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
  holeX: f32,
  holeY: f32,
  pushX: f32,
  pushY: f32,
  markerR: f32,
  lightX: f32,
  lightY: f32,
  lightZ: f32,
  showShape: u32,  // add the stress-free initial shape to the displayed field (both views)
  shape: u32,      // 0: rectangle, 1: ellipse inscribed in the bounding box
  pad1: u32,
  pad2: 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 sheet

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);
}

// Displayed field: the deviation w, plus the initial shape when requested (the total shape).
fn wAt(i: i32, j: i32) -> f32 {
  let ii = clamp(i, 0, i32(R.nx) - 1);
  let jj = clamp(j, 0, i32(R.ny) - 1);
  var z = w[u32(jj) * R.nx + u32(ii)];
  if (R.showShape != 0u) { z += w0[u32(jj) * R.nx + u32(ii)]; }
  return z;
}
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)];
}
// Height used by the 3D view: the same field as the color.
fn zAt(i: i32, j: i32) -> f32 { return wAt(i, j); }
// Slope along one axis, one-sided where a neighbor lies outside the sheet.
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(0.11, 0.12, 0.14, 1.0);
  if (abs(px) > 0.5 * Lx || abs(py) > 0.5 * Ly) { return bg; }
  if (R.shape == 1u) {
    let ex = px / (0.5 * Lx); let ey = py / (0.5 * Ly);
    if (ex * ex + ey * ey > 1.0) { return bg; }
  }
  let fi = (px + 0.5 * Lx) / R.hx;
  let fj = (py + 0.5 * Ly) / R.hy;
  let i0 = i32(floor(fi)); let j0 = i32(floor(fj));
  let a = fi - f32(i0); let b = fj - f32(j0);
  // Bilinear interpolation over the nodes of the sheet only (outside nodes carry no value).
  let c = vec4f((1.0 - a) * (1.0 - b), a * (1.0 - b), (1.0 - a) * b, a * b);
  let m = vec4f(nwAt(i0, j0), nwAt(i0 + 1, j0), nwAt(i0, j0 + 1), nwAt(i0 + 1, j0 + 1));
  let wgt = c * step(vec4f(1e-6), m);
  let den = wgt.x + wgt.y + wgt.z + wgt.w;
  if (den <= 0.0) { return bg; }
  let val = dot(wgt, vec4f(wAt(i0, j0), wAt(i0 + 1, j0), wAt(i0, j0 + 1), wAt(i0 + 1, j0 + 1))) / den;
  var col = colormap(val / R.colorRange);
  // Markers: hole (ring) and pushed patch (dashed-looking ring).
  let dh = distance(vec2f(px, py), vec2f(R.holeX, R.holeY));
  if (abs(dh - R.markerR) < 0.35 * R.markerR) { col = vec3f(0.1, 0.1, 0.1); }
  if (dh < 0.4 * R.markerR) { col = vec3f(0.11, 0.12, 0.14); }
  let dp = distance(vec2f(px, py), vec2f(R.pushX, R.pushY));
  if (abs(dp - R.markerR * 1.6) < 0.25 * R.markerR) { col = vec3f(0.95, 0.75, 0.1); }
  return vec4f(col, 1.0);
}

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

struct V3 { @builtin(position) pos: vec4f, @location(0) val: f32, @location(1) normal: vec3f };

@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(x, y, z, 1.0);
  o.val = val;
  o.normal = normalize(vec3f(-dzdx, -dzdy, 1.0));
  return o;
}

@fragment
fn fs3d(in: V3) -> @location(0) vec4f {
  let l = normalize(vec3f(R.lightX, R.lightY, R.lightZ));
  let n = normalize(in.normal);
  let diff = abs(dot(n, l));
  let base = colormap(in.val / R.colorRange);
  let col = base * (0.35 + 0.65 * diff) + vec3f(0.15) * pow(diff, 24.0);
  return vec4f(col, 1.0);
}