pro3/node_modules/svg-pathdata/src/mathUtils.ts

import { SVGPathData } from "./SVGPathData";
import { CommandA, CommandC } from "./types";

export function rotate([x, y]: [number, number], rad: number) {
  return [
    x * Math.cos(rad) - y * Math.sin(rad),
    x * Math.sin(rad) + y * Math.cos(rad),
  ];
}

const DEBUG_CHECK_NUMBERS = true;
export function assertNumbers(...numbers: number[]) {
  if (DEBUG_CHECK_NUMBERS) {
    for (let i = 0; i < numbers.length; i++) {
      if ("number" !== typeof numbers[i]) {
        throw new Error(
          `assertNumbers arguments[${i}] is not a number. ${typeof numbers[i]} == typeof ${numbers[i]}`);
      }
    }
  }
  return true;
}

const PI = Math.PI;

/**
 * https://www.w3.org/TR/SVG/implnote.html#ArcImplementationNotes
 * Fixes rX and rY.
 * Ensures lArcFlag and sweepFlag are 0 or 1
 * Adds center coordinates: command.cX, command.cY (relative or absolute, depending on command.relative)
 * Adds start and end arc parameters (in degrees): command.phi1, command.phi2; phi1 < phi2 iff. c.sweepFlag == true
 */
export function annotateArcCommand(c: CommandA, x1: number, y1: number) {
  c.lArcFlag = (0 === c.lArcFlag) ? 0 : 1;
  c.sweepFlag = (0 === c.sweepFlag) ? 0 : 1;
  // tslint:disable-next-line
  let {rX, rY, x, y} = c;

  rX = Math.abs(c.rX);
  rY = Math.abs(c.rY);
  const [x1_, y1_] = rotate([(x1 - x) / 2, (y1 - y) / 2], -c.xRot / 180 * PI);
  const testValue = Math.pow(x1_, 2) / Math.pow(rX, 2) + Math.pow(y1_, 2) / Math.pow(rY, 2);

  if (1 < testValue) {
    rX *= Math.sqrt(testValue);
    rY *= Math.sqrt(testValue);
  }
  c.rX = rX;
  c.rY = rY;
  const c_ScaleTemp = (Math.pow(rX, 2) * Math.pow(y1_, 2) + Math.pow(rY, 2) * Math.pow(x1_, 2));
  const c_Scale = (c.lArcFlag !== c.sweepFlag ? 1 : -1) *
    Math.sqrt(Math.max(0, (Math.pow(rX, 2) * Math.pow(rY, 2) - c_ScaleTemp) / c_ScaleTemp));
  const cx_ = rX * y1_ / rY * c_Scale;
  const cy_ = -rY * x1_ / rX * c_Scale;
  const cRot = rotate([cx_, cy_], c.xRot / 180 * PI);

  c.cX = cRot[0] + (x1 + x) / 2;
  c.cY = cRot[1] + (y1 + y) / 2;
  c.phi1 = Math.atan2((y1_ - cy_) / rY, (x1_ - cx_) / rX);
  c.phi2 = Math.atan2((-y1_ - cy_) / rY, (-x1_ - cx_) / rX);
  if (0 === c.sweepFlag && c.phi2 > c.phi1) {
    c.phi2 -= 2 * PI;
  }
  if (1 === c.sweepFlag && c.phi2 < c.phi1) {
    c.phi2 += 2 * PI;
  }
  c.phi1 *= 180 / PI;
  c.phi2 *= 180 / PI;
}

/**
 * Solves a quadratic system of equations of the form
 *      a * x + b * y = c
 *      x² + y² = 1
 * This can be understood as the intersection of the unit circle with a line.
 *      => y = (c - a x) / b
 *      => x² + (c - a x)² / b² = 1
 *      => x² b² + c² - 2 c a x + a² x² = b²
 *      => (a² + b²) x² - 2 a c x + (c² - b²) = 0
 */
export function intersectionUnitCircleLine(a: number, b: number, c: number): [number, number][] {
  assertNumbers(a, b, c);
  // cf. pqFormula
  const termSqr = a * a + b * b - c * c;

  if (0 > termSqr) {
    return [];
  } else if (0 === termSqr) {
    return [
      [
        (a * c) / (a * a + b * b),
        (b * c) / (a * a + b * b)]];
  }
  const term = Math.sqrt(termSqr);

  return [
    [
      (a * c + b * term) / (a * a + b * b),
      (b * c - a * term) / (a * a + b * b)],
    [
      (a * c - b * term) / (a * a + b * b),
      (b * c + a * term) / (a * a + b * b)]];

}

export const DEG = Math.PI / 180;

export function lerp(a: number, b: number, t: number) {
  return (1 - t) * a + t * b;
}

export function arcAt(c: number, x1: number, x2: number, phiDeg: number) {
  return c + Math.cos(phiDeg / 180 * PI) * x1 + Math.sin(phiDeg / 180 * PI) * x2;
}

export function bezierRoot(x0: number, x1: number, x2: number, x3: number) {
  const EPS = 1e-6;
  const x01 = x1 - x0;
  const x12 = x2 - x1;
  const x23 = x3 - x2;
  const a = 3 * x01 + 3 * x23 - 6 * x12;
  const b = (x12 - x01) * 6;
  const c = 3 * x01;
  // solve a * t² + b * t + c = 0

  if (Math.abs(a) < EPS) {
    // equivalent to b * t + c =>
    return [-c / b];
  }
  return pqFormula(b / a, c / a, EPS);

}

export function bezierAt(x0: number, x1: number, x2: number, x3: number, t: number) {
  // console.log(x0, y0, x1, y1, x2, y2, x3, y3, t)
  const s = 1 - t;
  const c0 = s * s * s;
  const c1 = 3 * s * s * t;
  const c2 = 3 * s * t * t;
  const c3 = t * t * t;

  return x0 * c0 + x1 * c1 + x2 * c2 + x3 * c3;
}

function pqFormula(p: number, q: number, PRECISION = 1e-6) {
  // 4 times the discriminant:in
  const discriminantX4 = p * p / 4 - q;

  if (discriminantX4 < -PRECISION) {
    return [];
  } else if (discriminantX4 <= PRECISION) {
    return [-p / 2];
  }
  const root = Math.sqrt(discriminantX4);

  return [-(p / 2) - root, -(p / 2) + root];

}

export function a2c(arc: CommandA, x0: number, y0: number): CommandC[] {
  if (!arc.cX) {
    annotateArcCommand(arc, x0, y0);
  }

  const phiMin = Math.min(arc.phi1!, arc.phi2!), phiMax = Math.max(arc.phi1!, arc.phi2!), deltaPhi = phiMax - phiMin;
  const partCount = Math.ceil(deltaPhi / 90 );

  const result: CommandC[] = new Array(partCount);
  let prevX = x0, prevY = y0;
  for (let i = 0; i < partCount; i++) {
    const phiStart = lerp(arc.phi1!, arc.phi2!, i / partCount);
    const phiEnd = lerp(arc.phi1!, arc.phi2!, (i + 1) / partCount);
    const deltaPhi = phiEnd - phiStart;
    const f = 4 / 3 * Math.tan(deltaPhi * DEG / 4);
    // x1/y1, x2/y2 and x/y coordinates on the unit circle for phiStart/phiEnd
    const [x1, y1] = [
      Math.cos(phiStart * DEG) - f * Math.sin(phiStart * DEG),
      Math.sin(phiStart * DEG) + f * Math.cos(phiStart * DEG)];
    const [x, y] = [Math.cos(phiEnd * DEG), Math.sin(phiEnd * DEG)];
    const [x2, y2] = [x + f * Math.sin(phiEnd * DEG), y - f * Math.cos(phiEnd * DEG)];
    result[i] = {relative: arc.relative, type: SVGPathData.CURVE_TO } as any;
    const transform = (x: number, y: number) => {
      const [xTemp, yTemp] = rotate([x * arc.rX, y * arc.rY], arc.xRot);
      return [arc.cX! + xTemp, arc.cY! + yTemp];
    };
    [result[i].x1, result[i].y1] = transform(x1, y1);
    [result[i].x2, result[i].y2] = transform(x2, y2);
    [result[i].x, result[i].y] = transform(x, y);
    if (arc.relative) {
      result[i].x1 -= prevX;
      result[i].y1 -= prevY;
      result[i].x2 -= prevX;
      result[i].y2 -= prevY;
      result[i].x -= prevX;
      result[i].y -= prevY;
    }
    [prevX, prevY] = [result[i].x, result[i].y];
  }
  return result;
}