// Simulation parameters (strike, listener, numerics), the grid with its mask,
// the plate as evaluated on the grid (material, thickness field, stress-free
// shape, mount), and the derived quantities the kernel needs. All values are
// SI. The cymbal 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]
  listenerAzimuth: number; // [deg], rotation about the plate's vertical axis (0 = on the normal)
  listenerElevation: number; // [deg]
  // Numerics and output
  spacing: number; // requested grid spacing [m]
  inPlaneMass: number; // factor by which the in-plane inertia is scaled; 1 is physical, larger lengthens the time step
  rigidProjection: boolean; // remove the six rigid-body modes every RB_INTERVAL steps (free plates only)
  fs: number; // audio sample rate [Hz]
  fps: number; // movie frame rate, also the batch rate [Hz]
  duration: number; // recorded duration after the impact [s]
}

export const defaultParams: SimParams = {
  strikeFracX: 0.7,
  strikeFracY: 0.5,
  strikeVelocity: 3,
  stickMass: 0.03,
  contactStiffness: 5e8,
  contactExponent: 1.5,
  contactRadius: 5e-3,
  listenerDist: 1.0,
  listenerAzimuth: 0,
  listenerElevation: 0,
  spacing: 0.008,
  inPlaneMass: 1,
  rigidProjection: false,
  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 CFL = 0.9; // fraction of the stability limit used for the time step
// The ring buffer of the retarded-time listener sum holds one batch of samples
// plus this margin, which bounds the spread of the delays across the plate.
export const HIST_MARGIN = 128; // [samples]
export const RB_INTERVAL = 32; // steps between rigid-body projections

// ---------- 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 `inside` 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 rather
 * than by nodes keeps the covered area unbiased; a node-based mask loses
 * about half a cell all around the edge, which raises every frequency by a
 * few percent. A node with no cell of its own would carry no mass, and the
 * trailing loop removes any such node. A hole in the outline (a cymbal's
 * center 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;
}

/** The ellipse inscribed in the bounding box (kept for the tests of the discretization). */
export function withEllipseMask(g: Grid): Grid {
  const a = ((g.nx - 1) * g.hx) / 2, b = ((g.ny - 1) * g.hy) / 2;
  return withMask(g, (x, y) => (x / a) ** 2 + (y / b) ** 2 <= 1);
}

/** 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. On a full rectangle this is the
 * trapezoidal rule (1 inside, 1/2 on an edge, 1/4 at a corner). 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 and plate ----------

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

/** Losses of the plate (see THEORY.md). */
export interface Loss {
  sigma0: number; // frequency-independent loss of all motion [1/s]
  sigma1: number; // loss proportional to the squared wavenumber, transverse motion [m^2/s]
  sigmaIn: number; // additional frequency-independent loss of the in-plane motion [1/s]
}

/**
 * The stand: the plate nodes within `radius` of (x, y) are tied to the ground
 * by a spring of total stiffness `stiffness` and a dashpot of total rate
 * `damping`, both spread over the nodes in proportion to their weight and
 * acting on all three displacement components.
 */
export interface Mount {
  x: number; // [m] from the center of the bounding box
  y: number;
  radius: number; // [m]
  stiffness: number; // [N/m]
  damping: number; // [N s/m]
}

/** A design evaluated on a grid: everything the simulation needs to know about the plate. */
export interface Plate {
  name: string;
  Lx: number; // bounding box [m]
  Ly: number;
  grid: Grid;
  mat: Material;
  /** Thickness at every node [m]; zero outside the plate. */
  h: Float64Array;
  /** Stress-free shape at every node [m], mean plane removed; zero outside the plate. */
  w0: Float64Array;
  mount: Mount | null;
  loss: Loss;
}

/** Bending stiffness [N m] of a plate of thickness h. */
export function bendingStiffness(m: Material, h: number): number {
  return (m.E * h ** 3) / (12 * (1 - m.nu * m.nu));
}
/** Membrane stiffness E h / (1 - nu^2) [N/m]. */
export function membraneStiffness(m: Material, h: number): number {
  return (m.E * h) / (1 - m.nu * m.nu);
}
/** Membrane shear stiffness E h / (2 (1 + nu)) [N/m]. */
export function shearStiffness(m: Material, h: number): number {
  return (m.E * h) / (2 * (1 + m.nu));
}

/** Mass of node (i, j) [kg]: density, local thickness, cell area, and the node's 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);
}

/** Thickness of a cell: the mean over its four corners (zero for a cell outside the plate). */
export function cellThickness(pl: Plate, ci: number, cj: number): number {
  const g = pl.grid;
  if (!insideCell(g, ci, cj)) return 0;
  const k = cj * g.nx + ci;
  return 0.25 * (pl.h[k] + pl.h[k + 1] + pl.h[k + g.nx] + pl.h[k + g.nx + 1]);
}

/** Smallest, mean, and largest thickness over the plate nodes. */
export function thicknessRange(pl: Plate): { min: number; mean: number; max: number } {
  const g = pl.grid;
  let lo = Infinity, hi = 0, sum = 0, sw = 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 h = pl.h[j * g.nx + i];
      lo = Math.min(lo, h); hi = Math.max(hi, h); sum += wgt * h; sw += wgt;
    }
  }
  return { min: isFinite(lo) ? lo : 0, mean: sw > 0 ? sum / sw : 0, max: hi };
}

/** Total mass [kg] and the moments of inertia about the in-plane axes through the center of the bounding box. */
export function massProperties(pl: Plate): { mass: number; Ix: number; Iy: number } {
  const g = pl.grid;
  let mass = 0, Ix = 0, Iy = 0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const mk = nodeMass(pl, i, j);
      mass += mk;
      Ix += mk * nodeY(g, j) ** 2;
      Iy += mk * nodeX(g, i) ** 2;
    }
  }
  return { mass, Ix, Iy };
}

/**
 * 60 dB decay time [s] of a bending mode of angular frequency omega under the
 * loss model sigma0 + sigma1 k^2, using the flat-plate dispersion k^2 = omega / kappa
 * for a plate of thickness h.
 */
export function t60(m: Material, h: number, loss: Loss, omega: number): number {
  const kappa = Math.sqrt(bendingStiffness(m, h) / (m.rho * h));
  const sigma = loss.sigma0 + loss.sigma1 * (omega / kappa);
  return (3 * Math.LN10) / sigma;
}

/**
 * Frequency [Hz] at which the three-point second difference lowers a bending
 * frequency by the relative amount `err` on a grid of spacing hmax, for a
 * plate of thickness h. A plane bending wave along a grid axis with
 * wavenumber k has the discrete frequency ratio (2 - 2 cos kh) / (kh)^2.
 */
export function dispersionFrequency(m: Material, h: number, g: Grid, err: number): number {
  const hg = Math.max(g.hx, g.hy);
  let lo = 0, hi = Math.PI;
  for (let it = 0; it < 60; it++) {
    const x = (lo + hi) / 2;
    if ((2 - 2 * Math.cos(x)) / (x * x) > 1 - err) lo = x; else hi = x;
  }
  const k = lo / hg;
  const kappa = Math.sqrt(bendingStiffness(m, h) / (m.rho * h));
  return (kappa * k * k) / (2 * Math.PI);
}

// ---------- Geometry of the excitation and the mount ----------

/** Strike point in plate coordinates. */
export function strikePoint(p: SimParams, pl: Plate): [number, number] {
  return [(p.strikeFracX - 0.5) * pl.Lx, (p.strikeFracY - 0.5) * pl.Ly];
}

/** The plate node nearest to a point, by index; -1 when the plate has no nodes. */
export function nearestNode(g: Grid, x: number, y: number): number {
  let nearest = -1, best = Infinity;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      if (nodeWeight(g, i, j) === 0) continue;
      const d2 = (nodeX(g, i) - x) ** 2 + (nodeY(g, j) - y) ** 2;
      if (d2 < best) { best = d2; nearest = j * g.nx + i; }
    }
  }
  return nearest;
}

export interface Patch {
  nodes: number[];
  /** The plate node nearest the center; always a member. */
  nearest: number;
  /** Total mass of the member nodes [kg]. */
  mass: number;
  /** Total node weight of the members. */
  weight: number;
  /** Mass-weighted center [m]. */
  center: [number, number];
  /** Index box enclosing the members (i0, i1, j0, j1, inclusive). */
  box: [number, number, number, number];
}

/**
 * The plate nodes within `radius` of (x, y), plus the nearest one. Used for
 * the drumstick contact patch and for the mount. The contact force is spread
 * over the patch in proportion to the node masses, and the contact coordinate
 * is their mass-weighted mean displacement, so the two are conjugate and the
 * contact has a potential energy. The mass-weighted center of the patch is
 * where the inertia-relief reaction to the force is taken.
 */
export function patchAround(pl: Plate, x: number, y: number, radius: number): Patch {
  const g = pl.grid;
  const nearest = nearestNode(g, x, y);
  const nodes: number[] = [];
  let mass = 0, weight = 0, cx = 0, cy = 0;
  const box: [number, number, number, number] = [g.nx, -1, g.ny, -1];
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const k = j * g.nx + i;
      const wgt = nodeWeight(g, i, j);
      if (wgt === 0) continue;
      const d2 = (nodeX(g, i) - x) ** 2 + (nodeY(g, j) - y) ** 2;
      if (d2 <= radius * radius || k === nearest) {
        nodes.push(k);
        const mk = nodeMass(pl, i, j);
        mass += mk; weight += wgt; cx += mk * nodeX(g, i); cy += mk * nodeY(g, j);
        box[0] = Math.min(box[0], i); box[1] = Math.max(box[1], i);
        box[2] = Math.min(box[2], j); box[3] = Math.max(box[3], j);
      }
    }
  }
  return { nodes, nearest, mass, weight, center: mass > 0 ? [cx / mass, cy / mass] : [x, y], box };
}

export function contactPatch(p: SimParams, pl: Plate): Patch {
  const [sx, sy] = strikePoint(p, pl);
  return patchAround(pl, sx, sy, p.contactRadius);
}

/** The mount patch, or null when the plate is free. */
export function mountPatch(pl: Plate): Patch | null {
  if (!pl.mount) return null;
  return patchAround(pl, pl.mount.x, pl.mount.y, pl.mount.radius);
}