// Simulation parameters (strike, listener, numerics), the grid with its mask,
// the plate as evaluated on the grid (material, thickness field, stress-free
// shape, stand, losses), and the derived quantities both solvers need. All
// values are SI. The design itself is produced by the script in design.ts.

export interface SimParams {
  // Strike
  strikeFracX: number; // strike point as a fraction of the bounding-box width from the left edge
  strikeFracY: number; // strike point as a fraction of the bounding-box height from the bottom edge
  strikeVelocity: number; // stick tip speed at impact [m/s]
  stickMass: number; // effective mass of the stick [kg]
  contactStiffness: number; // Hertz contact stiffness K [N/m^alpha]
  contactExponent: number; // Hertz exponent alpha (1.5 for a rounded tip)
  contactRadius: number; // radius of the contact patch [m]
  // Listener
  listenerDist: number; // [m]
  listenerAngle: number; // [deg] angle from the plate's normal (0 = straight above the plate)
  listenerAzimuth: number; // [deg] rotation about the normal (0 = toward +x)
  // Numerics and output
  spacing: number; // requested grid spacing [m]
  modeMaxFreq: number; // modes up to this frequency are kept in the linear model [Hz]
  padLiftoff: boolean; // full simulation: the pads push only while compressed
  fs: number; // audio sample rate [Hz]
  fps: number; // movie frame rate, also the batch rate of the full simulation [Hz]
  duration: number; // recorded duration after the impact [s]
}

export const defaultParams: SimParams = {
  strikeFracX: 0.9,
  strikeFracY: 0.5,
  strikeVelocity: 6,
  stickMass: 0.03,
  contactStiffness: 5e8,
  contactExponent: 1.5,
  contactRadius: 5e-3,
  listenerDist: 0.5,
  listenerAngle: 30,
  listenerAzimuth: 0,
  spacing: 0.008,
  modeMaxFreq: 16000,
  padLiftoff: true,
  fs: 48000,
  fps: 120,
  duration: 4,
};

export const SPEED_OF_SOUND = 343; // [m/s]
export const RHO_AIR = 1.2; // [kg/m^3]
export const GRAVITY = 9.81; // [m/s^2]
export const CFL = 0.9; // fraction of the stability limit used for the time step of the full simulation
export const HIST_MARGIN = 128; // ring buffer margin of the retarded-time listener sum [samples]
export const STICK_RELEASE = 5e-3; // the stick is withdrawn once the contact has been open this long [s]
export const PAD_POISSON = 0.3; // Poisson ratio of the felt, which sets its shear stiffness from E

// ---------- Grid ----------

export interface Grid {
  nx: number;
  ny: number;
  hx: number;
  hy: number;
  n: number;
  /** 1 for nodes that belong to the plate, 0 otherwise; absent for a full rectangle. */
  mask?: Uint8Array;
}

/** True when the point (x, y), relative to the center of the bounding box, lies in the plate. */
export type InsideFn = (x: number, y: number) => boolean;

/** The grid covering the bounding box Lx by Ly with about the requested spacing, restricted to the outline when one is given. */
export function makeGrid(Lx: number, Ly: number, spacing: number, inside?: InsideFn): Grid {
  const nx = Math.max(6, Math.round(Lx / spacing) + 1);
  const ny = Math.max(6, Math.round(Ly / spacing) + 1);
  const g: Grid = { nx, ny, hx: Lx / (nx - 1), hy: Ly / (ny - 1), n: nx * ny };
  return inside ? withMask(g, inside) : g;
}

/**
 * Restricts a grid to an outline. The edge is a staircase of whole cells: a
 * cell belongs to the plate when its center lies inside the outline, and a
 * node when it is a corner of such a cell. Deciding by cell centers keeps
 * the covered area unbiased. A node left with no cell of its own would carry
 * no mass, and the trailing loop removes any such node. A hole is handled by
 * the same rule.
 */
export function withMask(g: Grid, inside: InsideFn): Grid {
  return withCellMask(g, (ci, cj) => inside(nodeX(g, ci) + g.hx / 2, nodeY(g, cj) + g.hy / 2));
}

/** The same restriction with the membership of each cell (ci, cj) given directly. */
export function withCellMask(g: Grid, cellInside: (ci: number, cj: number) => boolean): Grid {
  const mask = new Uint8Array(g.n);
  for (let cj = 0; cj < g.ny - 1; cj++) {
    for (let ci = 0; ci < g.nx - 1; ci++) {
      if (cellInside(ci, cj)) {
        mask[cj * g.nx + ci] = 1; mask[cj * g.nx + ci + 1] = 1;
        mask[(cj + 1) * g.nx + ci] = 1; mask[(cj + 1) * g.nx + ci + 1] = 1;
      }
    }
  }
  const gm: Grid = { ...g, mask };
  for (let changed = true; changed; ) {
    changed = false;
    for (let j = 0; j < g.ny; j++) {
      for (let i = 0; i < g.nx; i++) {
        if (mask[j * g.nx + i] && nodeWeight(gm, i, j) === 0) {
          mask[j * g.nx + i] = 0;
          changed = true;
        }
      }
    }
  }
  return gm;
}

/** Node coordinates relative to the center of the bounding box. */
export function nodeX(g: Grid, i: number): number {
  return (i - (g.nx - 1) / 2) * g.hx;
}
export function nodeY(g: Grid, j: number): number {
  return (j - (g.ny - 1) / 2) * g.hy;
}

/** True when node (i, j) exists and belongs to the plate. */
export function insideNode(g: Grid, i: number, j: number): boolean {
  if (i < 0 || i >= g.nx || j < 0 || j >= g.ny) return false;
  return g.mask ? g.mask[j * g.nx + i] !== 0 : true;
}

/** True when cell (ci, cj), with nodes (ci..ci+1, cj..cj+1), lies within the plate. */
export function insideCell(g: Grid, ci: number, cj: number): boolean {
  return insideNode(g, ci, cj) && insideNode(g, ci + 1, cj) && insideNode(g, ci + 1, cj + 1) && insideNode(g, ci, cj + 1);
}

/**
 * Quadrature and lumped-mass weight of a node: the fraction of its four
 * surrounding cells that belong to the plate (1 inside, 1/2 on an edge, 1/4
 * at a corner of a full rectangle). Zero outside.
 */
export function nodeWeight(g: Grid, i: number, j: number): number {
  if (!insideNode(g, i, j)) return 0;
  let c = 0;
  if (insideCell(g, i, j)) c++;
  if (insideCell(g, i - 1, j)) c++;
  if (insideCell(g, i, j - 1)) c++;
  if (insideCell(g, i - 1, j - 1)) c++;
  return c / 4;
}

/** Per-node weights as a flat array. */
export function nodeWeights(g: Grid): Float32Array<ArrayBuffer> {
  const w = new Float32Array(g.n);
  for (let j = 0; j < g.ny; j++) for (let i = 0; i < g.nx; i++) w[j * g.nx + i] = nodeWeight(g, i, j);
  return w;
}

/** Per-cell membership (1 or 0) as a flat array of (nx - 1) * (ny - 1). */
export function cellMask(g: Grid): Float32Array<ArrayBuffer> {
  const c = new Float32Array((g.nx - 1) * (g.ny - 1));
  for (let cj = 0; cj < g.ny - 1; cj++) for (let ci = 0; ci < g.nx - 1; ci++) c[cj * (g.nx - 1) + ci] = insideCell(g, ci, cj) ? 1 : 0;
  return c;
}

/** Number of nodes in the plate. */
export function countInside(g: Grid): number {
  if (!g.mask) return g.n;
  let c = 0;
  for (let k = 0; k < g.n; k++) c += g.mask[k];
  return c;
}

// ---------- Material, stand, losses, plate ----------

export interface Material {
  E: number; // Young's modulus [Pa]
  nu: number; // Poisson ratio
  rho: number; // density [kg/m^3]
}

/** A felt pad of the stand: an annulus of felt between the plate and the stand (or the wing nut). */
export interface Pad {
  innerRadius: number; // [m]
  outerRadius: number; // [m]
  thickness: number; // [m]
  E: number; // Young's modulus of the felt in compression [Pa]
  lossFactor: number; // loss factor eta of the felt
}

/**
 * The stand: a rod through the center hole at (x, y) with a felt pad below
 * the plate and, when topPad is set, the same pad above it under the wing
 * nut, which compresses the top pad by `preload` at rest.
 */
export interface Stand {
  x: number;
  y: number;
  pad: Pad;
  topPad: boolean;
  preload: number; // compression of the top pad at rest [m]
}

/**
 * Decay times of the plate as a function of frequency, sampled by the design
 * script on a fixed log-spaced set of frequencies (see loss.ts).
 */
export interface Loss {
  freqs: Float64Array;
  t60: Float64Array;
}

/** The plate as evaluated on the grid. */
export interface Plate {
  name: string;
  Lx: number;
  Ly: number;
  grid: Grid;
  mat: Material;
  /** Thickness at the nodes [m]; zero outside the plate. */
  h: Float64Array;
  /** Stress-free height at the nodes [m], mean plane removed; zero outside the plate. */
  w0: Float64Array;
  stand: Stand | null;
  loss: Loss;
}

export function bendingStiffness(m: Material, h: number): number {
  return (m.E * h * h * h) / (12 * (1 - m.nu * m.nu));
}
export function membraneStiffness(m: Material, h: number): number {
  return (m.E * h) / (1 - m.nu * m.nu);
}
export function shearStiffness(m: Material, h: number): number {
  return (m.E * h) / (2 * (1 + m.nu));
}
/** In-plane wave speed, which sets the time step of the full simulation. */
export function inPlaneSpeed(m: Material): number {
  return Math.sqrt(m.E / (m.rho * (1 - m.nu * m.nu)));
}
/** Bending-wave constant kappa = sqrt(D / rho h), so that omega = kappa k^2. */
export function bendingConstant(m: Material, h: number): number {
  return Math.sqrt(bendingStiffness(m, h) / (m.rho * h));
}

/** Thickness of a cell: the mean of its four corners. */
export function cellThickness(pl: Plate, ci: number, cj: number): number {
  const nx = pl.grid.nx;
  return 0.25 * (pl.h[cj * nx + ci] + pl.h[cj * nx + ci + 1] + pl.h[(cj + 1) * nx + ci] + pl.h[(cj + 1) * nx + ci + 1]);
}

/** Lumped mass of a node: rho h dA times its weight. */
export function nodeMass(pl: Plate, i: number, j: number): number {
  const g = pl.grid;
  return pl.mat.rho * pl.h[j * g.nx + i] * g.hx * g.hy * nodeWeight(g, i, j);
}

/** Per-node masses as a flat array. */
export function nodeMasses(pl: Plate): Float64Array {
  const g = pl.grid;
  const m = new Float64Array(g.n);
  for (let j = 0; j < g.ny; j++) for (let i = 0; i < g.nx; i++) m[j * g.nx + i] = nodeMass(pl, i, j);
  return m;
}

/** Total mass, the mass-weighted center, and the moments of inertia about the in-plane axes through it. */
export function massProperties(pl: Plate): { mass: number; cx: number; cy: number; Ix: number; Iy: number; area: number } {
  const g = pl.grid;
  let mass = 0, sx = 0, sy = 0, area = 0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const m = nodeMass(pl, i, j);
      mass += m; sx += m * nodeX(g, i); sy += m * nodeY(g, j);
      area += g.hx * g.hy * nodeWeight(g, i, j);
    }
  }
  const cx = mass > 0 ? sx / mass : 0, cy = mass > 0 ? sy / mass : 0;
  let Ix = 0, Iy = 0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const m = nodeMass(pl, i, j);
      Ix += m * (nodeY(g, j) - cy) ** 2;
      Iy += m * (nodeX(g, i) - cx) ** 2;
    }
  }
  return { mass, cx, cy, Ix, Iy, area };
}

/** Mean thickness over the plate (area-weighted). */
export function meanThickness(pl: Plate): number {
  const g = pl.grid;
  let s = 0, a = 0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const w = nodeWeight(g, i, j);
      s += w * pl.h[j * g.nx + i]; a += w;
    }
  }
  return a > 0 ? s / a : 0;
}

/** Smallest and largest thickness over the plate. */
export function thicknessRange(pl: Plate): { min: number; max: number } {
  const g = pl.grid;
  let lo = Infinity, hi = 0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      if (!insideNode(g, i, j)) continue;
      const h = pl.h[j * g.nx + i];
      lo = Math.min(lo, h); hi = Math.max(hi, h);
    }
  }
  return { min: isFinite(lo) ? lo : 0, max: hi };
}

// ---------- Stand as seen by the solvers ----------

/**
 * The pads as per-node spring rates. `kw[k]` is the transverse stiffness of
 * the pads at node k (both pads summed), `ku[k]` the in-plane (shear)
 * stiffness, both in N/m; `kwBottom` is the bottom pad alone, which the full
 * simulation needs for the lift-off rule. `eta` is the loss factor, and
 * `preloadTop`, `preloadBottom` are the pad compressions at rest.
 */
export interface StandRates {
  kw: Float64Array;
  ku: Float64Array;
  kwBottom: Float64Array;
  nodes: number[];
  eta: number;
  preloadTop: number;
  preloadBottom: number;
  /** Total transverse stiffness of the pads [N/m]. */
  totalKw: number;
  /** Bounce frequency of the plate on the pads [Hz]. */
  bounceHz: number;
}

/**
 * Per-node pad stiffness of the stand, or null for a free plate. The pads
 * act on the plate nodes within the annulus; because a coarse grid covers
 * the annulus with a handful of nodes, the per-node rates are scaled so
 * that their sum equals the stiffness of the exact annulus area.
 */
export function standRates(pl: Plate): StandRates | null {
  const st = pl.stand;
  if (!st) return null;
  const g = pl.grid;
  const kw = new Float64Array(g.n), ku = new Float64Array(g.n), kwBottom = new Float64Array(g.n);
  const nodes: number[] = [];
  const pad = st.pad;
  const kArea = pad.E / pad.thickness; // N/m^3
  const gArea = pad.E / (2 * (1 + PAD_POISSON)) / pad.thickness;
  const nPads = st.topPad ? 2 : 1;
  const annulus = Math.PI * (pad.outerRadius ** 2 - pad.innerRadius ** 2);
  let nodeArea = 0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const wgt = nodeWeight(g, i, j);
      if (wgt === 0) continue;
      const r = Math.hypot(nodeX(g, i) - st.x, nodeY(g, j) - st.y);
      if (r < pad.innerRadius || r > pad.outerRadius) continue;
      nodes.push(j * g.nx + i);
      nodeArea += g.hx * g.hy * wgt;
    }
  }
  const empty = { kw, ku, kwBottom, nodes, eta: pad.lossFactor, preloadTop: 0, preloadBottom: 0, totalKw: 0, bounceHz: 0 };
  if (nodes.length === 0 || nodeArea === 0) return empty;
  const scale = annulus / nodeArea;
  let totalKw = 0;
  for (const k of nodes) {
    const dA = scale * g.hx * g.hy * nodeWeight(g, k % g.nx, Math.floor(k / g.nx));
    kwBottom[k] = kArea * dA;
    kw[k] = nPads * kArea * dA;
    ku[k] = nPads * gArea * dA;
    totalKw += kw[k];
  }
  const { mass } = massProperties(pl);
  const preloadTop = st.topPad ? st.preload : 0;
  // The bottom pad carries the top pad's preload plus the weight of the plate.
  const preloadBottom = preloadTop + (mass * GRAVITY) / (kArea * annulus);
  return { kw, ku, kwBottom, nodes, eta: pad.lossFactor, preloadTop, preloadBottom, totalKw, bounceHz: Math.sqrt(totalKw / mass) / (2 * Math.PI) };
}

// ---------- Patches ----------

/** A set of plate nodes with the quantities the strike needs. */
export interface Patch {
  nodes: number[];
  nearest: number;
  mass: number;
  cx: number;
  cy: number;
}

/** The plate nodes within `radius` of (x, y), always including the nearest one. */
export function patchAround(pl: Plate, x: number, y: number, radius: number): Patch {
  const g = pl.grid;
  const nodes: number[] = [];
  let nearest = -1, best = Infinity;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      if (nodeMass(pl, i, j) === 0) continue;
      const d = Math.hypot(nodeX(g, i) - x, nodeY(g, j) - y);
      if (d < best) { best = d; nearest = j * g.nx + i; }
      if (d <= radius) nodes.push(j * g.nx + i);
    }
  }
  if (nearest >= 0 && !nodes.includes(nearest)) nodes.push(nearest);
  let mass = 0, cx = 0, cy = 0;
  for (const k of nodes) {
    const m = nodeMass(pl, k % g.nx, Math.floor(k / g.nx));
    mass += m; cx += m * nodeX(g, k % g.nx); cy += m * nodeY(g, Math.floor(k / g.nx));
  }
  return { nodes, nearest, mass, cx: mass > 0 ? cx / mass : 0, cy: mass > 0 ? cy / mass : 0 };
}

/** The strike point in plate coordinates from the fractions of the bounding box. */
export function strikePoint(pl: Plate, p: SimParams): { x: number; y: number } {
  return { x: (p.strikeFracX - 0.5) * pl.Lx, y: (p.strikeFracY - 0.5) * pl.Ly };
}

export function strikePatch(pl: Plate, p: SimParams): Patch {
  const { x, y } = strikePoint(pl, p);
  return patchAround(pl, x, y, p.contactRadius);
}

// ---------- Listener ----------

/** Listener position relative to the center of the plate, z along the plate's normal. */
export function listenerPosition(p: SimParams): { x: number; y: number; z: number } {
  const th = (p.listenerAngle * Math.PI) / 180, ph = (p.listenerAzimuth * Math.PI) / 180;
  return { x: p.listenerDist * Math.sin(th) * Math.cos(ph), y: p.listenerDist * Math.sin(th) * Math.sin(ph), z: p.listenerDist * Math.cos(th) };
}

/**
 * Per-node terms of the Rayleigh integral for the listener: the weight
 * rho_air dA / (2 pi r) and the delay r / c in seconds, for every node (zero
 * outside the plate). The profile is included in the node positions.
 */
export function listenerTerms(pl: Plate, p: SimParams): { weight: Float64Array; delay: Float64Array } {
  const g = pl.grid;
  const L = listenerPosition(p);
  const weight = new Float64Array(g.n), delay = new Float64Array(g.n);
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const wgt = nodeWeight(g, i, j);
      if (wgt === 0) continue;
      const k = j * g.nx + i;
      const r = Math.hypot(L.x - nodeX(g, i), L.y - nodeY(g, j), L.z - pl.w0[k]);
      weight[k] = (RHO_AIR * g.hx * g.hy * wgt) / (2 * Math.PI * Math.max(r, 1e-3));
      delay[k] = r / SPEED_OF_SOUND;
    }
  }
  return { weight, delay };
}

// ---------- Grid dispersion ----------

/**
 * Frequencies at which grid dispersion lowers a bending partial by the given
 * fraction, for a plate of thickness h: a plane wave along a grid axis has the
 * discrete frequency ratio (2 - 2 cos kh) / (kh)^2.
 */
export function dispersionFrequency(m: Material, h: number, spacing: number, fraction: number): number {
  let lo = 0, hi = Math.PI;
  for (let it = 0; it < 60; it++) {
    const mid = (lo + hi) / 2;
    const ratio = (2 - 2 * Math.cos(mid)) / (mid * mid);
    if (1 - ratio < fraction) lo = mid; else hi = mid;
  }
  const k = lo / spacing;
  return (bendingConstant(m, h) * k * k) / (2 * Math.PI);
}