One Hat Cyber Team

Edit File: SVGPathDataTransformer.ts

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

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

export namespace SVGPathDataTransformer {
  // Predefined transforming functions
  // Rounds commands values
  export function ROUND(roundVal = 1e13) {
    assertNumbers(roundVal);
    function rf(val: number) { return Math.round(val * roundVal) / roundVal; }
    return function round(command: any) {
      if ("undefined" !== typeof command.x1) {
        command.x1 = rf(command.x1);
      }
      if ("undefined" !== typeof command.y1) {
        command.y1 = rf(command.y1);
      }

if ("undefined" !== typeof command.x2) {
        command.x2 = rf(command.x2);
      }
      if ("undefined" !== typeof command.y2) {
        command.y2 = rf(command.y2);
      }

if ("undefined" !== typeof command.x) {
        command.x = rf(command.x);
      }
      if ("undefined" !== typeof command.y) {
        command.y = rf(command.y);
      }

if ("undefined" !== typeof command.rX) {
        command.rX = rf(command.rX);
      }
      if ("undefined" !== typeof command.rY) {
        command.rY = rf(command.rY);
      }

return command;
    };
  }
  // Relative to absolute commands
  export 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
  export 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
  export 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)
   */
  export 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.
   */
  export 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;
    });
  }
  export 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: any) {
      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 ("undefined" !== typeof command.x) {
        prevXAbs = (command.relative ? prevXAbs + command.x : command.x);
      }
      if ("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
   */
  export 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
  export 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;
    });
  }
  export 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);
  }
  export function TRANSLATE(dX: number, dY = 0) {
    assertNumbers(dX, dY);
    return MATRIX(1, 0, 0, 1, dX, dY);
  }
  export function SCALE(dX: number, dY = dX) {
    assertNumbers(dX, dY);
    return MATRIX(dX, 0, 0, dY, 0, 0);
  }
  export function SKEW_X(a: number) {
    assertNumbers(a);
    return MATRIX(1, 0, Math.atan(a), 1, 0, 0);
  }
  export function SKEW_Y(a: number) {
    assertNumbers(a);
    return MATRIX(1, Math.atan(a), 0, 1, 0, 0);
  }
  export function X_AXIS_SYMMETRY(xOffset = 0) {
    assertNumbers(xOffset);
    return MATRIX(-1, 0, 0, 1, xOffset, 0);
  }
  export function Y_AXIS_SYMMETRY(yOffset = 0) {
    assertNumbers(yOffset);
    return MATRIX(1, 0, 0, -1, 0, yOffset);
  }
  // Convert arc commands to curve commands
  export 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
  export 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;
    });
  }
  export function CLONE() {
    return (c: SVGCommand) => {
      const result = {} as SVGCommand;
      // tslint:disable-next-line
      for (const key in c) {
        result[key as keyof SVGCommand] = c[key as keyof SVGCommand];
      }
      return result;
    };
  }
  // @see annotateArcCommand
  export 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;
  }
}