SVGPathDataTransformer.ts

/* eslint @typescript-eslint/no-explicit-any:0 */

// Transform SVG PathData
// http://www.w3.org/TR/SVG/paths.html#PathDataBNF

import {
  a2c,
  annotateArcCommand,
  arcAt,
  assertNumbers,
  bezierAt,
  bezierRoot,
  intersectionUnitCircleLine,
} from './mathUtils.js';
import { SVGPathData } from './SVGPathData.js';
import type { SVGCommand, TransformFunction } from './types.js';

// Predefined transforming functions
// Rounds commands values
function ROUND(roundVal = 1e13) {
  assertNumbers(roundVal);
  function rf(val: number) {
    return Math.round(val * roundVal) / roundVal;
  }
  return function round(command: SVGCommand) {
    if ('x1' in command && 'undefined' !== typeof command.x1) {
      command.x1 = rf(command.x1);
    }
    if ('y1' in command && 'undefined' !== typeof command.y1) {
      command.y1 = rf(command.y1);
    }

    if ('x2' in command && 'undefined' !== typeof command.x2) {
      command.x2 = rf(command.x2);
    }
    if ('y2' in command && 'undefined' !== typeof command.y2) {
      command.y2 = rf(command.y2);
    }

    if ('x' in command && 'undefined' !== typeof command.x) {
      command.x = rf(command.x);
    }
    if ('y' in command && 'undefined' !== typeof command.y) {
      command.y = rf(command.y);
    }

    if ('rX' in command && 'undefined' !== typeof command.rX) {
      command.rX = rf(command.rX);
    }
    if ('rY' in command && 'undefined' !== typeof command.rY) {
      command.rY = rf(command.rY);
    }

    return command;
  };
}

// Relative to absolute commands
function TO_ABS() {
  return INFO((command, prevX, prevY) => {
    if (command.relative) {
      // x1/y1 values
      if ('undefined' !== typeof command.x1) {
        command.x1 += prevX;
      }
      if ('undefined' !== typeof command.y1) {
        command.y1 += prevY;
      }
      // x2/y2 values
      if ('undefined' !== typeof command.x2) {
        command.x2 += prevX;
      }
      if ('undefined' !== typeof command.y2) {
        command.y2 += prevY;
      }
      // Finally x/y values
      if ('undefined' !== typeof command.x) {
        command.x += prevX;
      }
      if ('undefined' !== typeof command.y) {
        command.y += prevY;
      }
      command.relative = false;
    }
    return command;
  });
}
// Absolute to relative commands
function TO_REL() {
  return INFO((command, prevX, prevY) => {
    if (!command.relative) {
      // x1/y1 values
      if ('undefined' !== typeof command.x1) {
        command.x1 -= prevX;
      }
      if ('undefined' !== typeof command.y1) {
        command.y1 -= prevY;
      }
      // x2/y2 values
      if ('undefined' !== typeof command.x2) {
        command.x2 -= prevX;
      }
      if ('undefined' !== typeof command.y2) {
        command.y2 -= prevY;
      }
      // Finally x/y values
      if ('undefined' !== typeof command.x) {
        command.x -= prevX;
      }
      if ('undefined' !== typeof command.y) {
        command.y -= prevY;
      }
      command.relative = true;
    }
    return command;
  });
}
// Convert H, V, Z and A with rX = 0 to L
function NORMALIZE_HVZ(
  normalizeZ = true,
  normalizeH = true,
  normalizeV = true,
) {
  return INFO((command, prevX, prevY, pathStartX, pathStartY) => {
    if (isNaN(pathStartX) && !(command.type & SVGPathData.MOVE_TO)) {
      throw new Error('path must start with moveto');
    }
    if (normalizeH && command.type & SVGPathData.HORIZ_LINE_TO) {
      command.type = SVGPathData.LINE_TO;
      command.y = command.relative ? 0 : prevY;
    }
    if (normalizeV && command.type & SVGPathData.VERT_LINE_TO) {
      command.type = SVGPathData.LINE_TO;
      command.x = command.relative ? 0 : prevX;
    }
    if (normalizeZ && command.type & SVGPathData.CLOSE_PATH) {
      command.type = SVGPathData.LINE_TO;
      command.x = command.relative ? pathStartX - prevX : pathStartX;
      command.y = command.relative ? pathStartY - prevY : pathStartY;
    }
    if (
      command.type & SVGPathData.ARC &&
      (0 === command.rX || 0 === command.rY)
    ) {
      command.type = SVGPathData.LINE_TO;
      delete command.rX;
      delete command.rY;
      delete command.xRot;
      delete command.lArcFlag;
      delete command.sweepFlag;
    }
    return command;
  });
}
/*
 * Transforms smooth curves and quads to normal curves and quads (SsTt to CcQq)
 */
function NORMALIZE_ST() {
  let prevCurveC2X = NaN;
  let prevCurveC2Y = NaN;
  let prevQuadCX = NaN;
  let prevQuadCY = NaN;

  return INFO((command, prevX, prevY) => {
    if (command.type & SVGPathData.SMOOTH_CURVE_TO) {
      command.type = SVGPathData.CURVE_TO;
      prevCurveC2X = isNaN(prevCurveC2X) ? prevX : prevCurveC2X;
      prevCurveC2Y = isNaN(prevCurveC2Y) ? prevY : prevCurveC2Y;
      command.x1 = command.relative
        ? prevX - prevCurveC2X
        : 2 * prevX - prevCurveC2X;
      command.y1 = command.relative
        ? prevY - prevCurveC2Y
        : 2 * prevY - prevCurveC2Y;
    }
    if (command.type & SVGPathData.CURVE_TO) {
      prevCurveC2X = command.relative ? prevX + command.x2 : command.x2;
      prevCurveC2Y = command.relative ? prevY + command.y2 : command.y2;
    } else {
      prevCurveC2X = NaN;
      prevCurveC2Y = NaN;
    }
    if (command.type & SVGPathData.SMOOTH_QUAD_TO) {
      command.type = SVGPathData.QUAD_TO;
      prevQuadCX = isNaN(prevQuadCX) ? prevX : prevQuadCX;
      prevQuadCY = isNaN(prevQuadCY) ? prevY : prevQuadCY;
      command.x1 = command.relative
        ? prevX - prevQuadCX
        : 2 * prevX - prevQuadCX;
      command.y1 = command.relative
        ? prevY - prevQuadCY
        : 2 * prevY - prevQuadCY;
    }
    if (command.type & SVGPathData.QUAD_TO) {
      prevQuadCX = command.relative ? prevX + command.x1 : command.x1;
      prevQuadCY = command.relative ? prevY + command.y1 : command.y1;
    } else {
      prevQuadCX = NaN;
      prevQuadCY = NaN;
    }

    return command;
  });
}
/*
 * A quadratic bézier curve can be represented by a cubic bézier curve which has
 * the same end points as the quadratic and both control points in place of the
 * quadratic"s one.
 *
 * This transformer replaces QqTt commands with Cc commands respectively.
 * This is useful for reading path data into a system which only has a
 * representation for cubic curves.
 */
function QT_TO_C() {
  let prevQuadX1 = NaN;
  let prevQuadY1 = NaN;

  return INFO((command, prevX, prevY) => {
    if (command.type & SVGPathData.SMOOTH_QUAD_TO) {
      command.type = SVGPathData.QUAD_TO;
      prevQuadX1 = isNaN(prevQuadX1) ? prevX : prevQuadX1;
      prevQuadY1 = isNaN(prevQuadY1) ? prevY : prevQuadY1;
      command.x1 = command.relative
        ? prevX - prevQuadX1
        : 2 * prevX - prevQuadX1;
      command.y1 = command.relative
        ? prevY - prevQuadY1
        : 2 * prevY - prevQuadY1;
    }
    if (command.type & SVGPathData.QUAD_TO) {
      prevQuadX1 = command.relative ? prevX + command.x1 : command.x1;
      prevQuadY1 = command.relative ? prevY + command.y1 : command.y1;
      const x1 = command.x1;
      const y1 = command.y1;

      command.type = SVGPathData.CURVE_TO;
      command.x1 = ((command.relative ? 0 : prevX) + x1 * 2) / 3;
      command.y1 = ((command.relative ? 0 : prevY) + y1 * 2) / 3;
      command.x2 = (command.x + x1 * 2) / 3;
      command.y2 = (command.y + y1 * 2) / 3;
    } else {
      prevQuadX1 = NaN;
      prevQuadY1 = NaN;
    }

    return command;
  });
}
function INFO(
  f: (
    command: any,
    prevXAbs: number,
    prevYAbs: number,
    pathStartXAbs: number,
    pathStartYAbs: number,
  ) => any | any[],
) {
  let prevXAbs = 0;
  let prevYAbs = 0;
  let pathStartXAbs = NaN;
  let pathStartYAbs = NaN;

  return function transform(command: SVGCommand) {
    if (isNaN(pathStartXAbs) && !(command.type & SVGPathData.MOVE_TO)) {
      throw new Error('path must start with moveto');
    }

    const result = f(command, prevXAbs, prevYAbs, pathStartXAbs, pathStartYAbs);

    if (command.type & SVGPathData.CLOSE_PATH) {
      prevXAbs = pathStartXAbs;
      prevYAbs = pathStartYAbs;
    }

    if ('x' in command && 'undefined' !== typeof command.x) {
      prevXAbs = command.relative ? prevXAbs + command.x : command.x;
    }
    if ('y' in command && 'undefined' !== typeof command.y) {
      prevYAbs = command.relative ? prevYAbs + command.y : command.y;
    }

    if (command.type & SVGPathData.MOVE_TO) {
      pathStartXAbs = prevXAbs;
      pathStartYAbs = prevYAbs;
    }

    return result;
  };
}

/*
 * remove 0-length segments
 */
function SANITIZE(EPS = 0) {
  assertNumbers(EPS);
  let prevCurveC2X = NaN;
  let prevCurveC2Y = NaN;
  let prevQuadCX = NaN;
  let prevQuadCY = NaN;

  return INFO((command, prevX, prevY, pathStartX, pathStartY) => {
    const abs = Math.abs;
    let skip = false;
    let x1Rel = 0;
    let y1Rel = 0;

    if (command.type & SVGPathData.SMOOTH_CURVE_TO) {
      x1Rel = isNaN(prevCurveC2X) ? 0 : prevX - prevCurveC2X;
      y1Rel = isNaN(prevCurveC2Y) ? 0 : prevY - prevCurveC2Y;
    }
    if (command.type & (SVGPathData.CURVE_TO | SVGPathData.SMOOTH_CURVE_TO)) {
      prevCurveC2X = command.relative ? prevX + command.x2 : command.x2;
      prevCurveC2Y = command.relative ? prevY + command.y2 : command.y2;
    } else {
      prevCurveC2X = NaN;
      prevCurveC2Y = NaN;
    }
    if (command.type & SVGPathData.SMOOTH_QUAD_TO) {
      prevQuadCX = isNaN(prevQuadCX) ? prevX : 2 * prevX - prevQuadCX;
      prevQuadCY = isNaN(prevQuadCY) ? prevY : 2 * prevY - prevQuadCY;
    } else if (command.type & SVGPathData.QUAD_TO) {
      prevQuadCX = command.relative ? prevX + command.x1 : command.x1;
      prevQuadCY = command.relative ? prevY + command.y1 : command.y2;
    } else {
      prevQuadCX = NaN;
      prevQuadCY = NaN;
    }

    if (
      command.type & SVGPathData.LINE_COMMANDS ||
      (command.type & SVGPathData.ARC &&
        (0 === command.rX || 0 === command.rY || !command.lArcFlag)) ||
      command.type & SVGPathData.CURVE_TO ||
      command.type & SVGPathData.SMOOTH_CURVE_TO ||
      command.type & SVGPathData.QUAD_TO ||
      command.type & SVGPathData.SMOOTH_QUAD_TO
    ) {
      const xRel =
        'undefined' === typeof command.x
          ? 0
          : command.relative
            ? command.x
            : command.x - prevX;
      const yRel =
        'undefined' === typeof command.y
          ? 0
          : command.relative
            ? command.y
            : command.y - prevY;

      x1Rel = !isNaN(prevQuadCX)
        ? prevQuadCX - prevX
        : 'undefined' === typeof command.x1
          ? x1Rel
          : command.relative
            ? command.x
            : command.x1 - prevX;
      y1Rel = !isNaN(prevQuadCY)
        ? prevQuadCY - prevY
        : 'undefined' === typeof command.y1
          ? y1Rel
          : command.relative
            ? command.y
            : command.y1 - prevY;

      const x2Rel =
        'undefined' === typeof command.x2
          ? 0
          : command.relative
            ? command.x
            : command.x2 - prevX;
      const y2Rel =
        'undefined' === typeof command.y2
          ? 0
          : command.relative
            ? command.y
            : command.y2 - prevY;

      if (
        abs(xRel) <= EPS &&
        abs(yRel) <= EPS &&
        abs(x1Rel) <= EPS &&
        abs(y1Rel) <= EPS &&
        abs(x2Rel) <= EPS &&
        abs(y2Rel) <= EPS
      ) {
        skip = true;
      }
    }

    if (command.type & SVGPathData.CLOSE_PATH) {
      if (abs(prevX - pathStartX) <= EPS && abs(prevY - pathStartY) <= EPS) {
        skip = true;
      }
    }

    return skip ? [] : command;
  });
}

// SVG Transforms : http://www.w3.org/TR/SVGTiny12/coords.html#TransformList
// Matrix : http://apike.ca/prog_svg_transform.html
// a c e
// b d f
function MATRIX(
  a: number,
  b: number,
  c: number,
  d: number,
  e: number,
  f: number,
) {
  assertNumbers(a, b, c, d, e, f);

  return INFO((command, prevX, prevY, pathStartX) => {
    const origX1 = command.x1;
    const origX2 = command.x2;
    // if isNaN(pathStartX), then this is the first command, which is ALWAYS an
    // absolute MOVE_TO, regardless what the relative flag says
    const comRel = command.relative && !isNaN(pathStartX);
    const x = 'undefined' !== typeof command.x ? command.x : comRel ? 0 : prevX;
    const y = 'undefined' !== typeof command.y ? command.y : comRel ? 0 : prevY;

    if (command.type & SVGPathData.HORIZ_LINE_TO && 0 !== b) {
      command.type = SVGPathData.LINE_TO;
      command.y = command.relative ? 0 : prevY;
    }
    if (command.type & SVGPathData.VERT_LINE_TO && 0 !== c) {
      command.type = SVGPathData.LINE_TO;
      command.x = command.relative ? 0 : prevX;
    }

    if ('undefined' !== typeof command.x) {
      command.x = command.x * a + y * c + (comRel ? 0 : e);
    }
    if ('undefined' !== typeof command.y) {
      command.y = x * b + command.y * d + (comRel ? 0 : f);
    }
    if ('undefined' !== typeof command.x1) {
      command.x1 = command.x1 * a + command.y1 * c + (comRel ? 0 : e);
    }
    if ('undefined' !== typeof command.y1) {
      command.y1 = origX1 * b + command.y1 * d + (comRel ? 0 : f);
    }
    if ('undefined' !== typeof command.x2) {
      command.x2 = command.x2 * a + command.y2 * c + (comRel ? 0 : e);
    }
    if ('undefined' !== typeof command.y2) {
      command.y2 = origX2 * b + command.y2 * d + (comRel ? 0 : f);
    }
    function sqr(x: number) {
      return x * x;
    }
    const det = a * d - b * c;

    if ('undefined' !== typeof command.xRot) {
      // Skip if this is a pure translation
      if (1 !== a || 0 !== b || 0 !== c || 1 !== d) {
        // Special case for singular matrix
        if (0 === det) {
          // In the singular case, the arc is compressed to a line. The actual geometric image of the original
          // curve under this transform possibly extends beyond the starting and/or ending points of the segment, but
          // for simplicity we ignore this detail and just replace this command with a single line segment.
          delete command.rX;
          delete command.rY;
          delete command.xRot;
          delete command.lArcFlag;
          delete command.sweepFlag;
          command.type = SVGPathData.LINE_TO;
        } else {
          // Convert to radians
          const xRot = (command.xRot * Math.PI) / 180;

          // Convert rotated ellipse to general conic form
          // x0^2/rX^2 + y0^2/rY^2 - 1 = 0
          // x0 = x*cos(xRot) + y*sin(xRot)
          // y0 = -x*sin(xRot) + y*cos(xRot)
          // --> A*x^2 + B*x*y + C*y^2 - 1 = 0, where
          const sinRot = Math.sin(xRot);
          const cosRot = Math.cos(xRot);
          const xCurve = 1 / sqr(command.rX);
          const yCurve = 1 / sqr(command.rY);
          const A = sqr(cosRot) * xCurve + sqr(sinRot) * yCurve;
          const B = 2 * sinRot * cosRot * (xCurve - yCurve);
          const C = sqr(sinRot) * xCurve + sqr(cosRot) * yCurve;

          // Apply matrix to A*x^2 + B*x*y + C*y^2 - 1 = 0
          // x1 = a*x + c*y
          // y1 = b*x + d*y
          //      (we can ignore e and f, since pure translations don"t affect the shape of the ellipse)
          // --> A1*x1^2 + B1*x1*y1 + C1*y1^2 - det^2 = 0, where
          const A1 = A * d * d - B * b * d + C * b * b;
          const B1 = B * (a * d + b * c) - 2 * (A * c * d + C * a * b);
          const C1 = A * c * c - B * a * c + C * a * a;

          // Unapply newXRot to get back to axis-aligned ellipse equation
          // x1 = x2*cos(newXRot) - y2*sin(newXRot)
          // y1 = x2*sin(newXRot) + y2*cos(newXRot)
          // A1*x1^2 + B1*x1*y1 + C1*y1^2 - det^2 =
          //   x2^2*(A1*cos(newXRot)^2 + B1*sin(newXRot)*cos(newXRot) + C1*sin(newXRot)^2)
          //   + x2*y2*(2*(C1 - A1)*sin(newXRot)*cos(newXRot) + B1*(cos(newXRot)^2 - sin(newXRot)^2))
          //   + y2^2*(A1*sin(newXRot)^2 - B1*sin(newXRot)*cos(newXRot) + C1*cos(newXRot)^2)
          //   (which must have the same zeroes as)
          // x2^2/newRX^2 + y2^2/newRY^2 - 1
          //   (so we have)
          // 2*(C1 - A1)*sin(newXRot)*cos(newXRot) + B1*(cos(newXRot)^2 - sin(newXRot)^2) = 0
          // (A1 - C1)*sin(2*newXRot) = B1*cos(2*newXRot)
          // 2*newXRot = atan2(B1, A1 - C1)
          const newXRot = ((Math.atan2(B1, A1 - C1) + Math.PI) % Math.PI) / 2;
          // For any integer n, (atan2(B1, A1 - C1) + n*pi)/2 is a solution to the above; incrementing n just swaps
          // the x and y radii computed below (since that"s what rotating an ellipse by pi/2 does).  Choosing the
          // rotation between 0 and pi/2 eliminates the ambiguity and leads to more predictable output.

          // Finally, we get newRX and newRY from the same-zeroes relationship that gave us newXRot
          const newSinRot = Math.sin(newXRot);
          const newCosRot = Math.cos(newXRot);

          command.rX =
            Math.abs(det) /
            Math.sqrt(
              A1 * sqr(newCosRot) +
                B1 * newSinRot * newCosRot +
                C1 * sqr(newSinRot),
            );
          command.rY =
            Math.abs(det) /
            Math.sqrt(
              A1 * sqr(newSinRot) -
                B1 * newSinRot * newCosRot +
                C1 * sqr(newCosRot),
            );
          command.xRot = (newXRot * 180) / Math.PI;
        }
      }
    }
    // sweepFlag needs to be inverted when mirroring shapes
    // see http://www.itk.ilstu.edu/faculty/javila/SVG/SVG_drawing1/elliptical_curve.htm
    // m 65,10 a 50,25 0 1 0 50,25
    // M 65,60 A 50,25 0 1 1 115,35
    if ('undefined' !== typeof command.sweepFlag && 0 > det) {
      command.sweepFlag = +!command.sweepFlag;
    }
    return command;
  });
}

function ROTATE(a: number, x = 0, y = 0) {
  assertNumbers(a, x, y);
  const sin = Math.sin(a);
  const cos = Math.cos(a);

  return MATRIX(
    cos,
    sin,
    -sin,
    cos,
    x - x * cos + y * sin,
    y - x * sin - y * cos,
  );
}

function TRANSLATE(dX: number, dY = 0) {
  assertNumbers(dX, dY);
  return MATRIX(1, 0, 0, 1, dX, dY);
}

function SCALE(dX: number, dY = dX) {
  assertNumbers(dX, dY);
  return MATRIX(dX, 0, 0, dY, 0, 0);
}

function SKEW_X(a: number) {
  assertNumbers(a);
  return MATRIX(1, 0, Math.atan(a), 1, 0, 0);
}

function SKEW_Y(a: number) {
  assertNumbers(a);
  return MATRIX(1, Math.atan(a), 0, 1, 0, 0);
}

function X_AXIS_SYMMETRY(xOffset = 0) {
  assertNumbers(xOffset);
  return MATRIX(-1, 0, 0, 1, xOffset, 0);
}

function Y_AXIS_SYMMETRY(yOffset = 0) {
  assertNumbers(yOffset);
  return MATRIX(1, 0, 0, -1, 0, yOffset);
}

// Convert arc commands to curve commands
function A_TO_C() {
  return INFO((command, prevX, prevY) => {
    if (SVGPathData.ARC === command.type) {
      return a2c(
        command,
        command.relative ? 0 : prevX,
        command.relative ? 0 : prevY,
      );
    }
    return command;
  });
}

// @see annotateArcCommand
function ANNOTATE_ARCS() {
  return INFO((c, x1, y1) => {
    if (c.relative) {
      x1 = 0;
      y1 = 0;
    }
    if (SVGPathData.ARC === c.type) {
      annotateArcCommand(c, x1, y1);
    }
    return c;
  });
}
function CLONE<T extends SVGCommand>() {
  return (c: T): T => {
    return { ...c };
  };
}

// @see annotateArcCommand
function CALCULATE_BOUNDS() {
  const clone = CLONE();
  const toAbs = TO_ABS();
  const qtToC = QT_TO_C();
  const normST = NORMALIZE_ST();
  const f: TransformFunction & {
    minX: number;
    maxX: number;
    minY: number;
    maxY: number;
  } = INFO((command, prevXAbs, prevYAbs) => {
    const c = normST(qtToC(toAbs(clone(command))));
    function fixX(absX: number) {
      if (absX > f.maxX) {
        f.maxX = absX;
      }
      if (absX < f.minX) {
        f.minX = absX;
      }
    }
    function fixY(absY: number) {
      if (absY > f.maxY) {
        f.maxY = absY;
      }
      if (absY < f.minY) {
        f.minY = absY;
      }
    }
    if (c.type & SVGPathData.DRAWING_COMMANDS) {
      fixX(prevXAbs);
      fixY(prevYAbs);
    }
    if (c.type & SVGPathData.HORIZ_LINE_TO) {
      fixX(c.x);
    }
    if (c.type & SVGPathData.VERT_LINE_TO) {
      fixY(c.y);
    }
    if (c.type & SVGPathData.LINE_TO) {
      fixX(c.x);
      fixY(c.y);
    }
    if (c.type & SVGPathData.CURVE_TO) {
      // add start and end points
      fixX(c.x);
      fixY(c.y);
      const xDerivRoots = bezierRoot(prevXAbs, c.x1, c.x2, c.x);

      for (const derivRoot of xDerivRoots) {
        if (0 < derivRoot && 1 > derivRoot) {
          fixX(bezierAt(prevXAbs, c.x1, c.x2, c.x, derivRoot));
        }
      }
      const yDerivRoots = bezierRoot(prevYAbs, c.y1, c.y2, c.y);

      for (const derivRoot of yDerivRoots) {
        if (0 < derivRoot && 1 > derivRoot) {
          fixY(bezierAt(prevYAbs, c.y1, c.y2, c.y, derivRoot));
        }
      }
    }
    if (c.type & SVGPathData.ARC) {
      // add start and end points
      fixX(c.x);
      fixY(c.y);
      annotateArcCommand(c, prevXAbs, prevYAbs);
      // p = cos(phi) * xv + sin(phi) * yv
      // dp = -sin(phi) * xv + cos(phi) * yv = 0
      const xRotRad = (c.xRot / 180) * Math.PI;
      // points on ellipse for phi = 0° and phi = 90°
      const x0 = Math.cos(xRotRad) * c.rX;
      const y0 = Math.sin(xRotRad) * c.rX;
      const x90 = -Math.sin(xRotRad) * c.rY;
      const y90 = Math.cos(xRotRad) * c.rY;

      // annotateArcCommand returns phi1 and phi2 such that -180° < phi1 < 180° and phi2 is smaller or greater
      // depending on the sweep flag. Calculate phiMin, phiMax such that -180° < phiMin < 180° and phiMin < phiMax
      const [phiMin, phiMax] =
        c.phi1 < c.phi2
          ? [c.phi1, c.phi2]
          : -180 > c.phi2
            ? [c.phi2 + 360, c.phi1 + 360]
            : [c.phi2, c.phi1];
      const normalizeXiEta = ([xi, eta]: [number, number]) => {
        const phiRad = Math.atan2(eta, xi);
        const phi = (phiRad * 180) / Math.PI;

        return phi < phiMin ? phi + 360 : phi;
      };
      // xi = cos(phi), eta = sin(phi)

      const xDerivRoots = intersectionUnitCircleLine(x90, -x0, 0).map(
        normalizeXiEta,
      );
      for (const derivRoot of xDerivRoots) {
        if (derivRoot > phiMin && derivRoot < phiMax) {
          fixX(arcAt(c.cX, x0, x90, derivRoot));
        }
      }

      const yDerivRoots = intersectionUnitCircleLine(y90, -y0, 0).map(
        normalizeXiEta,
      );
      for (const derivRoot of yDerivRoots) {
        if (derivRoot > phiMin && derivRoot < phiMax) {
          fixY(arcAt(c.cY, y0, y90, derivRoot));
        }
      }
    }
    return command;
  }) as any;

  f.minX = Infinity;
  f.maxX = -Infinity;
  f.minY = Infinity;
  f.maxY = -Infinity;
  return f;
}

export const SVGPathDataTransformer = {
  ROUND,
  TO_ABS,
  TO_REL,
  NORMALIZE_HVZ,
  NORMALIZE_ST,
  QT_TO_C,
  INFO,
  SANITIZE,
  MATRIX,
  ROTATE,
  TRANSLATE,
  SCALE,
  SKEW_X,
  SKEW_Y,
  X_AXIS_SYMMETRY,
  Y_AXIS_SYMMETRY,
  A_TO_C,
  ANNOTATE_ARCS,
  CLONE,
  CALCULATE_BOUNDS,
};