, -0.0386), vec2(-0.0367, 0.0847), vec2(0.3, 0.46), vec2(0.0367, -0.0847), vec2(-0.06, 0.0557), vec2(0.48, 0.19), vec2(0.06, -0.0557), vec2(-0.0733, 0.0223), vec2(0.72, 0.07), vec2(0.0733, -0.0223), vec2(-0.02, 0.0), vec2(0.94, 0.05), vec2(0.02, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0)), w.x)
    let c_across = Cap.curve(abs(w.y) / hs.y, 3.0, vec2(0.0, 1.0), vec2(0.1567, 0.0), vec2(0.0, 0.0), vec2(0.94, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0))
    let c_edge = Cap.curve(Cap.edge_x(fp.x, hs, 0.1), 3.0, vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(0.06, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 1.0))
    return Cap.field(w, hs, fp, c_along, c_across, c_edge, vec2(1.0, 0.0), shape, vec4(0.0, 0.0, 0.0, 0.0), mark, mark_at, vec4(0.0, 0.0, 0.0, 0.0))
}

mod.widgets.SliderFader.draw_bg.vertex = fn() {
    let m = lm_fader_room(self.cap_light, self.cap_shadow_blur, self.cap_glow)
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.SliderFader.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let m = lm_fader_room(self.cap_light, self.cap_shadow_blur, self.cap_glow)
    let sz = self.rect_size
    let o = self.rect_pos
    let p = self.pos * (sz + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let vert = self.is_vertical
    let live = 1.0 - self.disabled
    // The fader's frame: `a` along the travel from the value's zero (up the
    // screen when the fader stands), `b` across it.
    let a = mix(p.x, sz.y - p.y, vert)
    let b = mix(p.y, p.x, vert)
    let ab = vec2(a, b)
    let along = mix(sz.x, sz.y, vert)
    let across = mix(sz.y, sz.x, vert)
    let travel = max(along - self.inset_px * 2.0 - self.cap_px, 1.0)
    let foot = self.inset_px + self.cap_px * 0.5
    // The slot's middle and the cap's centre on the device pixel grid, so the
    // slot's two walls antialias alike and the cap keeps one shape as it
    // moves.
    let mid = lm_snap(across * 0.5, mix(o.y, o.x, vert), px)
    let at_free = foot + self.slide_pos * travel
    let sa = Finish.snap(mix(o.x + at_free, o.y + sz.y - at_free, vert), px)
    let at = mix(sa - o.x, o.y + sz.y - sa, vert)
    // The cap's half size: cap_size along the travel, cap_cross of the
    // fader's width across, held to 4 points and to the width as the widget
    // holds it.
    let hs = vec2(self.cap_px * 0.5, min(max(across * self.cap_cross, 4.0), across) * 0.5)
    // The key light on screen, and turned into the fader's frame.
    let l = normalize(self.cap_light)
    let lt = Cap.light(l, vert)
    // Under the hand or held the light runs a little hotter; held, the cap
    // is pressed; disabled, the light goes out.
    let hot = max(self.hover, self.drag) * live
    let press = self.drag * live
    let lit = step(0.5, live)
    let ground = self.ground_color.rgb
    let light_ink = self.light_color.rgb
    let shadow_ink = self.shadow_color.rgb
    let body = self.handle_color.rgb
    let mark_ink = mix(self.mark_color.rgb, self.mark_color_disabled.rgb, self.disabled)
    let fill_ink = mix(self.fill_color.rgb * (1.0 + 0.15 * hot), self.fill_color_disabled.rgb, self.disabled)
    // THE GROUND: his slot, track_size wide, its ends rounded by half its
    // half width, held track_inset off the fader's ends; no well and no
    // scale. The fill runs from the slot's end (or out of the default, when
    // the widget asks) to the value; lit, it glows beside the cap; disabled,
    // it is a dark bar on the slot's floor.
    let tw = self.track_size
    let tlen = max(along - self.inset_px * 2.0, 1.0)
    let tbox = vec4(self.inset_px + tlen * 0.5, mid, tlen * 0.5, tw * 0.5)
    let lo = mix(foot + self.fill_lo * travel, self.inset_px, step(self.fill_lo, 0.0005))
    let hi = mix(foot + self.fill_hi * travel, along - self.inset_px, step(0.9995, self.fill_hi))
    var col = Cap.slot(ground, ab, tbox, tw * 0.25, 1.0 + lit, lo, hi, at, hs.x, lt, px, 0.0, 0.0, self.track_color.rgb, fill_ink, light_ink, shadow_ink, self.cap_inner, self.cap_ao)
    // THE CAP, his cove cap: corner 0.32 of the smaller half, edge 0.1, blend
    // 0.01, 14 points high, its top brought 16% toward the eye; a painted
    // line 1.6 points wide across its middle over 0.9 of its width. His plan
    // curve is flat at 1, which is no plan.
    let q = ab - vec2(at, mid)
    let shape = vec4(0.32, 0.1, 0.01, 14.0)
    let persp = 0.16
    let mark = vec4(1.0, 1.6, 0.35, 0.0)
    let mark_at = vec4(0.0, 0.5, 0.9, 0.0)
    let r = shape.x * min(hs.x, hs.y)
    var cap = body
    var cov = 0.0
    var under = 0.0
    var halo = 0.0
    // Only near the cap: the rest of a long track skips it.
    let far = abs(q) - hs
    if max(far.x, far.y) < m {
        var fp = Cap.sd_cap(q, hs, r, vec2(1.0, 0.0))
        // Where the cap or its magnified top can lie: the solid read three
        // times, each at the point the height read before brings toward the
        // eye. Farther out every read is the plain footprint's.
        if max(far.x - persp * hs.x, far.y - persp * hs.y) < px {
            var w = q / (1.0 + persp)
            fp = Cap.sd_cap(w, hs, r, vec2(1.0, 0.0))
            var f = lm_cove(w, hs, fp, shape, mark, mark_at)
            w = Cap.perspective(q, f.x, fp.x, persp)
            fp = Cap.sd_cap(w, hs, r, vec2(1.0, 0.0))
            f = lm_cove(w, hs, fp, shape, mark, mark_at)
            w = Cap.perspective(q, f.x, fp.x, persp)
            fp = Cap.sd_cap(w, hs, r, vec2(1.0, 0.0))
            f = lm_cove(w, hs, fp, shape, mark, mark_at)
            // The line is painted where the cap's own point lies, as the
            // bench paints it.
            let paint = Cap.mark_line(q, hs, mark, mark_at, px)
            let n = Cap.normal(f.yz, shape.w, vert)
            let v = Cap.view(q, hs, self.cap_reflection_perspective, vert)
            cap = Cap.shade(n, l, v, f.x, body, paint, 0.0, 1.0, self.cap_specular, self.cap_roughness, self.cap_gloss, self.cap_rim, self.cap_ao, self.cap_ao_reach, self.cap_reflection, self.cap_metal, self.cap_light_intensity, mark_ink, light_ink, shadow_ink, ground)
            let grain = Cap.spun(q, hs, lt.xy) * self.cap_spun * (1.0 - paint)
            cap = Cap.in_shadow(Cap.in_light(cap, clamp(grain, 0.0, 1.0) * 0.55, light_ink), clamp(-grain, 0.0, 1.0) * 0.42, shadow_ink)
            cap = Cap.emit(cap, f.x, body, light_ink, self.cap_glow)
            // The lit fill lights the cap's end walls beside it.
            cap = cap + fill_ink * Cap.fill_light(q, hs, f.yz * shape.w, lo, hi, at, tw) * (1.0 - paint) * lit
            // Under the hand the face a shade lighter, as every face here;
            // disabled, it dims toward the disabled face, the line its grey.
            cap = cap + vec3(0.018, 0.02, 0.022) * self.hover * live * (1.0 - press) * (1.0 - paint)
            cap = mix(cap, self.handle_color_disabled.rgb, 0.45 * self.disabled * (1.0 - paint))
            cov = Cap.cover(fp.x, px)
        }
        // Under it the cast shadow, thrown from his top outline and a little
        // shorter while the cap is pressed, and the contact shadow; disabled,
        // both halve, as every face's shadow here does.
        let rise = shape.w - 0.5 * press
        let dim = 1.0 - 0.5 * self.disabled
        let sh = Cap.shadow(q, hs, r, vec3(0.2235, 0.9529, 1.0), lt, rise, self.cap_shadow_blur, self.cap_shadow * dim, px)
        let ct = Cap.contact(fp.x, max(rise * 0.3, 1.0), self.cap_contact * dim)
        under = clamp(sh + ct, 0.0, 1.0)
        halo = Cap.glow(fp.x, hs, self.cap_glow)
    }
    col = mix(col, col * shadow_ink, under * (1.0 - cov))
    col = col + body * halo * 0.9 * (1.0 - cov)
    col = mix(col, cap, cov)
    let ex = pow(2.0, self.cap_exposure)
    let res = lm_on_ground(Cap.tone(col, ex, self.cap_rolloff), Cap.tone(ground, ex, self.cap_rolloff))
    return res * lm_fader_fade(p, sz, m)
}

// ---------------------------------------------------------------- knobs

// A knob: a round bezel with a well punched in it, and in the well a cut
// wing knob, as the knob bench draws it: a short cylindrical cap whose top
// is milled down on both sides, leaving a raised wing -- a band 0.56 of the
// cap's radius wide running the whole diameter -- that turns with the value
// and is the pointer. The cap is flat on top out to 0.82 of its radius,
// where a crisp edge drops into a steep rounded side down to the floor of
// the well. Two cutters take the top away either side of the wing, 0.55 of
// the cap's height deep the whole way along; each cutter's profile is a
// rounded shoulder at the wing's wall, a filleted root a sixth of a radius
// out, then a floor running away a little to the edge. One solid in the
// faders' charcoal: its flat face in their material and light, from the
// cap engine, and every face turned off the flat lit as the bench lights
// it, relative to the flat face as it shows and at the bench's strength --
// the wing's top and the floors keep the flat face's tone, the wall toward
// the light a little over it, the wall away from the light goes to the
// shade, the side ring toward the light brightens and away from it darkens
// as far as the bench's, the edges and the shoulders turned toward the
// light catch it, and a hairline round the outline is lit on the side
// toward the light. The wing throws its shadow across the floor away from
// the light, and, as in the bench, its swept crest throws one on the end
// turned toward the light, a darker notch below the top's lit edge; the
// cap throws its own on the floor of the well. Along the wing the sheet's pale
// line, laid over the lit solid as the bench lays its mark, runs from half
// the radius out to 0.95 of it, over the edge and down the side in the
// flat face's light, whichever way it points. Round the cap the value arc,
// orange with a pale core, its light falling on the floor of the well and
// catching the cap's side, at 1.18 of the cap's radius; on it twelve ticks
// stand outward, eleven steps across the sweep, lit orange where the arc
// is lit and grey past it. Under the hand the light lifts a little and the
// outlines brighten; held or focused, the value runs a little hotter, and
// focus rings the bezel in the sheet's lit line; disabled, the light goes
// out, the solid dims, the line fades and the shadows halve. Angles run
// from straight down, clockwise, the gap at the bottom.

// The cut wing's solid at `q` (points from the cap's centre): its height in
// shares of the cap's height, 1 on top. `rc` the cap's radius, `side` the
// unit vector across the wing, `hpt` the cap's height in points, `kmin` the
// least fillet. The revolve first, flat to 0.82 of the radius and falling
// to the floor at its rim (and on down past it, eight heights a radius);
// then the cutters, their section read by the distance out from the
// wing's wall, taken away by the smooth minimum. The fillet is 0.03 of the
// radius measured along the surface, so its height band shrinks where the
// crossing is steep.
let lm_cw_h = fn(q: vec2, rc: float, side: vec2, hpt: float, kmin: float) -> float {
    let rn = length(q) / rc
    let pr = Cap.curve(rn, 4.0, vec2(0.0, 1.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(0.82, 1.0), vec2(0.0, 0.0), vec2(-0.026667, 0.148148), vec2(0.9, 0.55), vec2(0.026667, -0.148148), vec2(-0.016667, 0.091667), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0))
    let h = pr.x - max(rn - 1.0, 0.0) * 8.0
    let x = (abs(dot(q, side)) - 0.28 * rc) / rc
    // Inside the wing the cutter's section runs on up at its wall's slope,
    // so the smooth minimum rounds the shoulder over the fillet instead of
    // stepping where the cutter stops.
    var v = 1.0 - 5.125 * x
    var dv = -5.125
    if x < -0.1 {
        return h
    }
    if x >= 0.0 {
        let wp = Cap.curve(min(x, 0.999), 3.0, vec2(0.0, 1.0), vec2(0.026667, -0.136667), vec2(-0.053333, 0.053333), vec2(0.16, 0.18), vec2(0.053333, -0.053333), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0), vec2(0.0, 0.0), vec2(0.0, 0.0), vec2(1.0, 0.0))
        v = wp.x + wp.y * max(x - 1.0, 0.0)
        dv = wp.y
    }
    let hc = 1.0 - 0.55 * (1.0 - v)
    let sc = 0.55 * abs(dv) / rc
    let sb = abs(pr.y) / rc
    let dg = sqrt(sc * sc + sb * sb)
    let k = max(max(0.03 * rc, kmin) * dg / sqrt(1.0 + dg * dg * hpt * hpt), 0.0001)
    let hh = clamp(0.5 - 0.5 * (hc - h) / k, 0.0, 1.0)
    return mix(h, hc, hh) - k * hh * (1.0 - hh)
}

// How far one look along the ray toward the light, `t` points out, finds
// the solid standing over the ray: the overhang in points across, as the
// bench measures it, 0 where the ray clears the solid and 1 once the solid
// stands `pen` over it (a quarter of the cap's height); a ray that clears
// it is never shaded.
let lm_cw_look = fn(q: vec2, t: float, h0: float, ld: vec2, tanel: float, rc: float, side: vec2, hpt: float, kmin: float, pen: float) -> float {
    if t <= 0.0 {
        return 0.0
    }
    let hj = lm_cw_h(q + ld * t, rc, side, hpt, kmin)
    let over = ((hj - h0) * hpt - t * tanel) / max(tanel, 0.05)
    return clamp(over / pen, 0.0, 1.0)
}

// The wing's shadow on the cut and the side's on itself: looks along the
// ray toward the light, as far as the top can throw. Two of them land just
// past where the ray climbs onto the wing's top (the band, and the band
// within the flat of the cap), the crisp edges every shadow here is thrown
// from; three more are spread along the rest.
let lm_cw_self = fn(q: vec2, h0: float, ld: vec2, tanel: float, rc: float, side: vec2, hpt: float, kmin: float, px: float) -> float {
    let tb = (1.0 - h0) * hpt / max(tanel, 0.05)
    if tb < 0.5 * px {
        return 0.0
    }
    let pen = max(0.25 * hpt / max(tanel, 0.05), px)
    let gap = 0.28 * rc
    let s0 = dot(q, side)
    var sv = dot(ld, side)
    if abs(sv) < 0.0001 {
        sv = 0.0001
    }
    let ta = (-gap - s0) / sv
    let tz = (gap - s0) / sv
    let b_in = min(ta, tz)
    let b_out = max(ta, tz)
    let rt = 0.82 * rc
    let bq = dot(q, ld)
    let cq = dot(q, q) - rt * rt
    let disc = bq * bq - cq
    var top_in = -1.0
    if disc > 0.0 {
        let sq = sqrt(disc)
        let t0 = max(b_in, -bq - sq)
        let t1 = min(b_out, -bq + sq)
        if t1 > max(t0, 0.0) {
            top_in = max(t0, 0.0)
        }
    }
    var occ = 0.0
    if b_out > 0.0 && b_in < tb {
        occ = max(occ, lm_cw_look(q, max(b_in, 0.0) + 0.5 * px, h0, ld, tanel, rc, side, hpt, kmin, pen))
    }
    if top_in >= 0.0 && top_in < tb {
        occ = max(occ, lm_cw_look(q, top_in + 0.5 * px, h0, ld, tanel, rc, side, hpt, kmin, pen))
    }
    occ = max(occ, lm_cw_look(q, 0.15 * tb, h0, ld, tanel, rc, side, hpt, kmin, pen))
    occ = max(occ, lm_cw_look(q, 0.45 * tb, h0, ld, tanel, rc, side, hpt, kmin, pen))
    occ = max(occ, lm_cw_look(q, 0.85 * tb, h0, ld, tanel, rc, side, hpt, kmin, pen))
    return occ
}

// The hull of two discs, centres `a` and `b`, radii `ra` and `rb`: in .x
// the signed distance from `p`, in .y where along a to b the nearest point
// lies.
let lm_cw_hull2 = fn(p: vec2, a: vec2, b: vec2, ra: float, rb: float) -> vec2 {
    let ba = b - a
    let l = length(ba)
    let dr = ra - rb
    if l <= abs(dr) + 0.0001 {
        let da = length(p - a) - ra
        let db = length(p - b) - rb
        if da < db {
            return vec2(da, 0.0)
        }
        return vec2(db, 1.0)
    }
    let ax = ba / l
    let pa = p - a
    let y = dot(pa, ax)
    let x = abs(ax.x * pa.y - ax.y * pa.x)
    let sb = dr / l
    let cb = sqrt(1.0 - sb * sb)
    let k = cb * y - sb * x
    if k < 0.0 {
        return vec2(length(pa) - ra, 0.0)
    }
    if k > cb * l {
        return vec2(length(p - b) - rb, 1.0)
    }
    return vec2(x * cb + y * sb - ra, k / (cb * l))
}
let lm_cw_cross = fn(a: vec2, b: vec2, p: vec2) -> float {
    let ea = b - a
    let wa = p - a
    return ea.x * wa.y - ea.y * wa.x
}

// THE WING'S SHADOW ON THE CAP'S OWN TOP, as the bench throws it: the wing
// taken as a swept solid, a disc at each end of it (0.68 of the radius out
// along it) at its crest and one at the height just over the receiver
// `zp`, as wide there as the section is (the crest 0.68 of the base's
// 0.41 radii), each moved down-light by its height over the receiver
// (`sh` points a cap's height); the shadow is the hull of the four. The
// discs at the crest reach past the flat top to 0.96 of the radius, so the
// end of the wing turned to the light, the steep side from 0.82 of the
// radius out, falls under its own crest: a darker notch with the top's
// edge lit above it and the rim lit below. The penumbra is the bench's: a
// 10 point blur on a 56 point cap, halved, never under a pixel and a half.
let lm_cw_hull = fn(q: vec2, zp: float, rc: float, dir: vec2, sh: vec2, px: float) -> float {
    let zb = 0.5838
    let z0 = max(zb, zp + 0.12)
    if z0 + 0.001 > 1.0 {
        return 0.0
    }
    let f = clamp((z0 - zb) / (1.0 - zb), 0.0, 1.0) * 3.0
    var tw = mix(1.0, 0.8767, f)
    if f >= 1.0 {
        tw = mix(0.8767, 0.7818, f - 1.0)
    }
    if f >= 2.0 {
        tw = mix(0.7818, 0.6774, f - 2.0)
    }
    let half = 0.6835 * rc
    let rb = 0.4133 * rc * tw
    let rt = 0.4133 * rc * 0.6774
    let pb0 = -dir * half + sh * (z0 - zp)
    let pb1 = dir * half + sh * (z0 - zp)
    let pt0 = -dir * half + sh * (1.0 - zp)
    let pt1 = dir * half + sh * (1.0 - zp)
    // The nearest of its four edges -- the base, the crest and the two
    // ends -- and the height there.
    let e0 = lm_cw_hull2(q, pb0, pb1, rb, rb)
    var dm = e0.x
    var zm = z0
    let e1 = lm_cw_hull2(q, pt0, pt1, rt, rt)
    if e1.x < dm {
        dm = e1.x
        zm = 1.0
    }
    let e2 = lm_cw_hull2(q, pb0, pt0, rb, rt)
    if e2.x < dm {
        dm = e2.x
        zm = mix(z0, 1.0, e2.y)
    }
    let e3 = lm_cw_hull2(q, pb1, pt1, rb, rt)
    if e3.x < dm {
        dm = e3.x
        zm = mix(z0, 1.0, e3.y)
    }
    let s1 = lm_cw_cross(pb0, pb1, q)
    let s2 = lm_cw_cross(pb1, pt1, q)
    let s3 = lm_cw_cross(pt1, pt0, q)
    let s4 = lm_cw_cross(pt0, pb0, q)
    if (s1 > 0.0 && s2 > 0.0 && s3 > 0.0 && s4 > 0.0) || (s1 < 0.0 && s2 < 0.0 && s3 < 0.0 && s4 < 0.0) {
        dm = min(dm, -rc)
    }
    let blur = 10.0 * rc / 56.0
    let bl = max(0.5 * blur * mix(0.3, 1.0, clamp(zm - zp, 0.0, 1.0)), (zm - zp) * 0.11 * length(sh))
    return 1.0 - smoothstep(-1.0, 1.0, dm / max(max(0.5 * bl, 1.5 * px), 0.001))
}

// The highlight's lobe at `nh` (the normal against the half vector) for a
// roughness `a`, normalised so that 0.5 peaks at the highlight's strength.
let lm_cw_ggx = fn(nh: float, a: float) -> float {
    let a2 = a * a
    let dd = nh * nh * (a2 - 1.0) + 1.0
    return 0.25 * a2 / max(dd * dd, 0.000001)
}
// THE BENCH'S FACE LIGHT, for a face of normal `n` under the light `l` of
// strength `li`: in .x the direct light relative to a flat face (1 flat,
// toward 0 turned away, over 1 turned toward the light), the difference
// eased in on both sides so a face turned only a little keeps the flat
// face's tone; in .y the highlight a flat face would not have, a lobe of
// strength `spec` widened by `rough`, the flat face's own subtracted.
let lm_cw_lit = fn(n: vec3, l: vec3, li: float, spec: float, rough: float) -> vec2 {
    let ndl = dot(n, l)
    let key = (smoothstep(-0.35, 1.0, ndl) - smoothstep(-0.35, 1.0, l.z)) * li * 1.5
    let dl = 1.0 + smoothstep(0.0, 1.0, key) - smoothstep(0.0, 1.0, -key)
    let rk = max(sqrt(rough * rough + 0.01), 0.03)
    let hv = normalize(l + vec3(0.0, 0.0, 1.0))
    let lobe = lm_cw_ggx(max(dot(n, hv), 0.0), rk) - lm_cw_ggx(hv.z, rk)
    return vec2(dl, max(lobe, 0.0) * spec * li * step(0.0, ndl))
}

let lm_knob = fn(p: vec2, c: vec2, rr: float, px: float, slide: float, origin: float, arc_origin: float, gap: float, hover: float, held: float, focus: float, dis: float) -> vec4 {
    let live = 1.0 - dis
    let q = p - c
    let rl = length(q)
    var res = lm_slab(p, c - vec2(rr, rr), c + vec2(rr, rr), rr, px, 1.0, hover * live, dis)
    res = lm_focus(res, p, c - vec2(rr, rr), c + vec2(rr, rr), rr, px, focus * live)
    let rw = rr - clamp(0.08 * rr, 2.0, 3.0)
    // A box too small to hold a well draws the bezel alone.
    if rw < 4.0 {
        return res
    }
    res = Finish.over(res, lm_well(p, c - vec2(rw, rw), c + vec2(rw, rw), rw, px, 1.0, dis))
    // The arc is a thin line (1.2 to 1.6 points) near the well's rim, the
    // floor inside it room for its glow and the knob, and outside it room
    // for the ticks: they run out from the arc's middle 0.14 of the cap's
    // radius (the arc's radius over 1.18), and at least a point past the
    // arc's outer edge, their round ends half a point inside the rim. On a
    // small knob that room is wanting at 0.86 of the well, so the arc, and
    // the cap with it, draw in until the ticks fit.
    let ring_w = clamp(0.07 * rr, 1.2, 1.6)
    let tick_w = max(1.8 * 0.86 * rw / (1.18 * 56.0), 1.0)
    let tick_room = rw - 0.5 - tick_w * 0.5
    let ring_mid = min(0.86 * rw, min(tick_room / (1.0 + 0.14 / 1.18), tick_room - ring_w * 0.5 - 1.0))
    let one = PI / 180.0
    let sweep = 2.0 * PI - gap * one
    let start = gap * one * 0.5
    let ve = start + sweep * slide
    let oe = start + sweep * origin
    let a0 = mix(start, min(oe, ve), arc_origin)
    let a1 = mix(ve, max(oe, ve), arc_origin)
    var ang = atan2(-q.x, q.y)
    if ang < 0.0 {
        ang = ang + 2.0 * PI
    }
    let es = 0.5 / max(ring_mid, 1.0)
    let inside_sweep = smoothstep(start - es, start + es, ang) * (1.0 - smoothstep(start + sweep - es, start + sweep + es, ang))
    // The unlit track: a faint line in the well.
    let tr = Finish.cover(abs(rl - ring_mid) - ring_w * 0.5, px) * inside_sweep
    res = Finish.over(res, vec4(vec3(0.1, 0.11, 0.125) * tr, tr))

    // THE CAP'S PROPORTIONS, the bench's: the arc and the ticks stand at
    // 1.18 of the cap's radius, so the cap is the arc's radius over 1.18
    // (0.73 of the well's, less on a small knob); its height is 0.6 of its
    // radius, the depth the bench gives it in charcoal. The ticks are 1.8
    // points wide on a 56 point cap, never under a point.
    let rc = ring_mid / 1.18
    let hpt = 0.6 * rc
    let kmin = 0.5 * px
    let dir = vec2(-sin(ve), cos(ve))
    let side = vec2(-dir.y, dir.x)
    let tick_r1 = min(ring_mid + max(0.14 * rc, ring_w * 0.5 + 1.0), tick_room)
    // The faders' material: their key light, charcoal, pale line, the
    // light's warm white and the shade's grey, the window's ground for the
    // sky, the highlight, sheen, rim and exposure; the light 1.2 strong for
    // their 0.95 on the flat face, as a knob seen from above turns less of
    // itself to the light than a cove cap's faces do, and three quarters of
    // that, the bench's 0.9, for the faces turned off it. Under the hand it
    // lifts a little.
    let l = normalize(vec3(-0.22, -0.72, 0.66))
    let ld = normalize(l.xy)
    let tanel = l.z / length(l.xy)
    let cap_ink = vec3(0.122, 0.122, 0.133)
    let mark_ink = vec3(0.949, 0.941, 0.918)
    let light_ink = vec3(0.957, 0.949, 0.933)
    let shadow_ink = vec3(0.275, 0.278, 0.298)
    let ex = pow(2.0, -0.35)
    let dim = 1.0 - 0.5 * dis
    let hot = 1.0 + 0.25 * max(held, focus)
    let li = (1.2 + 0.15 * hover * live) * mix(1.0, 0.8, dis)
    let dcap = rl - rc
    let ccap = Finish.cover(dcap, px)

    // THE TICKS, on the floor under everything that falls on it: a capsule
    // from 1.18 of the radius outward at each of the twelve stops. Unlit
    // ones first, a grey a little brighter than the track; the lit ones
    // are laid over the arc below.
    let tstep = sweep / 11.0
    let tk = clamp(floor((ang - start) / tstep + 0.5), 0.0, 11.0)
    let ta = start + tk * tstep
    let tdir = vec2(-sin(ta), cos(ta))
    let td = lm_seg(q, tdir * (1.18 * rc), tdir * tick_r1) - tick_w * 0.5
    let tcov = Finish.cover(td, px)
    let arcon = step(0.004, abs(a1 - a0))
    let tlit = step(a0 - 0.001, ta) * step(ta, a1 + 0.001) * arcon * live
    let tunl = tcov * (1.0 - tlit)
    res = Finish.over(res, vec4(mix(vec3(0.3, 0.318, 0.345), vec3(0.16, 0.17, 0.185), dis) * tunl, tunl))

    // Its shadow on the floor of the well, never past it: the cap's, thrown
    // by the height of the cut's floor, and the wing's, thrown by the full
    // height from a box along it; and a contact shadow hugging its foot.
    let sb = Cap.shadow(q, vec2(rc, rc), rc, vec3(0.9, 0.9, 1.0), l, 0.55 * hpt, 6.0, 0.7 * dim, px)
    let qw = vec2(dot(q, dir), dot(q, side))
    let lw = vec3(dot(l.xy, dir), dot(l.xy, side), l.z)
    let sw = Cap.shadow(qw, vec2(0.9 * rc, 0.42 * rc), 0.4 * rc, vec3(0.91, 0.67, 1.0), lw, hpt, 6.0, 0.6 * dim, px)
    let ct = Cap.contact(dcap, max(hpt * 0.15, 1.0), 0.5 * dim)
    let wfl = Finish.cover(rl - (rw - 0.5 * px), px)
    let fsh = clamp(max(sb, sw) + ct, 0.0, 1.0) * (1.0 - ccap) * wfl
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, fsh * 0.85))

    // The arc, with round ends: the distance to its middle line.
    let e0 = c + ring_mid * vec2(-sin(a0), cos(a0))
    let e1 = c + ring_mid * vec2(-sin(a1), cos(a1))
    let inr = step(a0, ang) * step(ang, a1)
    let ad = mix(min(length(p - e0), length(p - e1)), abs(rl - ring_mid), inr)
    let arc = Finish.cover(ad - ring_w * 0.5, px) * arcon
    // Its light on the dark floor of the well, both sides of the line: a
    // red-orange close to it (#9a2900 at a point), a deep red-brown that
    // reaches the knob and the well's rim.
    // It fades out across the bezel's rim rather than stopping at the well.
    let lit = hot * live * arcon * (1.0 - smoothstep(rw - 0.5, rr, rl)) * (1.0 - arc)
    let odd = max(ad - ring_w * 0.5, 0.0)
    let gf = 1.2 * exp(-odd / 5.0) * lit
    res = Finish.over(res, vec4(vec3(0.42, 0.1, 0.03) * gf, gf * 0.6))
    let gn = 1.2 * exp(-odd / 0.6) * lit
    res = Finish.over(res, vec4(vec3(0.85, 0.22, 0.03) * gn, gn * 0.6))
    // The line: orange at its edges, a pale hot core down its middle.
    let hq = ad / (0.3 * ring_w)
    var acol = mix(vec3(1.0, 0.5, 0.2), vec3(1.0, 0.75, 0.47), exp(-hq * hq) * (0.85 + 0.15 * max(held, focus)))
    acol = mix(acol, vec3(0.3, 0.28, 0.27), dis)
    res = Finish.over(res, vec4(acol * arc, arc))
    // The lit ticks: the arc's orange, a pale core along each, a little
    // brighter held or focused.
    let tl = tcov * tlit
    let tq = (td + tick_w * 0.5) / max(0.35 * tick_w, 0.3)
    let tcol = mix(vec3(1.0, 0.5, 0.2), vec3(1.0, 0.75, 0.47), exp(-tq * tq) * 0.8) * (0.9 + 0.1 * hot)
    res = Finish.over(res, vec4(tcol * tl, tl))

    // THE CAP: its height here and a device pixel either way, the normal
    // from their differences, as the bench reads its solid.
    let h0 = lm_cw_h(q, rc, side, hpt, kmin)
    let hx = lm_cw_h(q + vec2(px, 0.0), rc, side, hpt, kmin) - lm_cw_h(q - vec2(px, 0.0), rc, side, hpt, kmin)
    let hy = lm_cw_h(q + vec2(0.0, px), rc, side, hpt, kmin) - lm_cw_h(q - vec2(0.0, px), rc, side, hpt, kmin)
    let n = normalize(vec3(-vec2(hx, hy) * hpt / (2.0 * px), 1.0))
    // The light that reaches it past the wing and the side: the bench's
    // visibility, the shadow taking up to 0.385 of the key light; the
    // solid's own shadow, and the wing's as the bench throws it.
    let selfsh = max(lm_cw_self(q, h0, ld, tanel, rc, side, hpt, kmin, px), lm_cw_hull(q, h0, rc, dir, -ld * (hpt / tanel), px))
    let kvis = 1.0 - 0.385 * selfsh * dim
    // The pale line painted along the wing, square-ended, 2 points wide on
    // a 56 point cap, never under 1.2.
    let pw = max(2.0 * rc / 56.0, 1.2)
    let pal = dot(q, dir)
    let pd2 = vec2(abs(dot(q, side)) - pw * 0.5, max(0.5 * rc - pal, pal - 0.95 * rc))
    let pd = min(max(pd2.x, pd2.y), 0.0) + length(max(pd2, vec2(0.0, 0.0)))
    let paint = Finish.cover(pd, px) * mix(1.0, 0.45, dis)
    // The flat face in the faders' material, as it shows (exposed); then
    // every face lit as the bench lights it, relative to that, at the
    // bench's strength (0.9, three quarters of the sheet's light), so a face
    // turned a little keeps the flat face's tone, one turned to the light
    // brightens as much as the bench's does and one turned away goes to the
    // shade as far.
    let vw = Cap.view(q, vec2(rc, rc), 0.35, 0.0)
    let face = Cap.tone(Cap.shade(vec3(0.0, 0.0, 1.0), l, vw, clamp(h0, 0.0, 1.0), cap_ink, 0.0, 0.0, 1.0, 0.12, 0.84, 0.16, 0.35, 0.45, 1.2, 0.12, 0.0, li, mark_ink, light_ink, shadow_ink, lm_ground()), ex, 0.6)
    let lt = lm_cw_lit(n, l, li * 0.75, 0.12, 0.84)
    // The bench's hairline round the cap's outline, 1.4 points wide on a 56
    // point cap: its light raised where the side faces the light, lowered
    // where it faces away.
    let hband = 1.0 - smoothstep(0.0, max(1.4 * rc / 56.0, px), abs(dcap))
    let dl = lt.x + 0.3 * hband * dot(n.xy / max(length(n.xy), 0.0001), ld)
    var col = Cap.in_light(face * (shadow_ink + (vec3(1.0, 1.0, 1.0) - shadow_ink) * clamp(dl, 0.0, 1.0) * kvis), max(dl - 1.0, 0.0) * kvis, light_ink)
    col = col + light_ink * lt.y * kvis
    // And its rim: the last half point inside the outline lit as it faces
    // the light, 0.32 strong.
    let rimw = max(0.5 * rc / 56.0, 0.5 * px)
    col = Cap.in_light(col, (1.0 - smoothstep(0.0, rimw, -dcap)) * step(dcap, 0.0) * pow(max(dot(n, l), 0.0), 0.8) * 0.32 * dim, light_ink)
    // The arc's light catches the cap's side where it faces out, from the
    // top's edge down; the wing's walls inside stand clear of it.
    let outward = clamp(dot(n.xy, q / max(rl, 0.001)) * 1.4, 0.0, 1.0) * smoothstep(0.78 * rc, 0.9 * rc, rl)
    col = col + vec3(0.85, 0.22, 0.03) * gf * 0.5 * outward * ex
    // Under the hand a shade lighter, as every face here; disabled, dimmed
    // toward the disabled face.
    col = col + vec3(0.018, 0.02, 0.022) * hover * live * ex
    col = mix(col, vec3(0.086, 0.098, 0.114) * ex, 0.45 * dis)
    col = Cap.tone(col, 1.0, 0.6)
    // The line laid over the lit solid, as the bench lays its mark: in the
    // flat face's light the whole length, so it keeps its tone over the
    // edge and down the side whichever way the wing points.
    let line = Cap.tone(Cap.shade(vec3(0.0, 0.0, 1.0), l, vw, 1.0, cap_ink, 1.0, 0.0, 1.0, 0.12, 0.84, 0.16, 0.35, 0.45, 1.2, 0.12, 0.0, li, mark_ink, light_ink, shadow_ink, lm_ground()), ex, 0.6)
    col = mix(col, line, paint)
    return Finish.over(res, vec4(col * ccap, ccap))
}

mod.widgets.RotaryKnob.clip_x = false
mod.widgets.RotaryKnob.clip_y = false
mod.widgets.RotaryKnob.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.RotaryKnob.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let dia = min(self.rect_size.x, self.rect_size.y)
    let c = vec2(Finish.snap(self.rect_pos.x + self.rect_size.x * 0.5, px) - self.rect_pos.x, Finish.snap(self.rect_pos.y + self.rect_size.y - dia * 0.5, px) - self.rect_pos.y)
    return lm_knob(p, c, dia * 0.5 - 1.0, px, self.slide_pos, self.origin_pos, self.arc_origin, self.gap, self.hover, self.drag, self.focus, self.disabled) * lm_fade(self.pos, self.rect_size, m)
}
mod.widgets.RotaryFlat.clip_x = false
mod.widgets.RotaryFlat.clip_y = false
mod.widgets.RotaryFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.RotaryFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let dia = min(self.rect_size.x, self.rect_size.y - 24.0)
    let c = vec2(Finish.snap(self.rect_pos.x + self.rect_size.x * 0.5, px) - self.rect_pos.x, Finish.snap(self.rect_pos.y + 22.0 + dia * 0.5, px) - self.rect_pos.y)
    return lm_knob(p, c, dia * 0.5 - 1.0, px, self.slide_pos, self.origin_pos, self.arc_origin, self.gap, self.hover, self.drag, self.focus, self.disabled) * lm_fade(self.pos, self.rect_size, m)
}
// The dial's value: a small chip, a well with orange digits.
mod.widgets.Rotary.text_input.min_height = 0.0
mod.widgets.Rotary.text_input.padding = mod.turtle.Inset{left: 6.0 right: 6.0 top: 2.0 bottom: 2.0}
mod.widgets.Rotary.text_input.draw_text.color = #ff8a3c

// ---------------------------------------------------------------- fields

// A text field: a well punched in its bezel. Focused, the well's frame is
// lit, the light bleeding inward over the floor.
let lm_field = fn(p: vec2, lo: vec2, hi: vec2, o: vec2, px: float, hover: float, down: float, focus: float, dis: float, bezel: float) -> vec4 {
    let hh = hi.y - lo.y
    let rim = mix(0.0, clamp(0.12 * hh, 3.0, 3.5), bezel)
    let rb = min(7.0, 0.3 * hh)
    let wlo = vec2(lm_snap(lo.x + rim, o.x, px), lm_snap(lo.y + rim, o.y, px))
    let whi = vec2(lm_snap(hi.x - rim, o.x, px), lm_snap(hi.y - rim, o.y, px))
    let rw = max(rb - rim, 2.0)
    let live = 1.0 - dis
    var res = vec4(0.0, 0.0, 0.0, 0.0)
    if bezel > 0.5 {
        res = lm_slab(p, lo, hi, rb, px, 1.0, hover * live, dis)
    }
    res = Finish.over(res, lm_well(p, wlo, whi, rw, px, 1.0 + 0.6 * down * live, dis))
    res = lm_edge(res, p, wlo, whi, rw, px, (0.45 * hover + 0.55 * down) * live * (1.0 - focus))
    return lm_frame(res, p, wlo, whi, rw, px, focus * live)
}

mod.widgets.TextInputFlat.clip_x = false
mod.widgets.TextInputFlat.clip_y = false
mod.widgets.TextInputFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.TextInputFlat.draw_bg.pixel = fn() {
    if self.color.a < 0.01 {
        return vec4(0.0, 0.0, 0.0, 0.0)
    }
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(self.rect_size.x, o.x, px), lm_snap(self.rect_size.y, o.y, px))
    // A field lower than a row (the dial's value chip) is a bare well.
    let bezel = step(22.0, hi.y - lo.y)
    return lm_field(p, lo, hi, o, px, self.hover, self.down, self.focus, self.disabled, bezel) * lm_fade(self.pos, self.rect_size, m)
}
mod.widgets.TextInputFlat.padding = mod.turtle.Inset{left: 12.0 right: 12.0 top: 4.0 bottom: 4.0}
mod.widgets.TextInputFlat.draw_cursor.color = #ffc690
mod.widgets.TextInputFlat.draw_text.color = #d0d5db
mod.widgets.TextInputFlat.draw_text.color_empty = #7d8691
mod.widgets.TextInputFlat.draw_text.color_disabled = #5b636d

// The number field: the same well; its stepper two small keys stacked at
// the right, sharing the field's bezel.
mod.widgets.NumberField.clip_x = false
mod.widgets.NumberField.clip_y = false
mod.widgets.NumberField.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.NumberField.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(self.rect_size.x, o.x, px), lm_snap(self.rect_size.y, o.y, px))
    return lm_field(p, lo, hi, o, px, self.hover, 0.0, self.focus, self.disabled, 1.0) * lm_fade(self.pos, self.rect_size, m)
}
mod.widgets.NumberField.spin_width = 18.0
mod.widgets.NumberSpin.width = 18.0
mod.widgets.NumberSpin.draw_text.color = #00000000
mod.widgets.NumberSpin.draw_text.color_disabled = #00000000
mod.widgets.NumberSpin.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * self.rect_size
    let x0 = lm_snap(1.0, o.x, px)
    let x1 = lm_snap(self.rect_size.x - 3.5, o.x, px)
    let y0 = lm_snap(4.0, o.y, px)
    let y1 = lm_snap(self.rect_size.y - 4.0, o.y, px)
    let mid = lm_snap(self.rect_size.y * 0.5, o.y, px)
    let live = 1.0 - self.disabled
    let tu = step(p.y, mid)
    let hot = mix(max(0.0, -self.hot), max(0.0, self.hot), tu) * live
    let dn = mix(max(0.0, -self.down), max(0.0, self.down), tu) * live
    let lo = vec2(x0, mix(mid + px * 0.5, y0, tu))
    let hi = vec2(x1, mix(y1, mid - px * 0.5, tu))
    var res = lm_face(vec4(0.0, 0.0, 0.0, 0.0), p, lo, hi, 2.0, px, hot, dn, self.disabled, 1.0)
    let cx = (x0 + x1) * 0.5
    let cu = (y0 + mid) * 0.5
    let cd = (mid + y1) * 0.5
    let du = min(lm_seg(p, vec2(cx - 2.5, cu + 1.2), vec2(cx, cu - 1.3)), lm_seg(p, vec2(cx, cu - 1.3), vec2(cx + 2.5, cu + 1.2)))
    let dd = min(lm_seg(p, vec2(cx - 2.5, cd - 1.2), vec2(cx, cd + 1.3)), lm_seg(p, vec2(cx, cd + 1.3), vec2(cx + 2.5, cd - 1.2)))
    let k = Finish.cover(min(du, dd) - 0.6, px) * mix(1.0, 0.4, self.disabled)
    let ink = mix(vec3(0.788, 0.808, 0.831), vec3(1.0, 0.541, 0.235), max(hot, dn))
    return Finish.over(res, vec4(ink * k, k))
}

// The chevron of a drop-down: 8 x 4.5 points in a 1.5 point stroke; grey
// at rest, lit orange with a close halo when open.
let lm_chevron = fn(dst: vec4, p: vec2, cc: vec2, ink: vec3, open: float, dis: float, px: float) -> vec4 {
    let dk = min(lm_seg(p, vec2(cc.x - 4.0, cc.y - 2.0), vec2(cc.x, cc.y + 2.2)), lm_seg(p, vec2(cc.x, cc.y + 2.2), vec2(cc.x + 4.0, cc.y - 2.0))) - 0.75
    let hb = 0.4 * exp(-max(dk, 0.0) / 0.9) * (1.0 - Finish.cover(dk, px)) * open * (1.0 - dis)
    var res = Finish.over(dst, vec4(lm_glowc() * hb, hb * 0.45))
    let col = mix(mix(ink, vec3(1.0, 0.541, 0.235), open), vec3(0.36, 0.39, 0.43), dis)
    let k = Finish.cover(dk, px)
    return Finish.over(res, vec4(col * k, k))
}

// The drop-down: a raised key in its bezel, its chevron in a zone of its
// own at the right behind an engraved joint; open, held and the frame lit.
mod.widgets.DropDownFlat.padding = mod.turtle.Inset{left: 14.0 right: 34.0 top: 4.0 bottom: 4.0}
mod.widgets.DropDownFlat.clip_x = false
mod.widgets.DropDownFlat.clip_y = false
mod.widgets.DropDownFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
let lm_dropdown = fn(pos: vec2, size: vec2, o: vec2, dpi: float, hover: float, down: float, open: float, dis: float, focus: float) -> vec4 {
    let m = 5.0
    let px = lm_px(dpi)
    let p = pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    let hh = hi.y - lo.y
    let rim = lm_rim(hh)
    let flo = vec2(lm_snap(rim, o.x, px), lm_snap(rim, o.y, px))
    let fhi = vec2(lm_snap(size.x - rim, o.x, px), lm_snap(size.y - rim, o.y, px))
    let rb = min(7.0, 0.3 * hh)
    let rf = max(rb - rim + 0.5, 2.0)
    let live = 1.0 - dis
    let held = max(down, open)
    var res = lm_slab(p, lo, hi, rb, px, 1.0, hover * live, dis)
    res = lm_face(res, p, flo, fhi, rf, px, hover, held, dis, 1.0)
    res = lm_under(res, p, flo, fhi, rf, px, 0.28 * hover * live * (1.0 - held), hi.y)
    // The joint before the chevron zone: a dark line and a light one.
    let jx = lm_snap(size.x - rim - 22.0, o.x, px)
    let iny = step(flo.y + 3.0, p.y) * step(p.y, fhi.y - 3.0)
    let jd = step(jx - px, p.x) * step(p.x, jx) * iny
    let jl = step(jx, p.x) * step(p.x, jx + px) * iny
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, 0.8 * jd))
    res = Finish.over(res, vec4(vec3(0.2, 0.22, 0.245) * jl, jl))
    res = lm_frame(res, p, flo, fhi, rf, px, open * live)
    res = lm_focus(res, p, lo, hi, rb, px, focus * live * (1.0 - open))
    // The chevron is a glyph on a lit control when the list is open or the
    // frame is lit by focus: orange.
    res = lm_chevron(res, p, vec2(fhi.x - 11.0, (lo.y + hi.y) * 0.5), vec3(0.788, 0.808, 0.831), max(open, focus), dis, px)
    return res * lm_fade(pos, size, m)
}
mod.widgets.DropDownFlat.draw_bg.pixel = fn() {
    return lm_dropdown(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, self.active, self.disabled, self.focus)
}
mod.widgets.DropDownFlat.draw_text.color = #c9ced4
mod.widgets.DropDownFlat.draw_text.color_hover = #e4e8ec
mod.widgets.DropDownFlat.draw_text.color_focus = #e4e8ec
mod.widgets.DropDownFlat.draw_text.color_disabled = #5b636d

// The select wears a button of its own, built before this sheet: it is
// given the drop-down's face and room here.
mod.widgets.Select.clip_x = false
mod.widgets.Select.clip_y = false
mod.widgets.MultiSelect.clip_x = false
mod.widgets.MultiSelect.clip_y = false
mod.widgets.Select.face.clip_x = false
mod.widgets.Select.face.clip_y = false
mod.widgets.MultiSelect.face.clip_x = false
mod.widgets.MultiSelect.face.clip_y = false
mod.widgets.Select.face.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.MultiSelect.face.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.Select.face.draw_bg.pixel = fn() {
    return lm_dropdown(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, 0.0, self.disabled, self.focus)
}
mod.widgets.MultiSelect.face.draw_bg.pixel = fn() {
    return lm_dropdown(self.pos, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, self.hover, self.down, 0.0, self.disabled, self.focus)
}
mod.widgets.Select.face.padding = mod.turtle.Inset{left: 14.0 right: 34.0 top: 4.0 bottom: 4.0}
mod.widgets.MultiSelect.face.padding = mod.turtle.Inset{left: 14.0 right: 34.0 top: 4.0 bottom: 4.0}
mod.widgets.Select.face.min_height = 28.0
mod.widgets.MultiSelect.face.min_height = 28.0
mod.widgets.Select.face.draw_text.color = #c9ced4
mod.widgets.MultiSelect.face.draw_text.color = #c9ced4

// The combo box: a well one types in, in its bezel, the chevron at its
// right behind an engraved joint.
mod.widgets.ComboBoxFlat.padding = mod.turtle.Inset{left: 12.0 right: 34.0 top: 4.0 bottom: 4.0}
mod.widgets.ComboBoxFlat.input.min_height = 0.0
mod.widgets.ComboBoxFlat.clip_x = false
mod.widgets.ComboBoxFlat.clip_y = false
mod.widgets.ComboBoxFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.ComboBoxFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let size = self.rect_size
    let p = self.pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    var res = lm_field(p, lo, hi, o, px, self.hover, 0.0, self.focus, self.disabled, 1.0)
    let jx = lm_snap(size.x - 26.0, o.x, px)
    let iny = step(5.5, p.y) * step(p.y, size.y - 5.5)
    let jd = step(jx - px, p.x) * step(p.x, jx) * iny
    let jl = step(jx, p.x) * step(p.x, jx + px) * iny
    res = Finish.over(res, vec4(0.0, 0.0, 0.0, 0.9 * jd))
    res = Finish.over(res, vec4(vec3(0.16, 0.18, 0.2) * jl, jl))
    res = lm_chevron(res, p, vec2(size.x - 14.0, size.y * 0.5), vec3(0.788, 0.808, 0.831), self.focus, self.disabled, px)
    return res * lm_fade(self.pos, size, m)
}

// Open lists: a slab with its top line; rows lift a little under the hand,
// the chosen row in a lit frame.
let lm_menu = fn(p: vec2, size: vec2, px: float) -> vec4 {
    let r = min(7.0, min(size.x, size.y) * 0.5)
    let res = lm_slab(p, vec2(0.0, 0.0), size, r, px, 0.0, 0.0, 0.0)
    let d = Material.sd_box(p, size * 0.5, size * 0.5, r)
    let e = Finish.band(d, 0.0, px, px) * 0.5
    return Finish.over(res, vec4(vec3(0.25, 0.27, 0.3) * e, e) * step(p.y, size.y - px))
}
let lm_row = fn(p: vec2, size: vec2, px: float, hover: float, active: float, dis: float) -> vec4 {
    let lo = vec2(3.0, 1.5)
    let hi = size - vec2(3.0, 1.5)
    let r = min(4.0, (hi.y - lo.y) * 0.5)
    let d = Material.sd_box(p, (lo + hi) * 0.5, (hi - lo) * 0.5, r)
    let a = Finish.cover(d, px)
    let wash = 0.06 * hover * (1.0 - dis) * a
    var res = vec4(vec3(0.788, 0.808, 0.831) * wash, wash)
    if active > 0.001 {
        var sel = Finish.over(vec4(0.0, 0.0, 0.0, 0.0), vec4(vec3(0.075, 0.082, 0.094) * a, a))
        sel = lm_frame(sel, p, lo, hi, r, px, 1.0)
        res = mix(res, sel, active)
    }
    return res
}
mod.widgets.PopupMenuFlat.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    return lm_menu(self.pos * self.rect_size, self.rect_size, px)
}
mod.widgets.PopupMenuItem.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    return lm_row(self.pos * self.rect_size, self.rect_size, px, self.hover, self.active, self.disabled)
}
mod.widgets.PopupMenuItem.draw_text.color_active = #ff8a3c
mod.widgets.ComboBoxFlat.draw_popup_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    return lm_menu(self.pos * self.rect_size, self.rect_size, px)
}
mod.widgets.ComboBoxFlat.draw_item.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    return lm_row(self.pos * self.rect_size, self.rect_size, px, self.hover, self.active, 0.0)
}
mod.widgets.ComboBoxFlat.draw_item_text.color_active = #ff8a3c

// ---------------------------------------------------------------- tabs

// The segmented control: one bezel with a track punched along it, the
// answers standing in the track; the chosen answer is lit from within.
mod.widgets.SegmentedControl.segment_height = 24.0
mod.widgets.SegmentedControlFlat.segment_height = 24.0
mod.widgets.SegmentedControlFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.SegmentedControlFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let size = self.rect_size
    let p = self.pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    let rb = min(7.0, 0.3 * (hi.y - lo.y))
    var res = lm_slab(p, lo, hi, rb, px, 1.0, 0.0, 0.0)
    // The track: a sunken ridge punched along the bezel, 1 point in. Its
    // floor dark, the shade of its upper wall under the top edge, and its
    // lower wall a band facing up that catches what light there is.
    let tlo = vec2(lm_snap(1.0, o.x, px), lm_snap(1.0, o.y, px))
    let thi = vec2(lm_snap(size.x - 1.0, o.x, px), lm_snap(size.y - 1.0, o.y, px))
    res = Finish.over(res, lm_track(p, tlo, thi, max(rb - 1.0, 2.0), px))
    return res * lm_fade(self.pos, size, m)
}
// The chosen answer: its cell of the track lit from within, filling the
// segment's box less half a point either side; its light spills on the
// track's floor beside it, the rim and a little on the ground.
mod.widgets.SegmentedControlFlat.draw_pill.vertex = fn() {
    let m = 13.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.SegmentedControlFlat.draw_pill.pixel = fn() {
    let m = 13.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let size = self.rect_size
    let p = self.pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let clo = vec2(lm_snap(1.5, o.x, px), lm_snap(1.5, o.y, px))
    let chi = vec2(lm_snap(size.x - 1.5, o.x, px), lm_snap(size.y - 1.5, o.y, px))
    let res = lm_lit(vec4(0.0, 0.0, 0.0, 0.0), p, clo, chi, 4.5, px, 1.0, 0.0)
    return res * lm_fade(self.pos, size, m)
}
mod.widgets.SegmentedControlFlat.draw_text.text_style.font_size = 9.0
mod.widgets.SegmentedControlFlat.draw_text_selected.text_style.font_size = 9.0
mod.widgets.SegmentedControlFlat.draw_text.color = #aab2bc
mod.widgets.SegmentedControlFlat.draw_text_selected.color = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_primary_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_neutral_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_secondary_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_primary_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_neutral_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_secondary_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_tertiary_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_error_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_warning_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_success_container = #ffb47c
mod.widgets.SegmentedControlFlat.palette.on_info_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_tertiary_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_error_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_warning_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_success_container = #ffb47c
mod.widgets.SegmentedControl.palette.on_info_container = #ffb47c

// Tabs: the strip is one bezel; each quiet tab a raised face in it, the
// tab in use lit from within, its word lit orange on the dark glass.
mod.widgets.Tabs.height = 28.0
mod.widgets.Tabs.clip_x = false
mod.widgets.Tabs.clip_y = false
mod.widgets.Tabs.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.Tabs.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let size = self.rect_size
    let p = self.pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    return lm_slab(p, lo, hi, min(7.0, 0.3 * (hi.y - lo.y)), px, 1.0, 0.0, 0.0) * lm_fade(self.pos, size, m)
}
// A tab's close cross, drawn by the tab's own face so it can burn orange on
// the tab in use: where the strip puts its mark (15 points square, 5 in
// from the right, centred in height), two strokes 1.4 points thick. The
// strip shows it on the tab in use, the one under the pointer, and on every
// tab 108 points wide or more; the mark the strip draws there itself is
// left empty (below).
let lm_cross = fn(dst: vec4, p: vec2, size: vec2, px: float, ink: vec3, lit: float, show: float) -> vec4 {
    if show < 0.5 {
        return dst
    }
    let cc = vec2(size.x - 12.5, size.y * 0.5)
    let k = 2.76
    let dk = min(lm_seg(p, cc - vec2(k, k), cc + vec2(k, k)), lm_seg(p, cc + vec2(k, -k), cc + vec2(-k, k))) - 0.7
    let hb = 0.4 * exp(-max(dk, 0.0) / 0.9) * (1.0 - Finish.cover(dk, px)) * lit
    var res = Finish.over(dst, vec4(lm_glowc() * hb, hb * 0.45))
    let a = Finish.cover(dk, px)
    return Finish.over(res, vec4(ink * a, a))
}
let lm_tab = fn(p: vec2, size: vec2, o: vec2, dpi: float, hover: float, active: float) -> vec4 {
    let px = lm_px(dpi)
    let lo = vec2(lm_snap(1.0, o.x, px), lm_snap(3.0, o.y, px))
    let hi = vec2(lm_snap(size.x - 1.0, o.x, px), lm_snap(size.y - 3.0, o.y, px))
    var res = vec4(0.0, 0.0, 0.0, 0.0)
    if active > 0.5 {
        // The tab in use: its face lit from within, the light spilling on
        // the strip's bezel round it.
        res = lm_lit(res, p, lo, hi, 4.0, px, 1.0, 0.0)
        res = lm_cross(res, p, size, px, vec3(1.0, 0.706, 0.486), 1.0, 1.0)
    } else {
        res = lm_face(res, p, lo, hi, 4.0, px, hover, 0.0, 0.0, 1.0)
        res = lm_under(res, p, lo, hi, 4.0, px, 0.28 * hover, hi.y + 3.0)
        let ink = mix(vec3(0.604, 0.639, 0.682), vec3(0.894, 0.91, 0.925), hover)
        res = lm_cross(res, p, size, px, ink, 0.0, max(hover, step(108.0, size.x)))
    }
    return res
}
mod.widgets.Tabs.draw_tab.pixel = fn() {
    return lm_tab(self.pos * self.rect_size, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, 0.0, 0.0)
}
mod.widgets.Tabs.draw_tab_hover.pixel = fn() {
    return lm_tab(self.pos * self.rect_size, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, 1.0, 0.0)
}
// The tab in use grows its quad downward for the light under it.
mod.widgets.Tabs.draw_tab_active.vertex = fn() {
    let m = 12.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.Tabs.draw_tab_active.pixel = fn() {
    let m = 12.0
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    return lm_tab(p, self.rect_size, self.rect_pos, self.draw_pass.dpi_factor, 0.0, 1.0) * lm_fade(self.pos, self.rect_size, m)
}
mod.widgets.Tabs.draw_sep.pixel = fn() {
    return vec4(0.0, 0.0, 0.0, 0.0)
}
// The strip's own mark: the add plus in the grey line drawing; its close
// cross is drawn by the tab faces above, so here it draws nothing.
mod.widgets.Tabs.draw_mark.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * self.rect_size
    let cc = self.rect_size * 0.5
    let r = min(self.rect_size.x, self.rect_size.y) * 0.26
    let dk = min(lm_seg(p, cc - vec2(r, 0.0), cc + vec2(r, 0.0)), lm_seg(p, cc - vec2(0.0, r), cc + vec2(0.0, r))) - 0.7
    let a = Finish.cover(dk, px) * step(0.5, self.plus)
    return vec4(vec3(0.604, 0.639, 0.682) * a, a)
}
mod.widgets.Tabs.draw_mark.color = #9aa3ae
mod.widgets.Tabs.draw_text.color = #aab2bc
mod.widgets.Tabs.draw_text_active.color = #ffb47c
mod.widgets.Tabs.draw_text.text_style.font_size = 9.0
mod.widgets.Tabs.draw_text_active.text_style.font_size = 9.0

// ---------------------------------------------------------------- feedback

// The progress bar: a slab 10 points tall with a 6 point well, the lit
// fill in it.
mod.widgets.ProgressBarFlat.height = 10.0
mod.widgets.ProgressBarFlat.clip_x = false
mod.widgets.ProgressBarFlat.clip_y = false
mod.widgets.ProgressBarFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.ProgressBarFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let th = min(10.0, self.rect_size.y)
    let y0 = lm_snap((self.rect_size.y - th) * 0.5, o.y, px)
    let x0 = lm_snap(self.rect_size.x * self.start, o.x, px)
    let x1 = lm_snap(self.rect_size.x * self.end, o.x, px)
    var res = vec4(0.0, 0.0, 0.0, 0.0)
    let wlo = vec2(x0 + 1.333, y0 + 1.333)
    let whi = vec2(x1 - 1.333, y0 + th - 1.333)
    if self.track > 0.5 {
        res = lm_slab(p, vec2(x0, y0), vec2(x1, y0 + th), th * 0.5, px, 1.0, 0.0, 0.0)
        res = Finish.over(res, lm_well(p, wlo, whi, (whi.y - wlo.y) * 0.5, px, 1.0, 0.0))
    }
    let span = whi.x - wlo.x - 2.0
    var f0 = wlo.x + 1.0
    var f1 = f0 + span * clamp((self.value - self.start) / max(self.end - self.start, 0.001), 0.0, 1.0)
    if self.value < 0.0 {
        // Still: the sweep would need the pass clock, which a sheet may not
        // read, so the unknown amount is a lit stretch standing in the
        // middle with its ends fading.
        f0 = wlo.x + 1.0 + span * 0.3
        f1 = wlo.x + 1.0 + span * 0.7
    }
    var fill = lm_tube(vec4(0.0, 0.0, 0.0, 0.0), p, f0, f1, 2.0, px, 0.0, 0.0, wlo, whi, (whi.y - wlo.y) * 0.5, 0.0)
    // An intent other than the plain one tints the light with its colour.
    let ic = self.fill_color()
    let tint = step(0.5, self.intent)
    fill = vec4(mix(fill.rgb, fill.rgb * ic.rgb * 1.1, tint * 0.8), fill.a)
    if self.value < 0.0 {
        fill = fill * smoothstep(f0 - 1.0, f0 + span * 0.12, p.x) * smoothstep(f1 + 1.0, f1 - span * 0.12, p.x)
    }
    res = Finish.over(res, fill)
    return res * self.opacity * lm_fade(self.pos, self.rect_size, m)
}

// The level meter: cells 3 points long with 1.5 point gaps in a well in a
// slab; the light deep at the foot, orange, then hot, red-orange past the
// clip point; unlit cells dark; the clip lamp a lamp.
mod.widgets.LevelMeter.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let sz = self.rect_size
    let p = self.pos * sz
    let v = self.vertical
    let along = mix(sz.x, sz.y, v)
    let across = mix(sz.y, sz.x, v)
    let a = mix(p.x, sz.y - p.y, v)
    let b = mix(p.y, p.x, v)
    let lamp_room = self.lamp * (across + 3.0)
    let bar = max(4.0, along - lamp_room)
    let wa = min(across, 10.0)
    let wb0 = (across - wa) * 0.5
    let blo0 = mix(vec2(0.0, wb0), vec2(wb0, sz.y - bar), v)
    let bhi0 = mix(vec2(bar, wb0 + wa), vec2(wb0 + wa, sz.y), v)
    let blo = vec2(lm_snap(blo0.x, o.x, px), lm_snap(blo0.y, o.y, px))
    let bhi = vec2(lm_snap(bhi0.x, o.x, px), lm_snap(bhi0.y, o.y, px))
    var res = lm_slab(p, blo, bhi, 3.5, px, 0.0, 0.0, 0.0)
    res = Finish.over(res, lm_well(p, blo + vec2(2.0, 2.0), bhi - vec2(2.0, 2.0), 1.5, px, 1.0, 0.0))
    let pad = 3.0
    let span = max(1.0, bar - pad * 2.0)
    let pitch = 4.5
    let ca = a - pad
    let cell = Finish.cover(abs(fract(ca / pitch) * pitch - 1.5) - 1.5, px)
    let share = clamp((floor(ca / pitch) * pitch + 1.5) / span, 0.0, 1.0)
    let inb = step(pad, a) * step(a, bar - pad) * step(wb0 + 3.0, b) * step(b, wb0 + wa - 3.0)
    let ha = max(self.hot_at, 0.7)
    let ht = max(self.hot_to, 0.9)
    var lit = mix(lm_deep(), lm_orange(), smoothstep(0.0, 1.0, share / ha))
    lit = mix(lit, vec3(1.0, 0.56, 0.3), step(ha, share))
    lit = mix(lit, vec3(1.0, 0.24, 0.1), step(ht, share))
    let qm = (b - (wb0 + wa * 0.5)) / max(0.3 * (wa - 6.0), px * 0.8)
    lit = mix(lit, lm_core(), exp(-qm * qm) * 0.5 * (1.0 - step(ht, share)))
    let on = step(share, self.level) * step(0.001, self.level)
    // The lit cells warm the floor between them the dark red a lit tube
    // gives its groove.
    let lit_to = pad + span * self.level
    let wfl = Finish.cover(Material.sd_box(p, (blo + bhi) * 0.5, (bhi - blo) * 0.5 - vec2(2.0, 2.0), 1.5), px)
    let fl = (1.0 - smoothstep(lit_to - 0.5, lit_to + 1.5, a)) * step(0.001, self.level) * wfl * 0.8 * self.opacity
    res = Finish.over(res, vec4(vec3(0.27, 0.012, 0.0) * fl, fl))
    let ghost = vec3(0.1, 0.11, 0.125)
    let col = mix(ghost, lit, on)
    res = Finish.over(res, vec4(col, 1.0) * cell * inb * self.opacity)
    let hold_at = floor((span * self.hold) / pitch) * pitch
    let hc = step(abs(floor(ca / pitch) * pitch - hold_at), 0.1) * step(0.002, self.hold)
    res = Finish.over(res, vec4(lm_orange(), 1.0) * hc * cell * inb * 0.85)
    if self.lamp > 0.5 {
        let lc = mix(vec2(bar + 3.0 + across * 0.5, sz.y * 0.5), vec2(sz.x * 0.5, across * 0.5), v)
        let rl = max(across * 0.5 - 3.0, 1.5)
        res = lm_lamp(res, p, lc, rl, px, step(0.5, self.over), 0.0)
    }
    return res * self.opacity
}

// The spinner keeps the library's own turning face and takes the orange.
mod.widgets.SpinnerFlat.draw_bg.color = #ff6a1e
mod.widgets.SpinnerFlat.draw_bg.track_alpha = 0.18

// The rings, the arc and the stock bars keep their own faces; the plain
// intent reads orange, so the page has one accent.
mod.widgets.ProgressRingFlat.draw_bg.color_primary = #ff6a1e
mod.widgets.ProgressRing.draw_bg.color_primary = #ff6a1e
mod.widgets.ProgressArc.draw_bg.color_primary = #ff6a1e
mod.widgets.ActivityRings.draw_bg.color_primary = #ff6a1e
mod.widgets.ProgressBarFlat.draw_bg.color_primary = #ff6a1e
mod.widgets.ProgressBar.draw_bg.color_primary = #ff6a1e
mod.widgets.ProgressBarGradientX.draw_bg.color_primary = #ff6a1e
mod.widgets.ProgressBarGradientY.draw_bg.color_primary = #ff6a1e

// Words in the error intent beside a check box or a toggle: red-orange.
mod.widgets.CheckBoxFlat.draw_text.color_error = #ff6a4a
mod.widgets.ToggleFlat.draw_text.color_error = #ff6a4a

// ---------------------------------------------------------------- surfaces

// The scroll bar: no gutter; the thumb a slim dark slab with its outline,
// lighter under the hand.
mod.widgets.ScrollBar.bar_size = 8.0
mod.widgets.ScrollBar.bar_side_margin = 1.0
mod.widgets.ScrollBar.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let sz = self.rect_size
    let p = self.pos * sz
    let v = self.is_vertical
    let t0 = mix(sz.x * self.norm_scroll, sz.y * self.norm_scroll, v)
    let t1 = t0 + mix(sz.x * self.norm_handle, sz.y * self.norm_handle, v)
    let mid = mix(sz.y * 0.5, sz.x * 0.5, v)
    let tlo = mix(vec2(t0, mid - 3.0), vec2(mid - 3.0, t0), v)
    let thi = mix(vec2(t1, mid + 3.0), vec2(mid + 3.0, t1), v)
    let lo = vec2(lm_snap(tlo.x, o.x, px), lm_snap(tlo.y, o.y, px))
    let hi = vec2(lm_snap(thi.x, o.x, px), lm_snap(thi.y, o.y, px))
    let res = lm_face(vec4(0.0, 0.0, 0.0, 0.0), p, lo, hi, 3.0, px, max(self.hover, self.drag), 0.0, 0.0, 0.0)
    return res * self.opacity
}

// The faint free grain a slab carries, in its own device pixels.
let lm_grain = fn(p: vec2, px: float) -> float {
    return Finish.grain(p / px, 0.014)
}

// A PANEL: a slab. A large one carries a screw in each corner.
let lm_panel = fn(p: vec2, size: vec2, o: vec2, px: float, r: float, hover: float) -> vec4 {
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    var res = lm_slab(p, lo, hi, r, px, 1.4, hover, 0.0)
    let a = res.w
    let g = lm_grain(p, px) * a
    res = vec4(res.rgb + vec3(g, g, g) * step(0.99, a), res.w)
    if size.x > 120.0 && size.y > 70.0 {
        res = lm_screw(res, p, lo + vec2(7.0, 7.0), px)
        res = lm_screw(res, p, vec2(hi.x - 7.0, lo.y + 7.0), px)
        res = lm_screw(res, p, vec2(lo.x + 7.0, hi.y - 7.0), px)
        res = lm_screw(res, p, hi - vec2(7.0, 7.0), px)
    }
    return res
}
// 3. A PUNCHED PANEL with its LIT RIM: a bezel 3 points wide, a well in it,
// light leaking from behind the well's edge: a thin bright line along its
// inner rim, strongest along the top and in the corners, fading into the
// floor within 8 to 12 points; the middle stays dark.
let lm_tray = fn(p: vec2, size: vec2, o: vec2, px: float, r: float, lit: float) -> vec4 {
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    var res = lm_slab(p, lo, hi, r, px, 1.4, 0.0, 0.0)
    let wlo = vec2(lm_snap(3.0, o.x, px), lm_snap(3.0, o.y, px))
    let whi = vec2(lm_snap(size.x - 3.0, o.x, px), lm_snap(size.y - 3.0, o.y, px))
    let wr = max(r - 2.5, 2.0)
    res = Finish.over(res, lm_well(p, wlo, whi, wr, px, 1.4, 0.0))
    let c = (wlo + whi) * 0.5
    let h = (whi - wlo) * 0.5
    let d = Material.sd_box(p, c, h, wr)
    let a = Finish.cover(d, px)
    let x = max(-d, 0.0)
    // Strongest along the top edge and in the corners, weak down the sides
    // and weakest along the foot. Which edge a point belongs to is read off
    // the nearest edge's direction, so the light keeps its strength all the
    // way into the panel from the top edge and fades by distance alone.
    let n = lm_normal(p, c, h, wr)
    let top = smoothstep(-0.3, 0.7, -n.y)
    let qx = abs(p.x - c.x) - (h.x - 14.0)
    let qy = abs(p.y - c.y) - (h.y - 14.0)
    let corner = smoothstep(0.0, 14.0, min(qx, qy))
    let foot = smoothstep(-0.3, 0.7, n.y)
    let strength = max(max(top, corner), 0.3 - 0.18 * foot) * lit
    let rimline = Finish.band(d, px, px * 2.5, px) * a * strength
    // Falls into the floor by distance: a tenth of the line by about 8
    // points, near nothing by 12; the middle of the panel stays dark.
    let fall = exp(-max(x - px * 2.0, 0.0) / 7.5) * a * strength * 0.62 * (1.0 - Finish.band(d, 0.0, px * 2.5, px))
    res = Finish.over(res, vec4(mix(lm_deep(), lm_glowc(), 0.35) * fall, fall * 0.8))
    let rc = mix(lm_orange(), lm_core(), 0.35 * max(top, corner))
    res = Finish.over(res, vec4(rc * rimline, rimline))
    let g = lm_grain(p, px) * 0.5 * a
    return vec4(res.rgb + vec3(g, g, g), res.w)
}

mod.widgets.PanelView.clip_x = false
mod.widgets.PanelView.clip_y = false
mod.widgets.PanelView.padding = mod.turtle.Inset{left: 12.0 right: 12.0 top: 12.0 bottom: 12.0}
mod.widgets.PanelView.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.PanelView.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    if self.sunken > 0.5 {
        return lm_tray(p, self.rect_size, self.rect_pos, px, 7.0, 1.0) * lm_fade(self.pos, self.rect_size, m)
    }
    return lm_panel(p, self.rect_size, self.rect_pos, px, 7.0, 0.0) * lm_fade(self.pos, self.rect_size, m)
}

// The rounded view keeps the colour its caller gives it, with a true
// corner and, when it is opaque, a one device pixel edge lighter on top.
mod.widgets.RoundedView.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * self.rect_size
    let lo = vec2(self.border_inset.x, self.border_inset.y)
    let hi = self.rect_size - vec2(self.border_inset.z, self.border_inset.w)
    let c = (lo + hi) * 0.5
    let h = max((hi - lo) * 0.5, vec2(0.5, 0.5))
    let r = min(2.0 * max(1.0, self.border_radius), min(h.x, h.y))
    let d = Material.sd_box(p, c, h, r)
    let n = lm_normal(p, c, h, r)
    var fill = self.color
    if self.color_2.x > -0.5 {
        fill = mix(self.color, self.color_2, mix(self.pos.y, self.pos.x, self.gradient_fill_horizontal))
    }
    var ink = self.border_color
    if self.border_size < 0.01 {
        ink = vec4(mix(vec3(0.141, 0.157, 0.184), vec3(0.212, 0.235, 0.267), smoothstep(-0.25, 0.75, -n.y)), fill.a)
    }
    let a = Finish.cover(d, px)
    let bd = Finish.band(d, 0.0, max(self.border_size, px), px)
    let col = mix(fill.rgb, ink.rgb, bd * ink.a)
    return vec4(col * a * fill.a, a * fill.a) + vec4(ink.rgb * ink.a, ink.a) * bd * a * (1.0 - fill.a)
}

// The card: a slab. Elevated it throws a longer shadow; outlined it is the
// bezel's edge alone; under the hand its top line brightens.
mod.widgets.Card.clip_x = false
mod.widgets.Card.clip_y = false
mod.widgets.Card.padding = mod.turtle.Inset{left: 12.0 right: 12.0 top: 10.0 bottom: 10.0}
mod.widgets.Card.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.Card.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let fade = lm_fade(self.pos, self.rect_size, m)
    let o = self.rect_pos
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(self.rect_size.x, o.x, px), lm_snap(self.rect_size.y, o.y, px))
    if self.border_size > 0.01 {
        let c = (lo + hi) * 0.5
        let h = (hi - lo) * 0.5
        let d = Material.sd_box(p, c, h, 7.0)
        let n = lm_normal(p, c, h, 7.0)
        let ring = Finish.band(d, 0.0, px, px)
        let col = mix(vec3(0.227, 0.251, 0.282), vec3(0.33, 0.357, 0.392), smoothstep(-0.3, 0.7, -n.y)) + vec3(0.08, 0.08, 0.08) * self.hover
        return vec4(col * ring, ring) * fade
    }
    var res = lm_slab(p, lo, hi, 7.0, px, 1.4 + 0.3 * step(0.01, self.shadow_radius), self.hover, 0.0)
    let g = lm_grain(p, px) * res.w
    return vec4(res.rgb + vec3(g, g, g) * step(0.99, res.w), res.w) * fade
}

// A LIST SHARES ONE BEZEL. A scroll view the size of a list (under 320
// points tall; a page-sized one stays the ground) is a slab with a well
// punched in it, 3 points in, and its rows lie on the well's floor. The view
// gets a draw object of its own first, so the face written here reaches no
// other view.
mod.widgets.ScrollYView.draw_bg = mod.widgets.SolidView.draw_bg{}
mod.widgets.ScrollYView.show_bg = true
mod.widgets.ScrollYView.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let sz = self.rect_size
    if sz.y > 320.0 || sz.x < 40.0 {
        return vec4(0.0, 0.0, 0.0, 0.0)
    }
    let p = self.pos * sz
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(sz.x, o.x, px), lm_snap(sz.y, o.y, px))
    var res = lm_slab(p, lo, hi, 7.0, px, 0.0, 0.0, 0.0)
    let wlo = vec2(lm_snap(3.0, o.x, px), lm_snap(3.0, o.y, px))
    let whi = vec2(lm_snap(sz.x - 3.0, o.x, px), lm_snap(sz.y - 3.0, o.y, px))
    return Finish.over(res, lm_well(p, wlo, whi, 4.5, px, 1.2, 0.0))
}

// List rows: 10 points in, a device pixel divider (#232a31) under each;
// under the hand the row lifts a little; the chosen row sinks deeper in a
// lit frame, held 5 points in from the left so it clears a list bezel's rim.
mod.widgets.ListItem.padding = mod.turtle.Inset{left: 12.0 right: 12.0 top: 0.0 bottom: 0.0}
// The row's quad grows 6 points for the light a chosen row spills.
mod.widgets.ListItem.clip_x = false
mod.widgets.ListItem.clip_y = false
mod.widgets.ListItem.draw_bg.vertex = fn() {
    let m = 6.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.ListItem.draw_bg.pixel = fn() {
    let m = 6.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let live = 1.0 - self.disabled
    let yb = lm_snap(self.rect_size.y, o.y, px)
    let div = step(yb - px, p.y) * step(p.y, yb) * step(10.0, p.x) * step(p.x, self.rect_size.x - 10.0)
    var res = vec4(0.137, 0.165, 0.192, 1.0) * div * (1.0 - self.selected)
    let lo = vec2(lm_snap(5.0, o.x, px), lm_snap(2.0, o.y, px))
    // Held clear of the scroll bar that stands over a list's right edge.
    let hi = vec2(lm_snap(self.rect_size.x - 11.0, o.x, px), yb - px * 2.0)
    let wash = (0.045 * self.hover + 0.03 * self.down) * live
    let d = Material.sd_box(p, (lo + hi) * 0.5, (hi - lo) * 0.5, 4.0)
    let wa = Finish.cover(d, px) * wash
    res = Finish.over(res, vec4(vec3(0.788, 0.808, 0.831) * wa, wa))
    if self.selected > 0.001 {
        // Chosen: the row lit from within, as the chosen answer and the tab
        // in use are.
        let sl = lm_litrow(vec4(0.0, 0.0, 0.0, 0.0), p, lo, hi, 4.0, px, 1.0 + 0.12 * self.hover, 6.0)
        res = mix(res, sl, self.selected)
    }
    return res
}
mod.widgets.ListItem.draw_text.color = #d0d5db
mod.widgets.ListItem.draw_text_2.color = #8b95a1

// A chip is a small key in its bezel, cornered like every bezel (not a
// pill); keyed, its frame is lit.
mod.widgets.ChipFlat.draw_text.text_style.font_size = 9.0
mod.widgets.ChipFlat.palette.on_neutral = #c9ced4
mod.widgets.ChipFlat.palette.on_neutral_container = #c9ced4
mod.widgets.ChipFlat.palette.neutral = #c9ced4
mod.widgets.ChipFlat.palette.on_primary = #ff8a3c
mod.widgets.ChipFlat.palette.on_primary_container = #ff8a3c
mod.widgets.ChipFlat.palette.primary = #ff8a3c
mod.widgets.ChipFlat.palette.on_secondary_container = #c9ced4
mod.widgets.ChipFlat.palette.on_tertiary_container = #c9ced4
mod.widgets.ChipFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.ChipFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let size = self.rect_size
    let p = self.pos * (size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(size.x, o.x, px), lm_snap(size.y, o.y, px))
    let hh = hi.y - lo.y
    let rim = 3.0
    let flo = vec2(lm_snap(rim, o.x, px), lm_snap(rim, o.y, px))
    let fhi = vec2(lm_snap(size.x - rim, o.x, px), lm_snap(size.y - rim, o.y, px))
    let rb = min(7.0, 0.3 * hh)
    let rf = max(rb - rim + 0.5, 2.0)
    var res = lm_slab(p, lo, hi, rb, px, 1.0, self.hover, 0.0)
    res = lm_face(res, p, flo, fhi, rf, px, self.hover, self.down, 0.0, 1.0)
    res = lm_under(res, p, flo, fhi, rf, px, 0.28 * self.hover * (1.0 - self.down), hi.y)
    return lm_frame(res, p, flo, fhi, rf, px, self.keyed) * lm_fade(self.pos, size, m)
}

// A count is a small dark face with orange figures.
mod.widgets.BadgePalette.neutral = #1d2127
mod.widgets.BadgePalette.on_neutral = #ff8a3c
mod.widgets.BadgeFlat.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * self.rect_size
    let lo = vec2(lm_snap(0.0, o.x, px), lm_snap(0.0, o.y, px))
    let hi = vec2(lm_snap(self.rect_size.x - px * 0.49, o.x, px), lm_snap(self.rect_size.y - px * 0.49, o.y, px))
    let c = (lo + hi) * 0.5
    let h = (hi - lo) * 0.5
    let r = min(min(h.x, h.y), 3.5)
    let d = Material.sd_box(p, c, h, r)
    let n = lm_normal(p, c, h, r)
    let t = clamp((p.y - lo.y) / max(hi.y - lo.y, 1.0), 0.0, 1.0)
    var col = self.color.rgb + vec3(0.02, 0.02, 0.02) * (1.0 - t) - vec3(0.02, 0.02, 0.02) * t
    let ring = Finish.band(d, 0.0, px, px)
    col = mix(col, mix(vec3(0.227, 0.251, 0.282), vec3(0.33, 0.357, 0.392), smoothstep(-0.3, 0.7, -n.y)), ring)
    let a = Finish.cover(d, px) * max(self.color.a, ring)
    return vec4(col * a, a)
}

// Dividers never glow: one device pixel, #232a31.
mod.widgets.Hr.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * self.rect_size
    let y = Finish.snap(self.rect_pos.y + self.rect_size.y * 0.5, px) - self.rect_pos.y
    return vec4(0.137, 0.165, 0.192, 1.0) * step(y, p.y) * step(p.y, y + px)
}
mod.widgets.Vr.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * self.rect_size
    let x = Finish.snap(self.rect_pos.x + self.rect_size.x * 0.5, px) - self.rect_pos.x
    return vec4(0.137, 0.165, 0.192, 1.0) * step(x, p.x) * step(p.x, x + px)
}

// ---------------------------------------------------------------- own faces

// Templates that draw a face of their own on top of these roots keep the
// plain quad: the grown one is only for the faces written here.
mod.widgets.CloseButton.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.CopyButton.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.BurgerButton.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.ButtonFloating.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.ButtonFloatingSm.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.CheckBoxCustom.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.glass.CutButton.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.glass.RadioButton.draw_bg.vertex = fn() {
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos, self.rect_size)
}
mod.widgets.ButtonFlatterIcon.draw_icon.color = #c9ced4
mod.widgets.BurgerButton.draw_bg.bar_color = #c9ced4
mod.widgets.BurgerButton.draw_bg.bar_color_hover = #ff8a3c
mod.widgets.BurgerButton.draw_bg.bar_color_disabled = #5b636d
mod.widgets.CloseButton.draw_bg.cross_color_hover = #ff8a3c

// ---------------------------------------------------------------- field row

// A ROW OF FIELDS IS ONE HEIGHT. Left to themselves the library's fields each
// come out at a size of their own -- in the widget catalogue's toolbar the
// search box, the number beside it and the drop down after it stood at three
// different heights -- and a sheet that reshapes the text box alone widens
// that gap instead of closing it. So the box metrics are stated ONCE here and
// handed to each field below, and a field added to the library later joins
// the row by being named here rather than by having these numbers copied
// into it.
// Fields and buttons share the one 28 point row, bezel included.
let field_height = 28.0
let field_pad_v = 4.0
// Stock faces draw the corner doubled: 3.5 is a 7 point corner.
let field_radius = 3.5
// One device pixel; the faces written above draw their own edges.
let field_border = 0.34

// The room a Fit field takes. A minimum height rather than a height,
// because a line of text is shorter than a row, and the padding with it:
// where a field is Fit, the padding IS its height, and two fields padded
// differently part company again the moment the type grows.
let field_room = fn(w) {
    w.min_height = field_height
    w.padding.top = field_pad_v
    w.padding.bottom = field_pad_v
}
// The box a field draws. Given the draw object and not the widget, because
// not every field draws its own box, and because writing a corner onto a
// draw struct that has no corner would add a slot its shader never reads.
let field_face = fn(d) {
    d.border_radius = field_radius
    d.border_size = field_border
}
// A field that states a frame and lays its own parts out inside it: a number
// with a stepper, a date, a time. The height is all these take. A padding
// here would NOT hold the line off the box -- each of them measures its
// parts against the turtle's whole rect and draws them from the content
// origin, so the padding displaces the line instead of insetting it, and the
// number came out sitting on the bottom edge with its arrows split around it.
let field_frame = fn(w) {
    w.min_height = field_height
}

field_room(mod.widgets.TextInput)
field_face(mod.widgets.TextInput.draw_bg)
field_room(mod.widgets.ComboBox)
field_face(mod.widgets.ComboBox.draw_bg)
field_room(mod.widgets.DropDown)
field_face(mod.widgets.DropDown.draw_bg)
field_room(mod.widgets.DropDown2)
field_face(mod.widgets.DropDown2.draw_bg)
field_room(mod.widgets.FieldWell)
field_face(mod.widgets.FieldWell.draw_bg)
field_room(mod.widgets.TagField)
field_face(mod.widgets.TagField.draw_bg)
field_frame(mod.widgets.NumberField)
// The number's box strokes its own hairline and declares no border size.
mod.widgets.NumberField.draw_bg.border_radius = field_radius
// The drag-number's corner is written into its own shader, so it takes the
// room and keeps the box it draws.
field_frame(mod.widgets.ValueInput)
field_frame(mod.widgets.DateField)
field_frame(mod.widgets.TimeField)
// A picker is a date field in an anchor: the field inside fills the frame.
field_frame(mod.widgets.DatePicker)
field_frame(mod.widgets.DateRangePicker)
// The chrome-less input a well holds must impose no height of its own. It is
// a TextInput, so it inherits the minimum above, and a minimum as tall as the
// whole field, applied inside a well already that tall, pushed the line out
// through the bottom of the box.
mod.widgets.WellInput.min_height = 0.0

// ---------------------------------------------------------------- ground

// Plain views stop clipping so a slab's short shadow can fall past their
// edge; scroll views keep clipping their content.
mod.widgets.View.clip_x = false
mod.widgets.View.clip_y = false
mod.widgets.Window.pass.clear_color = #11161b
// The window's ground: blue-black #11161b, matte, a shade lighter toward
// the middle and darker at the corners, under a free grain (sd about
// 0.006, one value per device pixel: no lattice, nothing that repeats).
mod.widgets.Window.show_bg = true
mod.widgets.Window.draw_bg.pixel = fn() {
    let px = lm_px(self.draw_pass.dpi_factor)
    let p = self.pos * self.rect_size
    let sz = self.rect_size
    let q = (p - sz * 0.5) / max(sz * 0.62, vec2(1.0, 1.0))
    let v = smoothstep(0.0, 1.2, length(q))
    var col = mix(vec3(0.071, 0.09, 0.11), vec3(0.047, 0.062, 0.078), v)
    let g = Finish.grain(p / px, 0.016)
    return vec4(col + vec3(g, g, g), 1.0)
}

// ---------------------------------------------------------------- states

// Every held state is written as a plain value that cuts in at once (the
// library writes some as snap() values, which a state held as a default --
// the states page -- never applies). Live, the cut is the same as the snap.
mod.widgets.ButtonFlat.animator.hover.on.from = {all: Snap}
mod.widgets.ButtonFlat.animator.hover.on.apply = {draw_bg: {down: 0.0 hover: 1.0} draw_text: {down: 0.0 hover: 1.0}}
mod.widgets.ButtonFlat.animator.hover.down.from = {all: Snap}
mod.widgets.ButtonFlat.animator.hover.down.apply = {draw_bg: {down: 1.0 hover: 1.0} draw_text: {down: 1.0 hover: 1.0}}
mod.widgets.CheckBoxFlat.animator.hover.down.from = {all: Snap}
mod.widgets.CheckBoxFlat.animator.hover.down.apply = {draw_bg: {down: 1.0 hover: 1.0} draw_text: {down: 1.0 hover: 1.0}}
mod.widgets.RadioButtonFlat.animator.hover.down.from = {all: Snap}
mod.widgets.RadioButtonFlat.animator.hover.down.apply = {draw_bg: {down: 1.0 hover: 1.0} draw_text: {down: 1.0 hover: 1.0}}
mod.widgets.TextInputFlat.animator.hover.on.from = {all: Snap}
mod.widgets.TextInputFlat.animator.hover.on.apply = {draw_bg: {down: 0.0 hover: 1.0} draw_text: {down: 0.0 hover: 1.0}}
mod.widgets.TextInputFlat.animator.hover.down.from = {all: Snap}
mod.widgets.TextInputFlat.animator.hover.down.apply = {draw_bg: {down: 1.0 hover: 1.0} draw_text: {down: 1.0 hover: 1.0}}
mod.widgets.DropDownFlat.animator.hover.on.from = {all: Snap}
mod.widgets.DropDownFlat.animator.hover.on.apply = {draw_bg: {down: 0.0 hover: 1.0} draw_text: {down: 0.0 hover: 1.0}}
mod.widgets.DropDownFlat.animator.hover.down.from = {all: Snap}
mod.widgets.DropDownFlat.animator.hover.down.apply = {draw_bg: {down: 1.0 hover: 1.0} draw_text: {down: 1.0 hover: 1.0}}


// ---------------------------------------------------------------- band

// THE BAND is the sheet's own slider with two thumbs: the same track, the
// same lit value and the same thumb as the Slider, the value lit between
// the two thumbs. The widget's grab geometry is set to the thumbs' own, so
// what is drawn is what is dragged.
mod.widgets.RangeSliderFlat.clip_x = false
mod.widgets.RangeSliderFlat.clip_y = false
mod.widgets.RangeSliderFlat.track_inset = 0.0
mod.widgets.RangeSliderFlat.handle_size = 14.0
mod.widgets.RangeSliderFlat.draw_bg.vertex = fn() {
    let m = 5.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.RangeSliderFlat.draw_bg.pixel = fn() {
    let m = 5.0
    let px = lm_px(self.draw_pass.dpi_factor)
    let o = self.rect_pos
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let rad = 7.0
    let cy = lm_snap(self.label_px + (self.rect_size.y - self.label_px) * 0.5, o.y, px)
    let live = 1.0 - self.disabled
    var res = lm_groove(p, 0.0, self.rect_size.x, cy, o, px, 12.0, 9.333, self.disabled, self.hover)
    let wlo = vec2(lm_snap(0.0, o.x, px) + 1.333, cy - 4.667)
    let whi = vec2(lm_snap(self.rect_size.x, o.x, px) - 1.333, cy + 4.667)
    let span = self.rect_size.x - rad * 2.0
    let h0 = rad + self.start_pos * span
    let h1 = rad + self.end_pos * span
    res = lm_focus(res, p, vec2(lm_snap(0.0, o.x, px), cy - 6.0), vec2(lm_snap(self.rect_size.x, o.x, px), cy + 6.0), 6.0, px, self.focus * live)
    res = lm_tube(res, p, h0, h1, 2.667, px, self.disabled, max(max(self.hover, self.drag), self.focus), wlo, whi, 4.667, 0.0)
    res = lm_thumb(res, p, vec2(h0, cy), rad, px, self.hot_start, self.drag * self.hot_start, self.focus, self.disabled)
    return lm_thumb(res, p, vec2(h1, cy), rad, px, self.hot_end, self.drag * self.hot_end, self.focus, self.disabled) * lm_fade(self.pos, self.rect_size, m)
}

// ---------------------------------------------------------------- switches and meter

// THE SWITCHES are the sheet's own toggle, in proportion with the
// labels and the controls beside them: the rocker and the slide switch
// take the toggle's face, its size and shape, its quad and its label
// gap (the library's own faces for them are flat boxes sized for
// another face). The rocker turns on a click; the slide switch follows a
// drag, as the toggle does.
mod.widgets.ToggleRocker.draw_bg.size = uniform(18.0)
mod.widgets.ToggleSlide.draw_bg.size = uniform(18.0)
mod.widgets.ToggleRocker.draw_bg.pill_aspect = uniform(1.9)
mod.widgets.ToggleSlide.draw_bg.pill_aspect = uniform(1.9)
mod.widgets.ToggleRocker.draw_bg.knob_centred = uniform(1.0)
mod.widgets.ToggleSlide.draw_bg.knob_centred = uniform(1.0)
mod.widgets.ToggleRocker.draw_bg.knob_inset = uniform(3.5)
mod.widgets.ToggleSlide.draw_bg.knob_inset = uniform(3.5)
mod.widgets.ToggleRocker.label_walk.margin.left = 34.0
mod.widgets.ToggleSlide.label_walk.margin.left = 34.0
mod.widgets.ToggleRocker.draw_bg.pixel = mod.widgets.ToggleFlat.draw_bg.pixel
mod.widgets.ToggleSlide.draw_bg.pixel = mod.widgets.ToggleFlat.draw_bg.pixel

// THE METER sits in the same window as the readouts and the screen: the
// library's display housing drawn round its face -- the bezel ring, a shade
// of whatever ground it is set in with a device pixel of dark at its edge;
// the face with the surround's shadow falling across it from the top and a
// device pixel of black where the glass meets the bezel; the glass's quiet
// diagonal band and the light line inside its top edge; the lip of light on
// the ground under it -- with the same corner, so the meter and the
// readouts read as one family. The scale, the red zone, the needle and its
// pivot are the library's own.
mod.widgets.NeedleMeter.draw_bg.border_radius = uniform(theme.corner_radius * 0.5)
mod.widgets.NeedleMeter.draw_bg.color_bezel = uniform(theme.color_d_05)
mod.widgets.NeedleMeter.draw_bg.color_lip = uniform(theme.color_u_15)
mod.widgets.NeedleMeter.draw_bg.pixel = fn() {
    let p = self.pos * self.rect_size
    let px = 1.0 / max(self.draw_pass.dpi_factor, 0.5)
    let lo = vec2(Finish.snap(self.rect_pos.x, px), Finish.snap(self.rect_pos.y, px)) - self.rect_pos
    let hi = vec2(Finish.snap(self.rect_pos.x + self.rect_size.x, px), Finish.snap(self.rect_pos.y + self.rect_size.y, px) - px) - self.rect_pos
    let c = (lo + hi) * 0.5
    let ho = (hi - lo) * 0.5
    let r_out = min(self.border_radius, min(ho.x, ho.y))
    let outer = Material.sd_box(p, c, ho, r_out)
    let b = Finish.snap(2.0, px)
    let hf = max(ho - vec2(b, b), vec2(0.5, 0.5))
    let rf = max(r_out - b, 0.0)
    let face_d = Material.sd_box(p, c, hf, rf)
    let pv = self.pivot()
    let rr = self.scale_radius()
    let q = p - pv
    let r = length(q)
    let ang = atan2(q.x, 0.0 - q.y)
    let sweep = self.sweep * 0.017453293
    let t = ang / sweep + 0.5
    let on_scale = step(-0.0001, t) * step(t, 1.0001)
    var face = self.color.rgb
    // The scale: a hairline arc and a tick at every division.
    let arc = Finish.cover(abs(r - rr) - px * 0.5, px) * on_scale
    let n = max(floor(self.majors + 0.5), 1.0) * max(floor(self.minors + 0.5), 1.0)
    let k = floor(clamp(t, 0.0, 1.0) * n + 0.5)
    let ak = (k / n - 0.5) * sweep
    let perp = abs(q.x * cos(ak) + q.y * sin(ak))
    let mn = max(floor(self.minors + 0.5), 1.0)
    let major = 1.0 - step(0.5, k - mn * floor(k / mn + 0.0001))
    let len = mix(self.tick_minor, self.tick_major, major)
    let radial = max(rr - len - r, r - rr)
    let tick = Finish.cover(perp - px * mix(0.5, 1.0, major), px) * Finish.cover(radial, px) * step(0.0, 0.0 - q.y * cos(ak) + q.x * sin(ak))
    face = mix(face, self.color_scale.rgb, max(arc, tick))
    if self.zone < 0.999 {
        let zone_t = Finish.cover((self.zone - t) * sweep * r, px) * Finish.cover((t - 1.0) * sweep * r, px)
        let zone_r = Finish.cover(max(rr + px - r, r - rr - 2.5), px)
        face = mix(face, self.color_zone.rgb, zone_t * zone_r)
    }
    // The needle, from under the pivot cover to just past the scale.
    let na = self.needle_angle(self.value)
    let nd = vec2(sin(na), 0.0 - cos(na))
    let along = dot(q, nd)
    let across = abs(q.x * nd.y - q.y * nd.x)
    let needle = Finish.cover(across - px * 0.5, px) * Finish.cover(along - (rr + 3.0), px) * Finish.cover(0.0 - along - max(self.pivot_size - px, 0.0), px)
    face = mix(face, self.color_needle.rgb, needle)
    let pd = r - self.pivot_size
    face = mix(face, mix(self.color_needle.rgb, self.color.rgb, 0.35), Finish.cover(pd, px))
    face = mix(face, face * 0.55, Finish.band(pd, 0.0, px, px))
    // The housing: the surround's shadow across the face from the top, the
    // black device pixel at the glass's edge, and the glass over it all.
    let insh = Finish.inset(p, c, hf, rf, vec2(0.0, 2.0), 1.8)
    face = face * (1.0 - 0.55 * insh)
    face = mix(face, face * 0.4, Finish.band(face_d, 0.0, px, px))
    let u = (p - (c - hf)) / max(hf * 2.0, vec2(1.0, 1.0))
    let diag = u.x + u.y * 0.6
    let band = smoothstep(0.0, 0.12, diag) * (1.0 - smoothstep(0.28, 0.5, diag))
    let top = Finish.cover(abs(p.y - (c.y - hf.y) - px * 1.5) - px * 0.5, px) * 0.6
    let ga = clamp(0.03 * (band + top), 0.0, 1.0) * Finish.cover(face_d + px, px)
    face = face * (1.0 - ga) + vec3(ga, ga, ga)
    let bz = self.color_bezel
    var col = vec4(bz.rgb * bz.a, bz.a)
    col = Finish.over(col, vec4(0.0, 0.0, 0.0, 0.45 * Finish.band(outer, 0.0, px, px)))
    col = mix(col, vec4(face, 1.0), Finish.cover(face_d, px))
    col = col * Finish.cover(outer, px)
    let lip = Finish.ring_out(outer, 0.0, px, px) * step(hi.y, p.y)
    let la = self.color_lip.a * lip
    return Finish.over(vec4(self.color_lip.rgb * la, la), col) * self.color.a * self.opacity
}

// ---------------------------------------------------------------- lamps
// LAMPS: an LED, as the hardware in his pictures has them. The emitter is
// the light: at full current its middle burns toward white and its rim is
// its most saturated colour; at lower current the middle is no longer
// white, the colour deeper, the glow smaller; out, it is dark tinted glass,
// its colour barely there. Round it a bezel: a raised ring lit from the
// upper left, or a socket cut into the surface, its upper wall in shadow
// and a catch light on its lower rim. Over the lens one crisp highlight of
// a dome. Its light is added, never painted: a tight hot halo and a short
// bloom in its own hue, screened over whatever is there and gone in about
// two radii; on a pale ground, where light can barely brighten, its hue is
// also laid round it as a tint that keeps the ground's luminance (the
// library's halo rule: at most 0.45 one device pixel out, halving every
// 0.4 of its reach, gone at the reach), so it never darkens or greys its
// ground. A bar is the same light drawn out into a light pipe.
let lm_led_lamp_add = fn(res: vec4, light: vec3, ground: vec3) -> vec4 {
    let est = res.rgb + ground * (1.0 - res.a)
    let add = (vec3(1.0, 1.0, 1.0) - exp(-light)) * max(vec3(1.0, 1.0, 1.0) - est, vec3(0.0, 0.0, 0.0))
    return vec4(res.rgb + add, res.a)
}
// An LED's colour at full strength: its brightest channel at one.
let lm_led_lamp_full = fn(ink: vec3) -> vec3 {
    return ink / max(max(ink.x, max(ink.y, ink.z)), 0.01)
}
// The same colour at the emitter's own chroma: the hue kept and its
// saturation raised by `vivid` (0 leaves a pale colour pale; a colour with
// next to no hue, a white or a plain lamp, stays neutral either way).
let lm_led_lamp_hue = fn(ink: vec3, vivid: float) -> vec3 {
    let f = lm_led_lamp_full(ink)
    let mn = min(f.x, min(f.y, f.z))
    let ch = 1.0 - mn
    let pure = (f - vec3(mn, mn, mn)) / max(ch, 0.001)
    return mix(f, pure, clamp(vivid, 0.0, 1.0) * 0.72 * smoothstep(0.03, 0.12, ch))
}
// The lamp: its lens a rounded box `hb` either side of `c` (round when the
// two are equal), `lit` its current 0..1, `ink` its colour and `vivid` how
// far its chroma is raised, `ground` what shows through where nothing is
// drawn, `room` how far its light may reach, `bez` and `raised` its bezel
// (raised 0: a recess cut in what is under it; 1: a raised ring of `bez`;
// 2: the same ring polished metal). Premultiplied over `dst`.
let lm_led_lamp = fn(dst: vec4, p: vec2, c: vec2, hb: vec2, lit: float, ink: vec3, vivid: float, px: float, ground: vec3, room: float, bez: vec3, raised: float) -> vec4 {
    let rt = max(min(hb.x, hb.y), 0.4)
    let d = Material.sd_box(p, c, hb, rt)
    let bw = clamp(0.3 * rt, 0.7, 2.4)
    let ds = d - bw
    let L = clamp(lit, 0.0, 1.0)
    let b = lm_led_lamp_full(ink)
    let hue = lm_led_lamp_hue(ink, vivid)
    let pw = L * sqrt(L)
    let white = vec3(1.0, 1.0, 1.0)
    let lum = vec3(0.2126, 0.7152, 0.0722)
    let pale = smoothstep(0.35, 0.75, dot(ground, lum))
    var res = dst
    let x = max(ds, 0.0)
    let reach = max(room, 1.0)
    let win = 1.0 - smoothstep(0.55 * reach, reach, x)
    // The lens's own frame: `q` in lens radii from its centre line, `t` its
    // distance out, `nrm` the way its outline faces.
    let ex = max(hb.x - hb.y, 0.0)
    let ey = max(hb.y - hb.x, 0.0)
    let qx = p.x - c.x
    let qy = p.y - c.y
    let q = vec2(qx - clamp(qx, 0.0 - ex, ex), qy - clamp(qy, 0.0 - ey, ey)) / rt
    let t = clamp(length(q), 0.0, 1.0)
    let nrm = q / max(length(q), 0.001)
    // What the bead and its bezel throw on the ground: a soft shadow, down.
    let shd = Finish.drop(p, c, hb + vec2(bw, bw), rt + bw, vec2(0.0, 0.22 * rt + 0.3), 0.32 * rt + px) * mix(0.18, 0.34, min(raised, 1.0)) * (1.0 - 0.6 * pw)
    res = Finish.over(res, vec4(ground * 0.4 * shd, shd))
    if L > 0.001 && pale > 0.001 {
        // The tint, on a pale ground only: its hue laid over, never darker.
        let h = clamp(0.42 * pw * pow(2.0, -x / max(0.4 * reach, 0.5)) * win, 0.0, 0.45) * pale
        let est = res.rgb + ground * (1.0 - res.a)
        let w = clamp(dot(hue, lum) / max(dot(est, lum), 0.001), 0.0, 1.0)
        res = Finish.over(res, vec4(hue * h * w, h * w))
    }
    // The bezel: raised, a ring of `bez` rounded over, lit from the upper
    // left; or a socket cut into what is under it, its upper wall in shadow
    // and a catch light on its lower rim.
    let a_s = Finish.cover(ds, px)
    let u = clamp(d / max(bw, 0.01), 0.0, 1.0)
    let facing = dot(nrm * (u - 0.5) * 2.0, vec2(-0.45, -0.89))
    let metal = clamp(raised - 1.0, 0.0, 1.0)
    var rc = bez * (0.94 + mix(0.12, 0.55, metal) * facing)
    rc = mix(rc, min(bez + vec3(0.30, 0.30, 0.30), white), smoothstep(mix(0.35, 0.55, metal), 0.9, facing) * mix(0.6, 0.85, metal))
    rc = mix(rc, rc * 0.8, Finish.band(ds, 0.0, max(px, 0.45), px) * smoothstep(0.0, 0.8, nrm.y) * 0.8)
    let under = res.rgb / max(res.a, 0.001) * step(0.001, res.a) + ground * (1.0 - step(0.001, res.a))
    let gy = clamp(nrm.y * t, -1.0, 1.0)
    var sc = under * mix(0.55, 0.92, smoothstep(-0.9, 0.9, gy))
    sc = mix(sc, min(under * 1.06 + vec3(0.28, 0.28, 0.28), white), Finish.band(ds, 0.0, max(px, 0.45), px) * smoothstep(0.2, 0.95, nrm.y) * 0.85)
    sc = min(mix(sc, rc, min(raised, 1.0)), white)
    res = Finish.over(res, vec4(sc * a_s, a_s))
    // The light: a tight hot halo and a short bloom in its hue, gone in
    // about two radii, falling on the bezel too.
    if L > 0.001 {
        let xl = max(d, 0.0)
        let halo = exp(-xl / max(0.30 * rt, 0.4)) * 1.5 + exp(-xl / max(0.65 * rt, 0.7)) * 0.32
        let hwin = 1.0 - smoothstep(1.1 * rt, 2.0 * rt + 1.0, xl)
        res = lm_led_lamp_add(res, mix(hue, white, 0.15 * pw) * halo * pw * hwin * win, ground)
    }
    // THE BEAD: a glossy dome of coloured glass. Its colour deepens toward
    // the top; light pools low inside, where it comes through the dome; lit,
    // its middle burns toward white at full current and its rim is its most
    // saturated colour.
    let top = smoothstep(-1.0, 0.6, q.y)
    let pool = exp(-(q.y - 0.55) * (q.y - 0.55) / 0.09 - q.x * q.x / 0.30)
    var on = mix(hue * mix(0.55, 0.8, L), mix(b, hue, 0.5), top)
    on = mix(on, min(mix(b, hue, 0.4) + vec3(0.35, 0.35, 0.35), white), pool * 0.5)
    on = mix(on, vec3(1.0, 0.99, 0.975), exp(-t * t / 0.20) * smoothstep(0.5, 1.0, L) * 0.85)
    on = mix(on, hue * (0.82 + 0.18 * L), smoothstep(0.62, 1.0, t))
    on = on * (0.42 + 0.58 * L)
    // Out: dark tinted glass on a dark ground, a grey bead on a pale one,
    // its colour barely there, the same dome, a catch light along its lower
    // rim.
    let offc = mix(mix(vec3(0.085, 0.09, 0.115), ground * 0.62, pale), b * 0.4, 0.12)
    var off = mix(offc * 0.62, offc * 1.08, top)
    off = mix(off, min(offc + vec3(0.18, 0.18, 0.18), white), pool * 0.35)
    off = off * mix(1.0, 0.75, smoothstep(0.75, 1.0, t))
    let catchl = smoothstep(0.62, 0.9, t) * (1.0 - smoothstep(0.9, 1.0, t)) * smoothstep(0.2, 0.9, nrm.y)
    off = off + vec3(0.30, 0.30, 0.32) * catchl * (1.0 - 0.5 * pale)
    var col = mix(off, min(on, white), smoothstep(0.0, 0.35, L))
    // One crisp highlight: a white oval across its upper third.
    let e = length(vec2(q.x / 0.62, (q.y + 0.46) / 0.30))
    let spec = (1.0 - smoothstep(0.55, 1.0, e)) * mix(1.0, 0.3, clamp((q.y + 0.76) / 0.6, 0.0, 1.0))
    col = mix(col, white, spec * mix(0.8, 0.55, L) * smoothstep(0.9, 2.2, rt))
    // Out, a faint seam where the dome meets its bezel; lit, none: the rim
    // is the colour.
    col = mix(col, col * 0.7, Finish.band(d, 0.0, px * 0.6, px) * 0.6 * (1.0 - smoothstep(0.0, 0.25, L)))
    col = min(col, white)
    let a_l = Finish.cover(d, px)
    return Finish.over(res, vec4(col * a_l, a_l))
}

// The Lamp widget and the bar lamp: the lamp above, here in a dark ring with its own soft shadow.
// The halo's room is held in the lamp's own box (the library reserves a
// lens thickness either side once a halo is asked for), so the light is
// never cut at its edge.
mod.widgets.Lamp.halo = 0.3
mod.widgets.Lamp.halo_reach = 1.0
mod.widgets.Lamp.draw_bg.vertex = fn() {
    let m = 2.0
    self.vertex_pos = self.clip_and_transform_vertex(self.rect_pos - vec2(m, m), self.rect_size + vec2(2.0 * m, 2.0 * m))
}
mod.widgets.Lamp.draw_bg.pixel = fn() {
    let m = 2.0
    let p = self.pos * (self.rect_size + vec2(2.0 * m, 2.0 * m)) - vec2(m, m)
    let px = 1.0 / max(self.draw_pass.dpi_factor, 0.5)
    let reach = clamp(self.reach, 0.0, 1.0)
    let t = self.rect_size.y / (1.0 + 2.0 * reach)
    let room = t * reach
    let c = self.rect_size * 0.5
    let half_len = max((self.rect_size.x - 2.0 * room) * 0.5, t * 0.5)
    // The lens is the lamp's size; its socket stands round it in the room.
    let hb = vec2(mix(t * 0.5, half_len, self.bar), t * 0.5)
    let res = lm_led_lamp(vec4(0.0, 0.0, 0.0, 0.0), p, c, hb, self.lit, self.intent_color().rgb, 1.0 - step(3.5, self.intent), px, vec3(0.067, 0.086, 0.106), max(room - 0.5, 2.0), vec3(0.22, 0.235, 0.26), 1.0)
    return res * self.opacity
}
true