struct RU {
  mvp: mat4x4f,
  nx: u32,
  ny: u32,
  hx: f32,
  hy: f32,
  wScale: f32,     // vertical exaggeration in the 3D view
  colorRange: f32, // |w| mapped to full color [m]
  aspect: f32,     // canvas width / height
  mode: u32,       // 0: 2D, 1: 3D
  strikeX: f32,
  strikeY: f32,
  strikeR: f32,
  mountX: f32,
  mountY: f32,
  mountR: f32,
  lightX: f32,
  lightY: f32,
  lightZ: f32,
  showShape: u32,  // add the stress-free initial shape to the displayed field (both views)
  colorMode: u32,  // 0: color by the displayed field, 1: color by the thickness
  mountOn: u32,    // draw the mount marker
  hMin: f32,       // thickness range for colorMode 1 [m]
  hMax: f32,
  listenerX: f32,  // unit direction of the listener from the plate center
  listenerY: f32,
  listenerZ: f32,
  listenerAt: f32,  // distance from the plate center at which it is drawn [m]
  listenerRadius: f32, // widest radius of the microphone [m]
  listenerOn: u32,
};

@group(0) @binding(0) var<uniform> R: RU;
@group(0) @binding(1) var<storage, read> w: array<f32>;
@group(0) @binding(2) var<storage, read> w0: array<f32>;
@group(0) @binding(3) var<storage, read> nw: array<f32>; // node weights, 0 outside the plate
@group(0) @binding(4) var<storage, read> hn: array<f32>; // thickness per node
@group(0) @binding(5) var<storage, read> cm: array<f32>; // cell membership, (nx - 1) * (ny - 1)

const BG = vec3f(0.11, 0.12, 0.14);

// Diverging map for the displacement: blue, light gray, red.
fn colormap(t: f32) -> vec3f {
  let s = clamp(t, -1.0, 1.0);
  let mid = vec3f(0.93, 0.93, 0.93);
  let blue = vec3f(0.10, 0.35, 0.85);
  let red = vec3f(0.85, 0.20, 0.12);
  if (s < 0.0) { return mix(mid, blue, -s); }
  return mix(mid, red, s);
}
// Sequential map for the thickness: dark teal through green to pale yellow.
fn thickmap(t: f32) -> vec3f {
  let s = clamp(t, 0.0, 1.0);
  let a = vec3f(0.13, 0.22, 0.40);
  let b = vec3f(0.20, 0.60, 0.55);
  let c = vec3f(0.98, 0.93, 0.55);
  if (s < 0.5) { return mix(a, b, 2.0 * s); }
  return mix(b, c, 2.0 * s - 1.0);
}

fn idx(i: i32, j: i32) -> u32 {
  let ii = clamp(i, 0, i32(R.nx) - 1);
  let jj = clamp(j, 0, i32(R.ny) - 1);
  return u32(jj) * R.nx + u32(ii);
}
// Displayed field: the deviation w, plus the initial shape when requested (the total shape).
fn wAt(i: i32, j: i32) -> f32 {
  let k = idx(i, j);
  var z = w[k];
  if (R.showShape != 0u) { z += w0[k]; }
  return z;
}
fn hAt(i: i32, j: i32) -> f32 { return hn[idx(i, j)]; }
fn nwAt(i: i32, j: i32) -> f32 {
  if (i < 0 || i >= i32(R.nx) || j < 0 || j >= i32(R.ny)) { return 0.0; }
  return nw[u32(j) * R.nx + u32(i)];
}
fn cellAt(ci: i32, cj: i32) -> f32 {
  if (ci < 0 || ci >= i32(R.nx) - 1 || cj < 0 || cj >= i32(R.ny) - 1) { return 0.0; }
  return cm[u32(cj) * (R.nx - 1u) + u32(ci)];
}
// Color of a node from the displayed field value and the thickness.
fn colorOf(val: f32, h: f32) -> vec3f {
  if (R.colorMode == 1u) { return thickmap((h - R.hMin) / max(R.hMax - R.hMin, 1e-9)); }
  return colormap(val / R.colorRange);
}
// Height used by the 3D view: the same field as the color.
fn zAt(i: i32, j: i32) -> f32 { return wAt(i, j); }
// Surface markers, painted on the plate in both views at the point p of the
// plate (meters from the center): the mount as a dark ring at its radius, the
// strike point as a yellow ring a little outside the tip.
fn markerColor(p: vec2f, col: vec3f) -> vec3f {
  var c = col;
  if (R.mountOn != 0u) {
    let dm = distance(p, vec2f(R.mountX, R.mountY));
    if (abs(dm - R.mountR) < 0.12 * R.mountR + 0.0015) { c = vec3f(0.1, 0.1, 0.1); }
  }
  let ds = distance(p, vec2f(R.strikeX, R.strikeY));
  if (abs(ds - R.strikeR * 1.6) < 0.25 * R.strikeR) { c = vec3f(0.95, 0.75, 0.1); }
  return c;
}
// Slope along one axis, one-sided where a neighbor lies outside the plate.
fn slope(i: i32, j: i32, di: i32, dj: i32, h: f32) -> f32 {
  let hasP = nwAt(i + di, j + dj) > 0.0;
  let hasM = nwAt(i - di, j - dj) > 0.0;
  if (hasP && hasM) { return (zAt(i + di, j + dj) - zAt(i - di, j - dj)) / (2.0 * h); }
  if (hasP) { return (zAt(i + di, j + dj) - zAt(i, j)) / h; }
  if (hasM) { return (zAt(i, j) - zAt(i - di, j - dj)) / h; }
  return 0.0;
}

// ---------- 2D view: full-screen triangle, bilinear lookup in the fragment shader ----------

struct V2 { @builtin(position) pos: vec4f, @location(0) uv: vec2f };

@vertex
fn vs2d(@builtin(vertex_index) vi: u32) -> V2 {
  var p = array<vec2f, 3>(vec2f(-1.0, -1.0), vec2f(3.0, -1.0), vec2f(-1.0, 3.0));
  var o: V2;
  o.pos = vec4f(p[vi], 0.0, 1.0);
  o.uv = p[vi];
  return o;
}

@fragment
fn fs2d(in: V2) -> @location(0) vec4f {
  let Lx = f32(R.nx - 1u) * R.hx;
  let Ly = f32(R.ny - 1u) * R.hy;
  // Fit the plate into the canvas with a margin, preserving its aspect ratio.
  let margin = 0.92;
  var sx = margin; var sy = margin;
  let plateAspect = Lx / Ly;
  if (plateAspect > R.aspect) { sy = margin * R.aspect / plateAspect; } else { sx = margin * plateAspect / R.aspect; }
  let px = in.uv.x / sx * 0.5 * Lx;
  let py = in.uv.y / sy * 0.5 * Ly;
  let bg = vec4f(BG, 1.0);
  if (abs(px) > 0.5 * Lx || abs(py) > 0.5 * Ly) { return bg; }
  let fi = (px + 0.5 * Lx) / R.hx;
  let fj = (py + 0.5 * Ly) / R.hy;
  let i0 = min(i32(floor(fi)), i32(R.nx) - 2); let j0 = min(i32(floor(fj)), i32(R.ny) - 2);
  // Only the cells of the plate are drawn (staircase edge, hole included).
  if (cellAt(i0, j0) == 0.0) { return bg; }
  let a = fi - f32(i0); let b = fj - f32(j0);
  let c = vec4f((1.0 - a) * (1.0 - b), a * (1.0 - b), (1.0 - a) * b, a * b);
  let val = dot(c, vec4f(wAt(i0, j0), wAt(i0 + 1, j0), wAt(i0, j0 + 1), wAt(i0 + 1, j0 + 1)));
  let h = dot(c, vec4f(hAt(i0, j0), hAt(i0 + 1, j0), hAt(i0, j0 + 1), hAt(i0 + 1, j0 + 1)));
  let col = markerColor(vec2f(px, py), colorOf(val, h));
  return vec4f(col, 1.0);
}

// ---------- 3D view: height field ----------

struct V3 { @builtin(position) pos: vec4f, @location(0) color: vec3f, @location(1) normal: vec3f, @location(2) xy: vec2f };

/**
 * The plate's frame placed in the world: x and y run along the bounding box
 * and h along the plate's normal, and the world has the normal pointing up, so
 * that a cymbal lies flat the way it sits on a stand rather than standing on
 * edge like a hanging sheet. The map is linear, so it carries vectors (the
 * normals, the axis of the microphone) as well as points.
 */
fn world(x: f32, y: f32, h: f32) -> vec3f { return vec3f(x, h, -y); }

@vertex
fn vs3d(@builtin(vertex_index) vi: u32) -> V3 {
  let i = i32(vi % R.nx); let j = i32(vi / R.nx);
  let x = (f32(i) - 0.5 * f32(R.nx - 1u)) * R.hx;
  let y = (f32(j) - 0.5 * f32(R.ny - 1u)) * R.hy;
  let val = wAt(i, j);
  let z = zAt(i, j) * R.wScale;
  let dzdx = slope(i, j, 1, 0, R.hx) * R.wScale;
  let dzdy = slope(i, j, 0, 1, R.hy) * R.wScale;
  var o: V3;
  o.pos = R.mvp * vec4f(world(x, y, z), 1.0);
  o.color = colorOf(val, hAt(i, j));
  o.normal = world(-dzdx, -dzdy, 1.0);
  o.xy = vec2f(x, y);
  return o;
}

fn shade(col: vec3f, normal: vec3f) -> vec3f {
  let l = normalize(vec3f(R.lightX, R.lightY, R.lightZ));
  let diff = abs(dot(normalize(normal), l));
  return col * (0.35 + 0.65 * diff) + vec3f(0.15) * pow(diff, 24.0);
}

@fragment
fn fs3d(in: V3) -> @location(0) vec4f {
  // The markers are painted into the surface color, so the light falls on them
  // as it does on the plate and they read as part of the shape.
  return vec4f(shade(markerColor(in.xy, in.color), in.normal), 1.0);
}

// ---------- 3D view: the mount, as a post through the plate ----------
//
// A small cylinder standing at the mount center, rising a little above the
// plate and reaching further below it, in the manner of the rod and felt of a
// stand. It is narrower than the mount radius, so it does not cover the ring
// the surface shader paints there, and it shows through the center hole from
// above, where the ring alone can be hard to place on a steep bell. Its size
// is a fixed fraction of the mount radius and means nothing physically; the
// mount itself is a spring and a dashpot spread over the nodes inside the ring.

const MOUNT_SEG: u32 = 24u;
const MOUNT_CAP: u32 = MOUNT_SEG * 3u;
const MOUNT_SIDE: u32 = MOUNT_SEG * 6u;
/** Vertices of the post: the sides, then a fan over each cap. */
const MOUNT_VERTS: u32 = MOUNT_SIDE + 2u * MOUNT_CAP;
const TAU: f32 = 6.28318530718;

/**
 * The height of the displayed surface over the mount, as the weighted mean of
 * the plate nodes inside the mount radius. A mean rather than the value at the
 * center, since on a cymbal with a center hole the mount center lies in the
 * hole, where there is no plate to read.
 */
fn mountTop() -> f32 {
  let ci = R.mountX / R.hx + 0.5 * f32(R.nx - 1u);
  let cj = R.mountY / R.hy + 0.5 * f32(R.ny - 1u);
  let ri = i32(ceil(R.mountR / R.hx)) + 1;
  let rj = i32(ceil(R.mountR / R.hy)) + 1;
  var sum = 0.0;
  var wgt = 0.0;
  for (var j = i32(round(cj)) - rj; j <= i32(round(cj)) + rj; j = j + 1) {
    for (var i = i32(round(ci)) - ri; i <= i32(round(ci)) + ri; i = i + 1) {
      let m = nwAt(i, j);
      if (m <= 0.0) { continue; }
      let dx = (f32(i) - 0.5 * f32(R.nx - 1u)) * R.hx - R.mountX;
      let dy = (f32(j) - 0.5 * f32(R.ny - 1u)) * R.hy - R.mountY;
      if (dx * dx + dy * dy > R.mountR * R.mountR) { continue; }
      sum = sum + m * zAt(i, j);
      wgt = wgt + m;
    }
  }
  if (wgt <= 0.0) { return 0.0; }
  return sum / wgt * R.wScale;
}

@vertex
fn vs3dMount(@builtin(vertex_index) vi: u32) -> V3 {
  let surf = mountTop();
  let hi = surf + 0.6 * R.mountR;
  let lo = surf - 1.4 * R.mountR;
  let rad = 0.45 * R.mountR;
  var ang = 0.0;
  var rr = rad;
  var z = lo;
  var normal = vec3f(0.0, 0.0, -1.0);
  if (vi < MOUNT_SIDE) {
    let seg = vi / 6u;
    let k = vi % 6u;
    // Two triangles per segment: (hi a0, lo a0, lo a1), (hi a0, lo a1, hi a1).
    var firstEdge = array<bool, 6>(true, true, false, true, false, false);
    var atTop = array<bool, 6>(true, false, false, true, false, true);
    let a0 = TAU * f32(seg) / f32(MOUNT_SEG);
    let a1 = TAU * f32(seg + 1u) / f32(MOUNT_SEG);
    ang = select(a1, a0, firstEdge[k]);
    z = select(lo, hi, atTop[k]);
    normal = vec3f(cos(ang), sin(ang), 0.0);
  } else {
    let m = vi - MOUNT_SIDE;
    let top = m >= MOUNT_CAP;
    let n = m % MOUNT_CAP;
    let seg = n / 3u;
    let k = n % 3u;
    let a0 = TAU * f32(seg) / f32(MOUNT_SEG);
    let a1 = TAU * f32(seg + 1u) / f32(MOUNT_SEG);
    ang = select(a0, a1, k == 2u);
    rr = select(rad, 0.0, k == 0u);   // the fan's hub
    z = select(lo, hi, top);
    normal = vec3f(0.0, 0.0, select(-1.0, 1.0, top));
  }
  let x = R.mountX + rr * cos(ang);
  let y = R.mountY + rr * sin(ang);
  var o: V3;
  o.pos = R.mvp * vec4f(world(x, y, z), 1.0);
  o.color = vec3f(0.42, 0.39, 0.36);
  o.normal = world(normal.x, normal.y, normal.z);
  o.xy = vec2f(x, y);
  return o;
}

@fragment
fn fs3dMount(in: V3) -> @location(0) vec4f {
  return vec4f(shade(in.color, in.normal), 1.0);
}

// ---------- 3D view: the listener, as a microphone ----------
//
// A microphone standing on the line from the center of the plate to the
// listener, its grille facing the plate. It is a surface of revolution about
// that line, drawn as a stack of bands from a profile of radius and color.
//
// The microphone is drawn at a fixed size, and nearer than the listener really
// is: a listener a meter from a 16 inch cymbal cannot share a framing with it,
// so the drawn distance follows the true one through a saturating map (see
// drawnListenerDistance in renderer.ts). It therefore shows the direction
// faithfully and the distance only in the sense of moving out as the listener
// recedes; the distance that enters the sound is the field in the Listener
// group, through the 1/r spreading and the spread of the propagation delays.

const MIC_SEG: u32 = 16u;    // segments around the axis
const MIC_BANDS: u32 = 24u;  // bands along it
const MIC_SIDE: u32 = MIC_SEG * MIC_BANDS * 6u;
/** Vertices of the microphone: the surface of revolution, then a fan closing its back. */
const MIC_VERTS: u32 = MIC_SIDE + MIC_SEG * 3u;
const TAU_MIC: f32 = 6.28318530718;
/** Length of the body as a multiple of its widest radius. */
const MIC_ASPECT: f32 = 4.2;

/** Radius at t along the microphone, t = 0 at the nose facing the plate and 1 at the back, in fractions of its widest radius. */
fn micRadius(t: f32) -> f32 {
  if (t < 0.18) {
    let q = (0.18 - t) / 0.18;
    return 0.95 * sqrt(max(0.0, 1.0 - q * q));   // the rounded grille
  }
  if (t < 0.52) { return 0.95; }                 // the grille
  if (t < 0.60) { return 1.0; }                  // the collar behind it
  return 0.80;                                   // the body
}

fn micColor(t: f32) -> vec3f {
  if (t < 0.52) { return vec3f(0.15, 0.16, 0.18); }
  if (t < 0.60) { return vec3f(0.52, 0.52, 0.54); }
  return vec3f(0.62, 0.64, 0.67);
}

/** Any right-handed frame whose third axis is u. */
fn frameOf(u: vec3f) -> mat3x3f {
  var t = vec3f(0.0, 0.0, 1.0);
  if (abs(u.z) > 0.9) { t = vec3f(1.0, 0.0, 0.0); }
  let a = normalize(cross(t, u));
  return mat3x3f(a, cross(u, a), u);
}

@vertex
fn vs3dListener(@builtin(vertex_index) vi: u32) -> V3 {
  let u = normalize(vec3f(R.listenerX, R.listenerY, R.listenerZ));
  let F = frameOf(u);
  let rad = R.listenerRadius;
  let len = MIC_ASPECT * rad;
  var t = 1.0;
  var ang = 0.0;
  var rr = 0.0;
  if (vi < MIC_SIDE) {
    let band = (vi / 6u) / MIC_SEG;
    let seg = (vi / 6u) % MIC_SEG;
    let k = vi % 6u;
    var firstEdge = array<bool, 6>(true, true, false, true, false, false);
    var atBack = array<bool, 6>(true, false, false, true, false, true);
    let a0 = TAU_MIC * f32(seg) / f32(MIC_SEG);
    let a1 = TAU_MIC * f32(seg + 1u) / f32(MIC_SEG);
    ang = select(a1, a0, firstEdge[k]);
    let t0 = f32(band) / f32(MIC_BANDS);
    let t1 = f32(band + 1u) / f32(MIC_BANDS);
    t = select(t0, t1, atBack[k]);
    rr = micRadius(t);
  } else {
    // The disc closing the back.
    let n = vi - MIC_SIDE;
    let seg = n / 3u;
    let k = n % 3u;
    let a0 = TAU_MIC * f32(seg) / f32(MIC_SEG);
    let a1 = TAU_MIC * f32(seg + 1u) / f32(MIC_SEG);
    ang = select(a0, a1, k == 2u);
    rr = select(micRadius(1.0), 0.0, k == 0u);
  }
  // The nose sits at the drawn distance; the body extends away from the plate.
  let p = F * vec3f(rad * rr * cos(ang), rad * rr * sin(ang), R.listenerAt + len * t);
  // Normal of a surface of revolution: perpendicular to the slope of the profile.
  let eps = 0.5 / f32(MIC_BANDS);
  let slope = (micRadius(min(1.0, t + eps)) - micRadius(max(0.0, t - eps))) / (2.0 * eps) / MIC_ASPECT;
  var normal = normalize(vec3f(cos(ang), sin(ang), -slope));
  if (vi >= MIC_SIDE) { normal = vec3f(0.0, 0.0, 1.0); }
  let n = F * normal;
  var o: V3;
  o.pos = R.mvp * vec4f(world(p.x, p.y, p.z), 1.0);
  o.color = micColor(t);
  o.normal = world(n.x, n.y, n.z);
  o.xy = p.xy;
  return o;
}

@fragment
fn fs3dListener(in: V3) -> @location(0) vec4f {
  return vec4f(shade(in.color, in.normal), 1.0);
}