feuerwerk/src/core/model/curve.ts

/**
 * Curve assets (#247): an easing drawn by hand, read wherever a key or a `Lerp` node picks one.
 * One pure function evaluates it for the Curve tab, the animation player and the graph alike.
 *
 * A segment is a cubic Bezier from one point to the next, a line where neither end has a handle –
 * the same rule vector art draws by. It is solved for `t` like CSS `cubic-bezier`: with both inner
 * control points between the ends in `t`, `t` rises monotonically along the segment, so bisection
 * finds the one place a `t` is reached.
 */
import { isGraphAsset, type VectorPoint } from './Asset';
import { findAssetOf, type Project } from './Project';
import type { Vec2 } from './Properties';
import { cloneVectorPoint } from './vectorart';

/** The node type that eases along a curve, and its setting naming the curve. */
export const LERP = 'Lerp';
export const LERP_CURVE = 'curve';

/** How many animation keys and `Lerp` nodes ease along a curve – what deleting it has to warn about. */
export function curveUsages(project: Project, curveId: string): { keys: number; nodes: number } {
  let keys = 0;
  let nodes = 0;
  for (const asset of project.assets) {
    if (asset.type === 'animation')
      for (const track of asset.tracks)
        keys += track.keys.filter((key) => key.interpolation === `curve:${curveId}`).length;
    if (isGraphAsset(asset))
      nodes += asset.graph.nodes.filter((n) => n.type === LERP && n.params[LERP_CURVE] === curveId).length;
  }
  return { keys, nodes };
}

/** The points of the curve an id names; undefined once it is gone. */
export type CurveLookup = (curveId: string) => readonly VectorPoint[] | undefined;

export const NO_CURVES: CurveLookup = () => undefined;

export function curveLookup(project: Project): CurveLookup {
  return (curveId) => (curveId ? findAssetOf(project, curveId, 'curve')?.points : undefined);
}

/** What a new curve is: a straight line from (0, 0) to (1, 1), the same as `linear`. */
export function linearCurve(): VectorPoint[] {
  return [
    { x: 0, y: 0 },
    { x: 1, y: 1 },
  ];
}

/** Halvings of the segment; 2^-40 of a segment is far below anything a value could show. */
const BISECTIONS = 40;

/**
 * The value at `t`, held to 0…1. Between two points the segment decides; a segment without width –
 * two points on one `t` – is a jump, and the later point's value wins from there on.
 */
export function curveValue(points: readonly VectorPoint[], t: number): number {
  const first = points[0];
  if (!first) return t;
  const at = Math.min(Math.max(Number.isFinite(t) ? t : 0, 0), 1);
  if (at <= first.x) return first.y;
  for (let i = 1; i < points.length; i++) {
    const to = points[i]!;
    if (at > to.x) continue;
    return segmentValue(points[i - 1]!, to, at);
  }
  return points[points.length - 1]!.y;
}

function segmentValue(from: VectorPoint, to: VectorPoint, t: number): number {
  const span = to.x - from.x;
  if (span <= 0) return to.y;
  if (!from.out && !to.in) return from.y + ((to.y - from.y) * (t - from.x)) / span;
  // Held between the ends in `t`, whatever is stored: that is what keeps the solve unique.
  const c1x = clamp(from.x + (from.out?.x ?? 0), from.x, to.x);
  const c2x = clamp(to.x + (to.in?.x ?? 0), from.x, to.x);
  const c1y = from.y + (from.out?.y ?? 0);
  const c2y = to.y + (to.in?.y ?? 0);
  let lo = 0;
  let hi = 1;
  for (let step = 0; step < BISECTIONS; step++) {
    const mid = (lo + hi) / 2;
    if (cubic(from.x, c1x, c2x, to.x, mid) < t) lo = mid;
    else hi = mid;
  }
  return cubic(from.y, c1y, c2y, to.y, (lo + hi) / 2);
}

function cubic(a: number, b: number, c: number, d: number, s: number): number {
  const u = 1 - s;
  return u * u * u * a + 3 * u * u * s * b + 3 * u * s * s * c + s * s * s * d;
}

function clamp(value: number, min: number, max: number): number {
  return Math.min(Math.max(value, min), max);
}

/**
 * The curve as the rules want it, whatever was handed in. At least two points; sorted by `t`, `t`
 * held to 0…1, the first at 0 and the last at 1. The first point has no handle in and the last none
 * out. A handle pointing backwards in `t` is turned upright, and one reaching past its neighbour is
 * shortened along its own direction, so a smooth point stays smooth. What does not come out a number
 * is dropped; with fewer than two points left the curve is linear.
 */
export function sanitizedCurve(points: readonly VectorPoint[]): VectorPoint[] {
  const kept = points
    .filter((p) => Number.isFinite(p.x) && Number.isFinite(p.y))
    .map((p) => ({ ...cloneVectorPoint(p), x: clamp(p.x, 0, 1) }))
    .sort((a, b) => a.x - b.x);
  if (kept.length < 2) return linearCurve();
  kept[0]!.x = 0;
  kept[kept.length - 1]!.x = 1;
  for (const [i, point] of kept.entries()) {
    const before = kept[i - 1];
    const after = kept[i + 1];
    const handleIn = before && point.in ? heldHandle(point.in, before.x - point.x) : undefined;
    const handleOut = after && point.out ? heldHandle(point.out, after.x - point.x) : undefined;
    if (handleIn) point.in = handleIn;
    else delete point.in;
    if (handleOut) point.out = handleOut;
    else delete point.out;
    if (!point.in && !point.out) delete point.mode;
  }
  return kept;
}

/** A handle kept on its own side of the point, reaching `reach` in `t` at most (negative for `in`). */
function heldHandle(handle: Vec2, reach: number): Vec2 | undefined {
  const finite = Number.isFinite(handle.x) && Number.isFinite(handle.y);
  if (!finite) return undefined;
  let { x, y } = handle;
  if (x * reach < 0) x = 0;
  if (Math.abs(x) > Math.abs(reach)) {
    const scale = Math.abs(reach) / Math.abs(x);
    x *= scale;
    y *= scale;
  }
  return Math.hypot(x, y) < 1e-9 ? undefined : { x, y };
}

/** The lowest and highest value the curve can reach – its points and handles – and never less than 0…1. */
export function curveExtent(points: readonly VectorPoint[]): { min: number; max: number } {
  let min = 0;
  let max = 1;
  for (const point of points)
    for (const y of [point.y, point.y + (point.in?.y ?? 0), point.y + (point.out?.y ?? 0)]) {
      min = Math.min(min, y);
      max = Math.max(max, y);
    }
  return { min, max };
}