// Physical and numerical parameters of the simulation, and the derived
// quantities (grid, material constants, geometry of the excitation).
// All values are SI.

export type PlateShape = "rectangle" | "ellipse";
export type BowShape = "none" | "width" | "height" | "dish";
export type Excitation = "push" | "strike";
export type HitSequence = "single" | "steady" | "crescendo" | "decrescendo";

export interface PhysParams {
  // Sheet
  shape: PlateShape; // outline of the sheet within its bounding box
  Lx: number; // width along x [m] (bounding box for an ellipse)
  Ly: number; // height along y [m]
  h: number; // thickness [m]
  E: number; // Young's modulus [Pa]
  nu: number; // Poisson ratio
  rho: number; // density [kg/m^3]
  holeInset: number; // distance of the thread hole from the edges near the top-left corner [m]
  // Stress-free initial shape
  bowShape: BowShape;
  bowAmplitude: number; // sag of the initial shape at the center [m]
  // Losses
  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]
  // Excitation
  excitation: Excitation;
  pushAmount: number; // corner displacement [m]; negative pushes against the bow
  fingerRadius: number; // radius of the pushed patch [m]
  rampTime: number; // duration of the push ramp [s]
  holdMax: number; // maximum settle time before the release [s]
  releaseTime: number; // time over which the finger force falls to zero [s]
  settleSigma0: number; // artificial damping during push and settle [1/s]
  settleKE: number; // non-rigid kinetic energy below which the sheet counts as settled [J]
  strikeFracX: number; // strike point as a fraction of the width from the left edge
  strikeFracY: number; // strike point as a fraction of the height from the bottom edge
  strikeVelocity: number; // stick tip speed at impact [m/s]; the loudest hit of a sequence
  hitSequence: HitSequence; // one hit, or a series of hits every hitInterval seconds
  hitCount: number; // number of hits in a series
  hitInterval: number; // time between the hits of a series [s]
  strikeVelocityMin: number; // softest stick speed of a crescendo or decrescendo [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 sheet'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 while ringing
  fs: number; // audio sample rate [Hz]
  fps: number; // movie frame rate, also the batch rate [Hz]
  duration: number; // recorded duration after the release or the impact [s]
}

export const defaultParams: PhysParams = {
  shape: "rectangle",
  Lx: 12 * 0.0254,
  Ly: 18 * 0.0254,
  h: 0.79e-3,
  E: 170e9,
  nu: 0.29,
  rho: 7900,
  holeInset: 0.012,
  bowShape: "width",
  bowAmplitude: 3e-3,
  sigma0: 1.15,
  sigma1: 5e-4,
  sigmaIn: 20,
  excitation: "strike",
  pushAmount: 0.01,
  fingerRadius: 0.01,
  rampTime: 0.1,
  holdMax: 0.5,
  releaseTime: 0.02,
  settleSigma0: 300,
  settleKE: 1e-8,
  strikeFracX: 0.7,
  strikeFracY: 0.35,
  strikeVelocity: 3,
  hitSequence: "single",
  hitCount: 6,
  hitInterval: 0.5,
  strikeVelocityMin: 0.5,
  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 sheet.
export const HIST_MARGIN = 128; // [samples]
export const RB_INTERVAL = 32; // steps between rigid-body projections while ringing
export const RB_INTERVAL_HELD = 16; // while the finger constraint is active
// The held sheet counts as settled when its non-rigid kinetic energy drops
// below settleKE, or when it has stopped falling: it has not halved over the
// last SETTLE_WINDOW seconds (or 3 / settleSigma0, whichever is longer).
export const SETTLE_WINDOW = 0.05; // [s]
export const SETTLE_RATIO = 0.5;

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

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

export function makeGrid(p: PhysParams): Grid {
  const nx = Math.max(6, Math.round(p.Lx / p.spacing) + 1);
  const ny = Math.max(6, Math.round(p.Ly / p.spacing) + 1);
  const g: Grid = { nx, ny, hx: p.Lx / (nx - 1), hy: p.Ly / (ny - 1), n: nx * ny };
  return p.shape === "ellipse" ? withEllipseMask(g) : g;
}

/**
 * Restricts a grid to the ellipse inscribed in its bounding box. The edge is a
 * staircase of whole cells: a cell belongs to the sheet when its center lies
 * inside the ellipse, 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.
 */
export function withEllipseMask(g: Grid): Grid {
  const mask = new Uint8Array(g.n);
  const a = ((g.nx - 1) * g.hx) / 2, b = ((g.ny - 1) * g.hy) / 2;
  for (let cj = 0; cj < g.ny - 1; cj++) {
    for (let ci = 0; ci < g.nx - 1; ci++) {
      const X = (nodeX(g, ci) + g.hx / 2) / a, Y = (nodeY(g, cj) + g.hy / 2) / b;
      if (X * X + Y * Y <= 1) {
        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 sheet. */
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 sheet. */
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 sheet. 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;
}

/** Number of nodes in the sheet. */
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 ----------

export interface Material {
  D: number; // bending stiffness E h^3 / (12 (1 - nu^2)) [N m]
  C: number; // membrane stiffness E h / (1 - nu^2) [N/m]
  G: number; // membrane shear stiffness E h / (2 (1 + nu)) [N/m]
  nu: number;
  rhoh: number; // mass per unit area [kg/m^2]
}

export function makeMaterial(p: PhysParams): Material {
  return {
    D: (p.E * p.h ** 3) / (12 * (1 - p.nu * p.nu)),
    C: (p.E * p.h) / (1 - p.nu * p.nu),
    G: (p.E * p.h) / (2 * (1 + p.nu)),
    nu: p.nu,
    rhoh: p.rho * p.h,
  };
}

/**
 * 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.
 */
export function t60(m: Material, p: PhysParams, omega: number): number {
  const kappa = Math.sqrt(m.D / m.rhoh);
  const sigma = p.sigma0 + p.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. 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, g: Grid, err: number): number {
  const h = 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 / h;
  const kappa = Math.sqrt(m.D / m.rhoh);
  return (kappa * k * k) / (2 * Math.PI);
}

// ---------- Geometry of the excitation ----------

/** One drumstick hit: time after the first impact [s] and stick speed [m/s]. */
export interface Hit {
  t: number;
  v: number;
}

/**
 * Schedule of the drumstick hits. The first hit is always at t = 0. A series
 * has hitCount hits every hitInterval seconds, all at strikeVelocity for
 * "steady", rising from strikeVelocityMin to strikeVelocity for "crescendo",
 * and falling for "decrescendo".
 */
export function hitSchedule(p: PhysParams): Hit[] {
  if (p.hitSequence === "single") return [{ t: 0, v: p.strikeVelocity }];
  const count = Math.max(1, Math.round(p.hitCount));
  const dt = Math.max(0, p.hitInterval);
  const lo = Math.min(p.strikeVelocityMin, p.strikeVelocity), hi = p.strikeVelocity;
  const hits: Hit[] = [];
  for (let k = 0; k < count; k++) {
    const f = count > 1 ? k / (count - 1) : 1;
    let v = hi;
    if (p.hitSequence === "crescendo") v = lo + (hi - lo) * f;
    else if (p.hitSequence === "decrescendo") v = hi - (hi - lo) * f;
    hits.push({ t: k * dt, v });
  }
  return hits;
}

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

/**
 * Center of the thread hole. Rectangle: inset from the two edges of the
 * top-left corner. Ellipse: inset along the radius from the rim point in the
 * top-left direction (parametric angle 135 degrees).
 */
export function holePoint(p: PhysParams): [number, number] {
  if (p.shape === "ellipse") {
    const c = Math.SQRT1_2;
    return [-(p.Lx / 2 - p.holeInset) * c, (p.Ly / 2 - p.holeInset) * c];
  }
  return [-p.Lx / 2 + p.holeInset, p.Ly / 2 - p.holeInset];
}

/** Center of the pushed patch: the bottom-right corner, or the rim point opposite the hole. */
export function pushPoint(p: PhysParams): [number, number] {
  if (p.shape === "ellipse") {
    const c = Math.SQRT1_2;
    return [(p.Lx / 2) * c, -(p.Ly / 2) * c];
  }
  return [p.Lx / 2, -p.Ly / 2];
}

/**
 * Stress-free initial shape w0 at every node. All three shapes are parabolic
 * with the given sag at the center of the bounding box: "width" and "height"
 * are cylindrical with zero sag along the two opposite edges, and "dish" has
 * the same curvature in both directions, so its sag is measured relative to
 * the corners (the edge midpoints sit at half the sag).
 */
export function initialShape(p: PhysParams, g: Grid): Float32Array<ArrayBuffer> {
  const w0 = new Float32Array(g.n);
  if (p.bowShape === "none" || p.bowAmplitude === 0) return w0;
  for (let j = 0; j < g.ny; j++) {
    for (let i = 0; i < g.nx; i++) {
      const X = (2 * nodeX(g, i)) / p.Lx; // -1..1
      const Y = (2 * nodeY(g, j)) / p.Ly;
      let f = 0;
      if (p.bowShape === "width") f = 1 - X * X;
      else if (p.bowShape === "height") f = 1 - Y * Y;
      else f = 1 - 0.5 * (X * X + Y * Y);
      w0[j * g.nx + i] = p.bowAmplitude * f;
    }
  }
  return w0;
}

/**
 * Nodes of the drumstick contact patch: the sheet node nearest the strike
 * point, plus every sheet node within the contact radius. The contact force
 * is spread over these nodes in proportion to their mass, 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 contactPatch(p: PhysParams, g: Grid): { nodes: number[]; nearest: number; mass: number; center: [number, number]; box: [number, number, number, number] } {
  const m = makeMaterial(p);
  const [sx, sy] = strikePoint(p);
  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) - sx) ** 2 + (nodeY(g, j) - sy) ** 2;
      if (d2 < best) { best = d2; nearest = j * g.nx + i; }
    }
  }
  const nodes: number[] = [];
  let mass = 0, cx = 0, cy = 0;
  const box: [number, number, number, number] = [g.nx, -1, g.ny, -1]; // i0, i1, j0, j1 (inclusive)
  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) - sx) ** 2 + (nodeY(g, j) - sy) ** 2;
      if (d2 <= p.contactRadius ** 2 || k === nearest) {
        nodes.push(k);
        const mk = m.rhoh * g.hx * g.hy * wgt;
        mass += mk; 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, center: [cx / mass, cy / mass], box };
}