AFFiNE-Mirror/blocksuite/framework/global/src/gfx/model/vec.ts

// Inlined from https://raw.githubusercontent.com/tldraw/tldraw/24cad6959f59f93e20e556d018c391fd89d4ecca/packages/vec/src/index.ts
// Credits to tldraw

export type IVec = [number, number];

export type IVec3 = [number, number, number];

export class Vec {
  /**
   * Absolute value of a vector.
   * @param A
   * @returns
   */
  static abs = (A: number[]): number[] => {
    return [Math.abs(A[0]), Math.abs(A[1])];
  };

  /**
   * Add vectors.
   * @param A
   * @param B
   */
  static add = (A: number[], B: number[]): IVec => {
    return [A[0] + B[0], A[1] + B[1]];
  };

  /**
   * Add scalar to vector.
   * @param A
   * @param B
   */
  static addScalar = (A: number[], n: number): IVec => {
    return [A[0] + n, A[1] + n];
  };

  /**
   * Angle between vector A and vector B in radians
   * @param A
   * @param B
   */
  static ang = (A: number[], B: number[]): number => {
    return Math.atan2(Vec.cpr(A, B), Vec.dpr(A, B));
  };

  /**
   * Get the angle between the three vectors A, B, and C.
   * @param p1
   * @param pc
   * @param p2
   */
  static ang3 = (p1: IVec, pc: IVec, p2: IVec): number => {
    // this,
    const v1 = Vec.vec(pc, p1);
    const v2 = Vec.vec(pc, p2);
    return Vec.ang(v1, v2);
  };

  /**
   * Angle between vector A and vector B in radians
   * @param A
   * @param B
   */
  static angle = (A: IVec, B: IVec): number => {
    return Math.atan2(B[1] - A[1], B[0] - A[0]);
  };

  /**
   * Get whether p1 is left of p2, relative to pc.
   * @param p1
   * @param pc
   * @param p2
   */
  static clockwise = (p1: number[], pc: number[], p2: number[]): boolean => {
    return Vec.isLeft(p1, pc, p2) > 0;
  };

  /**
   * Cross product (outer product) | A X B |
   * @param A
   * @param B
   */
  static cpr = (A: number[], B: number[]): number => {
    return A[0] * B[1] - B[0] * A[1];
  };

  /**
   * Dist length from A to B
   * @param A
   * @param B
   */
  static dist = (A: number[], B: number[]): number => {
    return Math.hypot(A[1] - B[1], A[0] - B[0]);
  };

  /**
   * Dist length from A to B squared.
   * @param A
   * @param B
   */
  static dist2 = (A: IVec, B: IVec): number => {
    return Vec.len2(Vec.sub(A, B));
  };

  /**
   * Distance between a point and the nearest point on a bounding box.
   * @param bounds The bounding box.
   * @param P The point
   * @returns
   */
  static distanceToBounds = (
    bounds: {
      minX: number;
      minY: number;
      maxX: number;
      maxY: number;
    },
    P: number[]
  ): number => {
    return Vec.dist(P, Vec.nearestPointOnBounds(bounds, P));
  };

  /**
   * Distance between a point and the nearest point on a line segment between A and B
   * @param A The start of the line segment
   * @param B The end of the line segment
   * @param P The off-line point
   * @param clamp Whether to clamp the point between A and B.
   * @returns
   */
  static distanceToLineSegment = (
    A: IVec,
    B: IVec,
    P: IVec,
    clamp = true
  ): number => {
    return Vec.dist(P, Vec.nearestPointOnLineSegment(A, B, P, clamp));
  };

  /**
   * Distance between a point and a line with a known unit vector that passes through a point.
   * @param A Any point on the line
   * @param u The unit vector for the line.
   * @param P A point not on the line to test.
   * @returns
   */
  static distanceToLineThroughPoint = (A: IVec, u: IVec, P: IVec): number => {
    return Vec.dist(P, Vec.nearestPointOnLineThroughPoint(A, u, P));
  };

  /**
   * Vector division by scalar.
   * @param A
   * @param n
   */
  static div = (A: IVec, n: number): IVec => {
    return [A[0] / n, A[1] / n];
  };

  /**
   * Vector division by vector.
   * @param A
   * @param n
   */
  static divV = (A: IVec, B: IVec): IVec => {
    return [A[0] / B[0], A[1] / B[1]];
  };

  /**
   * Dot product
   * @param A
   * @param B
   */
  static dpr = (A: number[], B: number[]): number => {
    return A[0] * B[0] + A[1] * B[1];
  };

  /**
   * A faster, though less accurate method for testing distances. Maybe faster?
   * @param A
   * @param B
   * @returns
   */
  static fastDist = (A: number[], B: number[]): number[] => {
    const V = [B[0] - A[0], B[1] - A[1]];
    const aV = [Math.abs(V[0]), Math.abs(V[1])];
    let r = 1 / Math.max(aV[0], aV[1]);
    r = r * (1.29289 - (aV[0] + aV[1]) * r * 0.29289);
    return [V[0] * r, V[1] * r];
  };

  /**
   * Interpolate from A to B when curVAL goes fromVAL: number[] => to
   * @param A
   * @param B
   * @param from Starting value
   * @param to Ending value
   * @param s Strength
   */
  static int = (A: IVec, B: IVec, from: number, to: number, s = 1): IVec => {
    const t = (Vec.clamp(from, to) - from) / (to - from);
    return Vec.add(Vec.mul(A, 1 - t), Vec.mul(B, s));
  };

  /**
   * Check of two vectors are identical.
   * @param A
   * @param B
   */
  static isEqual = (A: number[], B: number[]): boolean => {
    return A[0] === B[0] && A[1] === B[1];
  };

  /**
   * Get whether p1 is left of p2, relative to pc.
   * @param p1
   * @param pc
   * @param p2
   */
  static isLeft = (p1: number[], pc: number[], p2: number[]): number => {
    //  isLeft: >0 for counterclockwise
    //          =0 for none (degenerate)
    //          <0 for clockwise
    return (
      (pc[0] - p1[0]) * (p2[1] - p1[1]) - (p2[0] - p1[0]) * (pc[1] - p1[1])
    );
  };

  /**
   * Length of the vector
   * @param A
   */
  static len = (A: number[]): number => {
    return Math.hypot(A[0], A[1]);
  };

  /**
   * Length of the vector squared
   * @param A
   */
  static len2 = (A: number[]): number => {
    return A[0] * A[0] + A[1] * A[1];
  };

  /**
   * Interpolate vector A to B with a scalar t
   * @param A
   * @param B
   * @param t scalar
   */
  static lrp = (A: IVec, B: IVec, t: number): IVec => {
    return Vec.add(A, Vec.mul(Vec.sub(B, A), t));
  };

  /**
   * Get a vector comprised of the maximum of two or more vectors.
   */
  static max = (...v: number[][]) => {
    return [Math.max(...v.map(a => a[0])), Math.max(...v.map(a => a[1]))];
  };

  /**
   * Mean between two vectors or mid vector between two vectors
   * @param A
   * @param B
   */
  static med = (A: IVec, B: IVec): IVec => {
    return Vec.mul(Vec.add(A, B), 0.5);
  };

  /**
   * Get a vector comprised of the minimum of two or more vectors.
   */
  static min = (...v: number[][]) => {
    return [Math.min(...v.map(a => a[0])), Math.min(...v.map(a => a[1]))];
  };

  /**
   * Vector multiplication by scalar
   * @param A
   * @param n
   */
  static mul = (A: IVec, n: number): IVec => {
    return [A[0] * n, A[1] * n];
  };

  /**
   * Multiple two vectors.
   * @param A
   * @param B
   */
  static mulV = (A: IVec, B: IVec): IVec => {
    return [A[0] * B[0], A[1] * B[1]];
  };

  /**
   * Get the nearest point on a bounding box to a point P.
   * @param bounds The bounding box
   * @param P The point point
   * @returns
   */
  static nearestPointOnBounds = (
    bounds: {
      minX: number;
      minY: number;
      maxX: number;
      maxY: number;
    },
    P: number[]
  ): number[] => {
    return [
      Vec.clamp(P[0], bounds.minX, bounds.maxX),
      Vec.clamp(P[1], bounds.minY, bounds.maxY),
    ];
  };

  /**
   * Get the nearest point on a line segment between A and B
   * @param A The start of the line segment
   * @param B The end of the line segment
   * @param P The off-line point
   * @param clamp Whether to clamp the point between A and B.
   * @returns
   */
  static nearestPointOnLineSegment = (
    A: IVec,
    B: IVec,
    P: IVec,
    clamp = true
  ): IVec => {
    const u = Vec.uni(Vec.sub(B, A));
    const C = Vec.add(A, Vec.mul(u, Vec.pry(Vec.sub(P, A), u)));

    if (clamp) {
      if (C[0] < Math.min(A[0], B[0])) return A[0] < B[0] ? A : B;
      if (C[0] > Math.max(A[0], B[0])) return A[0] > B[0] ? A : B;
      if (C[1] < Math.min(A[1], B[1])) return A[1] < B[1] ? A : B;
      if (C[1] > Math.max(A[1], B[1])) return A[1] > B[1] ? A : B;
    }

    return C;
  };

  /**
   * Get the nearest point on a line with a known unit vector that passes through point A
   * @param A Any point on the line
   * @param u The unit vector for the line.
   * @param P A point not on the line to test.
   * @returns
   */
  static nearestPointOnLineThroughPoint = (A: IVec, u: IVec, P: IVec): IVec => {
    return Vec.add(A, Vec.mul(u, Vec.pry(Vec.sub(P, A), u)));
  };

  /**
   * Negate a vector.
   * @param A
   */
  static neg = (A: number[]): number[] => {
    return [-A[0], -A[1]];
  };

  /**
   * Get normalized / unit vector.
   * @param A
   */
  static normalize = (A: IVec): IVec => {
    return Vec.uni(A);
  };

  /**
   * Push a point A towards point B by a given distance.
   * @param A
   * @param B
   * @param d
   * @returns
   */
  static nudge = (A: IVec, B: IVec, d: number): number[] => {
    if (Vec.isEqual(A, B)) return A;
    return Vec.add(A, Vec.mul(Vec.uni(Vec.sub(B, A)), d));
  };

  /**
   * Push a point in a given angle by a given distance.
   * @param A
   * @param B
   * @param d
   */
  static nudgeAtAngle = (A: number[], a: number, d: number): number[] => {
    return [Math.cos(a) * d + A[0], Math.sin(a) * d + A[1]];
  };

  /**
   * Perpendicular rotation of a vector A
   * @param A
   */
  static per = (A: IVec): IVec => {
    return [A[1], -A[0]];
  };

  static pointOffset = (A: IVec, B: IVec, offset: number): IVec => {
    let u = Vec.uni(Vec.sub(B, A));
    if (Vec.isEqual(A, B)) u = A;
    return Vec.add(A, Vec.mul(u, offset));
  };

  /**
   * Get an array of points between two points.
   * @param A The first point.
   * @param B The second point.
   * @param steps The number of points to return.
   */
  static pointsBetween = (A: IVec, B: IVec, steps = 6): number[][] => {
    return Array.from({ length: steps }).map((_, i) => {
      const t = i / (steps - 1);
      const k = Math.min(1, 0.5 + Math.abs(0.5 - t));
      return [...Vec.lrp(A, B, t), k];
    });
  };

  /**
   * Project A over B
   * @param A
   * @param B
   */
  static pry = (A: number[], B: number[]): number => {
    return Vec.dpr(A, B) / Vec.len(B);
  };

  static rescale = (a: number[], n: number): number[] => {
    const l = Vec.len(a);
    return [(n * a[0]) / l, (n * a[1]) / l];
  };

  /**
   * Vector rotation by r (radians)
   * @param A
   * @param r rotation in radians
   */
  static rot = (A: number[], r = 0): IVec => {
    return [
      A[0] * Math.cos(r) - A[1] * Math.sin(r),
      A[0] * Math.sin(r) + A[1] * Math.cos(r),
    ];
  };

  /**
   * Rotate a vector around another vector by r (radians)
   * @param A vector
   * @param C center
   * @param r rotation in radians
   */
  static rotWith = (A: IVec, C: IVec, r = 0): IVec => {
    if (r === 0) return A;

    const s = Math.sin(r);
    const c = Math.cos(r);

    const px = A[0] - C[0];
    const py = A[1] - C[1];

    const nx = px * c - py * s;
    const ny = px * s + py * c;

    return [nx + C[0], ny + C[1]];
  };

  /**
   * Get the slope between two points.
   * @param A
   * @param B
   */
  static slope = (A: number[], B: number[]) => {
    if (A[0] === B[0]) return NaN;
    return (A[1] - B[1]) / (A[0] - B[0]);
  };

  /**
   * Subtract vectors.
   * @param A
   * @param B
   */
  static sub = (A: IVec, B: IVec): IVec => {
    return [A[0] - B[0], A[1] - B[1]];
  };

  /**
   * Subtract scalar from vector.
   * @param A
   * @param B
   */
  static subScalar = (A: IVec, n: number): IVec => {
    return [A[0] - n, A[1] - n];
  };

  /**
   * Get the tangent between two vectors.
   * @param A
   * @param B
   * @returns
   */
  static tangent = (A: IVec, B: IVec): IVec => {
    return Vec.uni(Vec.sub(A, B));
  };

  /**
   * Round a vector to two decimal places.
   * @param a
   */
  static toFixed = (a: number[]): number[] => {
    return a.map(v => Math.round(v * 100) / 100);
  };

  static toPoint = (v: IVec) => {
    return {
      x: v[0],
      y: v[1],
    };
  };

  /**
   * Round a vector to a precision length.
   * @param a
   * @param n
   */
  static toPrecision = (a: number[], n = 4): number[] => {
    return [+a[0].toPrecision(n), +a[1].toPrecision(n)];
  };

  static toVec = (v: { x: number; y: number }): IVec => [v.x, v.y];

  /**
   * Get normalized / unit vector.
   * @param A
   */
  static uni = (A: IVec): IVec => {
    return Vec.div(A, Vec.len(A));
  };

  /**
   * Get the vector from vectors A to B.
   * @param A
   * @param B
   */
  static vec = (A: IVec, B: IVec): IVec => {
    // A, B as vectors get the vector from A to B
    return [B[0] - A[0], B[1] - A[1]];
  };

  /**
   * Clamp a value into a range.
   * @param n
   * @param min
   */
  static clamp(n: number, min: number): number;

  // eslint-disable-next-line @typescript-eslint/unified-signatures
  static clamp(n: number, min: number, max: number): number;

  static clamp(n: number, min: number, max?: number): number {
    return Math.max(min, max !== undefined ? Math.min(n, max) : n);
  }

  /**
   * Clamp a value into a range.
   * @param n
   * @param min
   */
  static clampV(A: number[], min: number): number[];

  // eslint-disable-next-line @typescript-eslint/unified-signatures
  static clampV(A: number[], min: number, max: number): number[];

  static clampV(A: number[], min: number, max?: number): number[] {
    return A.map(n =>
      max !== undefined ? Vec.clamp(n, min, max) : Vec.clamp(n, min)
    );
  }

  /**
   * Cross (for point in polygon)
   *
   */
  static cross(x: number[], y: number[], z: number[]): number {
    return (y[0] - x[0]) * (z[1] - x[1]) - (z[0] - x[0]) * (y[1] - x[1]);
  }

  /**
   * Snap vector to nearest step.
   * @param A
   * @param step
   * @example
   * ```ts
   * Vec.snap([10.5, 28], 10) // [10, 30]
   * ```
   */
  static snap(a: number[], step = 1) {
    return [Math.round(a[0] / step) * step, Math.round(a[1] / step) * step];
  }
}