All files / plugins _path.ts

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import * as _collections from './_collections';
import * as _tools from './_tools';
 
import { JsApi } from '../lib/jsapi';
 
const regPathInstructions = /([MmLlHhVvCcSsQqTtAaZz])\s*/;
const regPathData = /[-+]?(?:\d*\.\d+|\d+\.?)([eE][-+]?\d+)?/g;
const regNumericValues = /[-+]?(\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/;
const referencesProps = _collections.referencesProps;
const defaultStrokeWidth =
  _collections.attrsGroupsDefaults.presentation['stroke-width'];
const cleanupOutData = _tools.cleanupOutData;
const removeLeadingZero = _tools.removeLeadingZero;
let prevCtrlPoint: number[];
 
export interface PathItem {
  instruction: string;
  data?: number[];
  coords?: number[];
  base?: number[];
}
 
export type Point = [number, number];
 
export type Curve = [number, number, number, number, number, number];
 
export interface Circle {
  center: Point;
  radius: number;
}
 
/**
 * Convert path string to JS representation.
 */
export function path2js(path: JsApi) {
  // TODO: avoid this caching hackery...
  if (path.pathJS) {
    return path.pathJS;
  }
 
  // prettier-ignore
  const paramsLength: {[key: string]: number} = {
    // Number of parameters of every path command
    H: 1, V: 1, M: 2, L: 2, T: 2, Q: 4, S: 4, C: 6, A: 7,
    h: 1, v: 1, m: 2, l: 2, t: 2, q: 4, s: 4, c: 6, a: 7,
  };
  const pathData: Array<{ instruction: string; data?: number[] }> = [];
  let instruction: string;
  let startMoveto = false;
 
  // splitting path string into array like ['M', '10 50', 'L', '20 30']
  path
    .attr('android:pathData')
    .value.split(regPathInstructions)
    .forEach(data => {
      if (!data) {
        return;
      }
      if (!startMoveto) {
        if (data === 'M' || data === 'm') {
          startMoveto = true;
        } else {
          return;
        }
      }
 
      // Instruction item.
      if (regPathInstructions.test(data)) {
        instruction = data;
 
        // Z - instruction w/o data.
        if (instruction === 'Z' || instruction === 'z') {
          pathData.push({ instruction: 'z' });
        }
      } else {
        // Data item.
        const matchedData = data.match(regPathData);
        Iif (!matchedData) {
          return;
        }
 
        const matchedNumData = matchedData.map(Number);
 
        // Subsequent moveto pairs of coordinates are threated as implicit lineto commands
        // http://www.w3.org/TR/SVG/paths.html#PathDataMovetoCommands
        if (instruction === 'M' || instruction === 'm') {
          pathData.push({
            instruction: pathData.length === 0 ? 'M' : instruction,
            data: matchedNumData.splice(0, 2),
          });
          instruction = instruction === 'M' ? 'L' : 'l';
        }
 
        for (const pair = paramsLength[instruction]; matchedNumData.length; ) {
          pathData.push({ instruction, data: matchedNumData.splice(0, pair) });
        }
      }
    });
 
  // First moveto is actually absolute. Subsequent coordinates were separated above.
  Iif (pathData.length && pathData[0].instruction === 'm') {
    pathData[0].instruction = 'M';
  }
 
  // TODO: avoid this caching hackery...
  path.pathJS = pathData;
 
  return pathData;
}
 
/**
 * Convert absolute path data coordinates to relative.
 *
 * @param {Array} path input path data
 * @param {Object} params plugin params
 * @return {Array} output path data
 */
export function convertToRelative(path: PathItem[]) {
  const point = [0, 0];
  const subpathPoint = [0, 0];
  let baseItem: PathItem;
 
  path.forEach((item, index) => {
    let instruction = item.instruction;
    const data = item.data;
 
    // data !== !z
    if (data) {
      // already relative
      // recalculate current point
      if ('mcslqta'.indexOf(instruction) > -1) {
        point[0] += data[data.length - 2];
        point[1] += data[data.length - 1];
 
        if (instruction === 'm') {
          subpathPoint[0] = point[0];
          subpathPoint[1] = point[1];
          baseItem = item;
        }
      } else if (instruction === 'h') {
        point[0] += data[0];
      } else if (instruction === 'v') {
        point[1] += data[0];
      }
 
      // convert absolute path data coordinates to relative
      // if "M" was not transformed from "m"
      // M → m
      if (instruction === 'M') {
        if (index > 0) {
          instruction = 'm';
        }
 
        data[0] -= point[0];
        data[1] -= point[1];
 
        subpathPoint[0] = point[0] += data[0];
        subpathPoint[1] = point[1] += data[1];
 
        baseItem = item;
      } else if ('LT'.indexOf(instruction) > -1) {
        // L → l
        // T → t
        instruction = instruction.toLowerCase();
 
        // x y
        // 0 1
        data[0] -= point[0];
        data[1] -= point[1];
 
        point[0] += data[0];
        point[1] += data[1];
 
        // C → c
      } else if (instruction === 'C') {
        instruction = 'c';
 
        // x1 y1 x2 y2 x y
        // 0  1  2  3  4 5
        data[0] -= point[0];
        data[1] -= point[1];
        data[2] -= point[0];
        data[3] -= point[1];
        data[4] -= point[0];
        data[5] -= point[1];
 
        point[0] += data[4];
        point[1] += data[5];
 
        // S → s
        // Q → q
      } else if ('SQ'.indexOf(instruction) > -1) {
        instruction = instruction.toLowerCase();
 
        // x1 y1 x y
        // 0  1  2 3
        data[0] -= point[0];
        data[1] -= point[1];
        data[2] -= point[0];
        data[3] -= point[1];
 
        point[0] += data[2];
        point[1] += data[3];
 
        // A → a
      } else if (instruction === 'A') {
        instruction = 'a';
 
        // rx ry x-axis-rotation large-arc-flag sweep-flag x y
        // 0  1  2               3              4          5 6
        data[5] -= point[0];
        data[6] -= point[1];
 
        point[0] += data[5];
        point[1] += data[6];
 
        // H → h
      } else if (instruction === 'H') {
        instruction = 'h';
 
        data[0] -= point[0];
 
        point[0] += data[0];
 
        // V → v
      } else if (instruction === 'V') {
        instruction = 'v';
 
        data[0] -= point[1];
 
        point[1] += data[0];
      }
 
      item.instruction = instruction;
      item.data = data;
 
      // store absolute coordinates for later use
      item.coords = point.slice(-2);
    } else Eif (instruction === 'z') {
      // !data === z, reset current point
      Eif (baseItem) {
        item.coords = baseItem.coords;
      }
      point[0] = subpathPoint[0];
      point[1] = subpathPoint[1];
    }
 
    item.base = index > 0 ? path[index - 1].coords : [0, 0];
  });
 
  return path;
}
 
/**
 * Convert relative Path data to absolute.
 *
 * @param {Array} data input data
 * @return {Array} output data
 */
function relative2absolute(data: PathItem[]) {
  const currentPoint = [0, 0];
  const subpathPoint = [0, 0];
 
  return data.map(item => {
    const instruction = item.instruction;
    const itemData = item.data && item.data.slice();
 
    if (instruction === 'M') {
      set(currentPoint, itemData);
      set(subpathPoint, itemData);
    } else if ('mlcsqt'.indexOf(instruction) > -1) {
      for (let i = 0; i < itemData.length; i++) {
        itemData[i] += currentPoint[i % 2];
      }
      set(currentPoint, itemData);
      Iif (instruction === 'm') {
        set(subpathPoint, itemData);
      }
    } else if (instruction === 'a') {
      itemData[5] += currentPoint[0];
      itemData[6] += currentPoint[1];
      set(currentPoint, itemData);
    } else if (instruction === 'h') {
      itemData[0] += currentPoint[0];
      currentPoint[0] = itemData[0];
    } else if (instruction === 'v') {
      itemData[0] += currentPoint[1];
      currentPoint[1] = itemData[0];
    } else if ('MZLCSQTA'.indexOf(instruction) > -1) {
      set(currentPoint, itemData);
    } else if (instruction === 'H') {
      currentPoint[0] = itemData[0];
    } else if (instruction === 'V') {
      currentPoint[1] = itemData[0];
    } else Eif (instruction === 'z') {
      set(currentPoint, subpathPoint);
    }
    return instruction === 'z'
      ? { instruction: 'z' }
      : {
          instruction: instruction.toUpperCase(),
          data: itemData,
        };
  });
}
 
/**
 * Apply transformation(s) to the Path data.
 *
 * @param {Object} elem current element
 * @param {Array} path input path data
 * @param {Object} params whether to apply transforms to stroked lines and transform precision (used for stroke width)
 * @return {Array} output path data
 */
export function applyTransforms(
  group: JsApi,
  elem: JsApi,
  path: PathItem[],
  params: { transformPrecision: number; applyTransformsStroked: boolean },
) {
  // if there are no 'stroke' attr and references to other objects such as
  // gradiends or clip-path which are also subjects to transform.
  // if (
  //   !elem.hasAttr('transform') ||
  //   !elem.attr('transform').value ||
  //   elem.someAttr(attr => {
  //     const refProps = referencesProps;
  //     // tslint:disable-next-line:no-bitwise
  //     const res = ~refProps.indexOf(attr.name) && ~attr.value.indexOf('url(');
  //     return !!res;
  //   })
  // ) {
  //   return path;
  // }
 
  const groupAttrs = getGroupAttrs(group);
  const matrix = {
    name: 'matrix',
    data: groupToMatrix(groupAttrs),
  };
 
  // const stroke = elem.computedAttr('stroke');
  // const id = elem.computedAttr('id');
  const transformPrecision = params.transformPrecision;
  let newPoint: number[];
  // let scale: number;
 
  // if (stroke && stroke !== 'none') {
  //   if (
  //     !params.applyTransformsStroked ||
  //     ((matrix.data[0] !== matrix.data[3] ||
  //       matrix.data[1] !== -matrix.data[2]) &&
  //       (matrix.data[0] !== -matrix.data[3] ||
  //         matrix.data[1] !== matrix.data[2]))
  //   ) {
  //     return path;
  //   }
 
  //   // "stroke-width" should be inside the part with ID, otherwise it can be overrided in <use>
  //   if (id) {
  //     let idElem = elem;
  //     let hasStrokeWidth = false;
  //     do {
  //       if (idElem.hasAttr('stroke-width')) {
  //         hasStrokeWidth = true;
  //       }
  //     } while (
  //       !idElem.hasAttr('id', id) &&
  //       !hasStrokeWidth &&
  //       (idElem = idElem.parentNode)
  //     );
  //     if (!hasStrokeWidth) {
  //       return path;
  //     }
  //   }
 
  //   scale = +Math.sqrt(
  //     matrix.data[0] * matrix.data[0] + matrix.data[1] * matrix.data[1],
  //   ).toFixed(transformPrecision);
 
  //   if (scale !== 1) {
  //     // TODO: can we avoid the cast to string here?
  //     const strokeWidth = (elem.computedAttr('stroke-width') ||
  //       defaultStrokeWidth) as string;
 
  //     if (elem.hasAttr('stroke-width')) {
  //       elem.attrs['stroke-width'].value = elem.attrs['stroke-width'].value
  //         .trim()
  //         .replace(regNumericValues, num => removeLeadingZero(+num * scale));
  //     } else {
  //       elem.addAttr({
  //         name: 'stroke-width',
  //         prefix: '',
  //         local: 'stroke-width',
  //         value: strokeWidth.replace(regNumericValues, num =>
  //           removeLeadingZero(+num * scale),
  //         ),
  //       });
  //     }
  //   }
  // } else if (id) {
  //   // Stroke and stroke-width can be redefined with <use>
  //   return path;
  // }
 
  path.forEach(pathItem => {
    if (pathItem.data) {
      // h -> l
      if (pathItem.instruction === 'h') {
        pathItem.instruction = 'l';
        pathItem.data[1] = 0;
 
        // v -> l
      } else Iif (pathItem.instruction === 'v') {
        pathItem.instruction = 'l';
        pathItem.data[1] = pathItem.data[0];
        pathItem.data[0] = 0;
      }
 
      // if there is a translate() transform
      if (
        pathItem.instruction === 'M' &&
        (matrix.data[4] !== 0 || matrix.data[5] !== 0)
      ) {
        // then apply it only to the first absoluted M
        newPoint = transformPoint(
          matrix.data,
          pathItem.data[0],
          pathItem.data[1],
        );
        set(pathItem.data, newPoint);
        set(pathItem.coords, newPoint);
 
        // clear translate() data from transform matrix
        matrix.data[4] = 0;
        matrix.data[5] = 0;
      } else {
        if (pathItem.instruction === 'a') {
          transformArc(pathItem.data, matrix.data);
 
          // reduce number of digits in rotation angle
          Iif (Math.abs(pathItem.data[2]) > 80) {
            const a = pathItem.data[0];
            const rotation = pathItem.data[2];
            pathItem.data[0] = pathItem.data[1];
            pathItem.data[1] = a;
            pathItem.data[2] = rotation + (rotation > 0 ? -90 : 90);
          }
 
          newPoint = transformPoint(
            matrix.data,
            pathItem.data[5],
            pathItem.data[6],
          );
          pathItem.data[5] = newPoint[0];
          pathItem.data[6] = newPoint[1];
        } else {
          for (let i = 0; i < pathItem.data.length; i += 2) {
            newPoint = transformPoint(
              matrix.data,
              pathItem.data[i],
              pathItem.data[i + 1],
            );
            pathItem.data[i] = newPoint[0];
            pathItem.data[i + 1] = newPoint[1];
          }
        }
 
        pathItem.coords[0] =
          pathItem.base[0] + pathItem.data[pathItem.data.length - 2];
        pathItem.coords[1] =
          pathItem.base[1] + pathItem.data[pathItem.data.length - 1];
      }
    }
  });
 
  // remove transform attr
  // elem.removeAttr('transform');
 
  return path;
}
 
export function getGroupAttrs(group: JsApi) {
  const px = getGroupAttr(group, 'pivotX', 0);
  const py = getGroupAttr(group, 'pivotY', 0);
  const sx = getGroupAttr(group, 'scaleX', 1);
  const sy = getGroupAttr(group, 'scaleY', 1);
  const tx = getGroupAttr(group, 'translateX', 0);
  const ty = getGroupAttr(group, 'translateY', 0);
  const r = getGroupAttr(group, 'rotation', 0);
  return { px, py, sx, sy, tx, ty, r };
}
 
function getGroupAttr(
  group: JsApi,
  attrLocalName: string,
  defaultValue: number,
) {
  const attrName = `android:${attrLocalName}`;
  const result = group.hasAttr(attrName)
    ? +group.attr(attrName).value
    : defaultValue;
  return result;
}
 
function removeGroupAttrs(group: JsApi) {
  group.removeAttr('android:pivotX');
  group.removeAttr('android:pivotY');
  group.removeAttr('android:scaleX');
  group.removeAttr('android:scaleY');
  group.removeAttr('android:translateX');
  group.removeAttr('android:translateY');
  group.removeAttr('android:rotation');
}
 
export type Matrix = [number, number, number, number, number, number];
 
export interface GroupTransform {
  sx: number;
  sy: number;
  r: number;
  tx: number;
  ty: number;
  px: number;
  py: number;
}
 
/**
 * Extracts the x/y scaling from the transformation matrix.
 */
export function getScaling(matrix: Matrix) {
  const [a, b, c, d] = matrix;
  const sx = (a >= 0 ? 1 : -1) * Math.hypot(a, c);
  const sy = (d >= 0 ? 1 : -1) * Math.hypot(b, d);
  return { sx, sy };
}
/**
 * Extracts the rotation in degrees from the transformation matrix.
 */
export function getRotation(matrix: Matrix) {
  return { r: 180 / Math.PI * Math.atan2(-matrix[2], matrix[0]) };
}
 
/**
 * Extracts the x/y translation from the transformation matrix.
 */
export function getTranslation(matrix: Matrix) {
  return { tx: matrix[4], ty: matrix[5] };
}
 
function flattenMatrices(...matrices: Matrix[]) {
  const identity: Matrix = [1, 0, 0, 1, 0, 0];
  return matrices.reduce((m1, m2) => {
    // [a c e]   [a' c' e']
    // [b d f] * [b' d' f']
    // [0 0 1]   [0  0  1 ]
    return [
      m1[0] * m2[0] + m1[2] * m2[1],
      m1[1] * m2[0] + m1[3] * m2[1],
      m1[0] * m2[2] + m1[2] * m2[3],
      m1[1] * m2[2] + m1[3] * m2[3],
      m1[0] * m2[4] + m1[2] * m2[5] + m1[4],
      m1[1] * m2[4] + m1[3] * m2[5] + m1[5],
    ];
  }, identity);
}
 
function groupToMatrix({ sx, sy, r, tx, ty, px, py }: GroupTransform) {
  const cosr = Math.cos(r * Math.PI / 180);
  const sinr = Math.sin(r * Math.PI / 180);
  return flattenMatrices(
    [1, 0, 0, 1, px, py],
    [1, 0, 0, 1, tx, ty],
    [cosr, sinr, -sinr, cosr, 0, 0],
    [sx, 0, 0, sy, 0, 0],
    [1, 0, 0, 1, -px, -py],
  );
}
 
export function flattenGroups(groups: GroupTransform[]) {
  return flattenMatrices(...groups.map(groupToMatrix));
}
 
/**
 * Apply transform 3x3 matrix to x-y point.
 *
 * @param {Array} matrix transform 3x3 matrix
 * @param {Array} point x-y point
 * @return {Array} point with new coordinates
 */
function transformPoint(matrix: number[], x: number, y: number) {
  return [
    matrix[0] * x + matrix[2] * y + matrix[4],
    matrix[1] * x + matrix[3] * y + matrix[5],
  ];
}
 
/**
 * Compute Cubic Bézier bounding box.
 * @see http://processingjs.nihongoresources.com/bezierinfo/
 */
export function computeCubicBoundingBox(
  xa: number,
  ya: number,
  xb: number,
  yb: number,
  xc: number,
  yc: number,
  xd: number,
  yd: number,
) {
  let minx = Number.POSITIVE_INFINITY;
  let miny = Number.POSITIVE_INFINITY;
  let maxx = Number.NEGATIVE_INFINITY;
  let maxy = Number.NEGATIVE_INFINITY;
  let ts: number[];
  let t: number;
  let x: number;
  let y: number;
  let i: number;
 
  // X
  if (xa < minx) {
    minx = xa;
  }
  if (xa > maxx) {
    maxx = xa;
  }
  if (xd < minx) {
    minx = xd;
  }
  if (xd > maxx) {
    maxx = xd;
  }
 
  ts = computeCubicFirstDerivativeRoots(xa, xb, xc, xd);
 
  for (i = 0; i < ts.length; i++) {
    t = ts[i];
    if (t >= 0 && t <= 1) {
      x = computeCubicBaseValue(t, xa, xb, xc, xd);
      if (x < minx) {
        minx = x;
      }
      if (x > maxx) {
        maxx = x;
      }
    }
  }
 
  // Y
  if (ya < miny) {
    miny = ya;
  }
  if (ya > maxy) {
    maxy = ya;
  }
  if (yd < miny) {
    miny = yd;
  }
  if (yd > maxy) {
    maxy = yd;
  }
 
  ts = computeCubicFirstDerivativeRoots(ya, yb, yc, yd);
 
  for (i = 0; i < ts.length; i++) {
    t = ts[i];
    if (t >= 0 && t <= 1) {
      y = computeCubicBaseValue(t, ya, yb, yc, yd);
      if (y < miny) {
        miny = y;
      }
      if (y > maxy) {
        maxy = y;
      }
    }
  }
 
  return { minx, miny, maxx, maxy };
}
 
// Compute the value for the cubic bezier function at time t.
function computeCubicBaseValue(
  t: number,
  a: number,
  b: number,
  c: number,
  d: number,
) {
  const mt = 1 - t;
  return (
    mt * mt * mt * a + 3 * mt * mt * t * b + 3 * mt * t * t * c + t * t * t * d
  );
}
 
// Compute the value for the first derivative of the cubic bezier function at time t.
function computeCubicFirstDerivativeRoots(
  a: number,
  b: number,
  c: number,
  d: number,
) {
  const result = [-1, -1];
  const tl = -a + 2 * b - c;
  const tr = -Math.sqrt(-a * (c - d) + b * b - b * (c + d) + c * c);
  const dn = -a + 3 * b - 3 * c + d;
  if (dn !== 0) {
    result[0] = (tl + tr) / dn;
    result[1] = (tl - tr) / dn;
  }
  return result;
}
 
/**
 * Compute Quadratic Bézier bounding box.
 *
 * @see http://processingjs.nihongoresources.com/bezierinfo/
 */
export function computeQuadraticBoundingBox(
  xa: number,
  ya: number,
  xb: number,
  yb: number,
  xc: number,
  yc: number,
) {
  let minx = Number.POSITIVE_INFINITY;
  let miny = Number.POSITIVE_INFINITY;
  let maxx = Number.NEGATIVE_INFINITY;
  let maxy = Number.NEGATIVE_INFINITY;
  let t: number;
  let x: number;
  let y: number;
 
  // X
  if (xa < minx) {
    minx = xa;
  }
  if (xa > maxx) {
    maxx = xa;
  }
  if (xc < minx) {
    minx = xc;
  }
  if (xc > maxx) {
    maxx = xc;
  }
 
  t = computeQuadraticFirstDerivativeRoot(xa, xb, xc);
  if (t >= 0 && t <= 1) {
    x = computeQuadraticBaseValue(t, xa, xb, xc);
    if (x < minx) {
      minx = x;
    }
    if (x > maxx) {
      maxx = x;
    }
  }
 
  // Y
  if (ya < miny) {
    miny = ya;
  }
  if (ya > maxy) {
    maxy = ya;
  }
  if (yc < miny) {
    miny = yc;
  }
  if (yc > maxy) {
    maxy = yc;
  }
 
  t = computeQuadraticFirstDerivativeRoot(ya, yb, yc);
  if (t >= 0 && t <= 1) {
    y = computeQuadraticBaseValue(t, ya, yb, yc);
    if (y < miny) {
      miny = y;
    }
    if (y > maxy) {
      maxy = y;
    }
  }
 
  return { minx, miny, maxx, maxy };
}
 
// Compute the value for the quadratic bezier function at time t.
function computeQuadraticBaseValue(t: number, a: number, b: number, c: number) {
  const mt = 1 - t;
  return mt * mt * a + 2 * mt * t * b + t * t * c;
}
 
// Compute the value for the first derivative of the quadratic bezier function at time t.
function computeQuadraticFirstDerivativeRoot(a: number, b: number, c: number) {
  let t = -1;
  const denominator = a - 2 * b + c;
  if (denominator !== 0) {
    t = (a - b) / denominator;
  }
  return t;
}
 
/**
 * Convert path array to string.
 */
export function js2path(
  path: JsApi,
  data: PathItem[],
  params: {
    collapseRepeated: boolean;
    leadingZero: boolean;
    negativeExtraSpace: boolean;
  },
) {
  path.pathJS = data;
  Eif (params.collapseRepeated) {
    data = collapseRepeated(data);
  }
  path.attr('android:pathData').value = data.reduce((pathString, item) => {
    return (pathString +=
      item.instruction + (item.data ? cleanupOutData(item.data, params) : ''));
  }, '');
}
 
/**
 * Collapse repeated instructions data.
 */
function collapseRepeated(data: PathItem[]) {
  let prev: PathItem;
  let prevIndex: number;
 
  // Copy an array and modifieds item to keep original data untouched.
  return data.reduce(
    (newPath, item) => {
      if (prev && item.data && item.instruction === prev.instruction) {
        // Concat previous data with current.
        if (item.instruction !== 'M') {
          prev = newPath[prevIndex] = {
            instruction: prev.instruction,
            data: prev.data.concat(item.data),
            coords: item.coords,
            base: prev.base,
          };
        } else {
          prev.data = item.data;
          prev.coords = item.coords;
        }
      } else {
        newPath.push(item);
        prev = item;
        prevIndex = newPath.length - 1;
      }
      return newPath;
    },
    [] as PathItem[],
  );
}
 
function set(dest: number[], source: number[]) {
  dest[0] = source[source.length - 2];
  dest[1] = source[source.length - 1];
  return dest;
}
 
/**
 * Checks if two paths have an intersection by checking convex hulls
 * collision using Gilbert-Johnson-Keerthi distance algorithm
 * http://entropyinteractive.com/2011/04/gjk-algorithm/
 *
 * @param {Array} path1 JS path representation
 * @param {Array} path2 JS path representation
 * @return {Boolean}
 */
export function intersects(path1: PathItem[], path2: PathItem[]) {
  if (path1.length < 3 || path2.length < 3) {
    return false; // Nothing to fill.
  }
 
  // Collect points of every subpath.
  const points1 = relative2absolute(path1).reduce(gatherPoints, []);
  const points2 = relative2absolute(path2).reduce(gatherPoints, []);
 
  // Axis-aligned bounding box check.
  if (
    points1.maxX <= points2.minX ||
    points2.maxX <= points1.minX ||
    points1.maxY <= points2.minY ||
    points2.maxY <= points1.minY ||
    points1.every(set1 => {
      return points2.every(set2 => {
        return (
          set1[set1.maxX][0] <= set2[set2.minX][0] ||
          set2[set2.maxX][0] <= set1[set1.minX][0] ||
          set1[set1.maxY][1] <= set2[set2.minY][1] ||
          set2[set2.maxY][1] <= set1[set1.minY][1]
        );
      });
    })
  ) {
    return false;
  }
 
  // Get a convex hull from points of each subpath. Has the most complexity O(n·log n).
  const hullNest1 = points1.map(convexHull);
  const hullNest2 = points2.map(convexHull);
 
  // Check intersection of every subpath of the first path with every subpath of the second.
  return hullNest1.some(hull1 => {
    Iif (hull1.length < 3) {
      return false;
    }
 
    return hullNest2.some(hull2 => {
      Iif (hull2.length < 3) {
        return false;
      }
 
      const simplex = [getSupport(hull1, hull2, [1, 0])]; // create the initial simplex
      const direction = minus(simplex[0]); // set the direction to point towards the origin
 
      let iterations = 1e4; // infinite loop protection, 10 000 iterations is more than enough
      while (true) {
        Iif (iterations-- === 0) {
          console.error(
            'Error: infinite loop while processing mergePaths plugin.',
          );
          return true; // true is the safe value that means “do nothing with paths”
        }
        // add a new point
        simplex.push(getSupport(hull1, hull2, direction));
        // see if the new point was on the correct side of the origin
        if (dot(direction, simplex[simplex.length - 1]) <= 0) {
          return false;
        }
        // process the simplex
        if (processSimplex(simplex, direction)) {
          return true;
        }
      }
    });
  });
 
  type Polygon = number[][] & MinMax;
 
  function getSupport(a: Polygon, b: Polygon, direction: number[]) {
    return sub(supportPoint(a, direction), supportPoint(b, minus(direction)));
  }
 
  // Computes farthest polygon point in particular direction.
  // Thanks to knowledge of min/max x and y coordinates we can choose a quadrant to search in.
  // Since we're working on convex hull, the dot product is increasing until we find the farthest point.
  function supportPoint(polygon: Polygon, direction: number[]) {
    let index =
      direction[1] >= 0
        ? direction[0] < 0 ? polygon.maxY : polygon.maxX
        : direction[0] < 0 ? polygon.minX : polygon.minY;
    let max = -Infinity;
    let value;
    while ((value = dot(polygon[index], direction)) > max) {
      max = value;
      index = ++index % polygon.length;
    }
    return polygon[(index || polygon.length) - 1];
  }
}
 
function processSimplex(simplex: number[][], direction: number[]) {
  // wW only need to handle to 1-simplex and 2-simplex.
  if (simplex.length === 2) {
    // 1-simplex
    const a = simplex[1];
    const b = simplex[0];
    const AO = minus(simplex[1]);
    const AB = sub(b, a);
    // AO is in the same direction as AB
    Eif (dot(AO, AB) > 0) {
      // get the vector perpendicular to AB facing O
      set(direction, orth(AB, a));
    } else {
      set(direction, AO);
      // only A remains in the simplex
      simplex.shift();
    }
  } else {
    // 2-simplex
    const a = simplex[2]; // [a, b, c] = simplex
    const b = simplex[1];
    const c = simplex[0];
    const AB = sub(b, a);
    const AC = sub(c, a);
    const AO = minus(a);
    const ACB = orth(AB, AC); // the vector perpendicular to AB facing away from C
    const ABC = orth(AC, AB); // the vector perpendicular to AC facing away from B
 
    if (dot(ACB, AO) > 0) {
      Eif (dot(AB, AO) > 0) {
        // region 4
        set(direction, ACB);
        simplex.shift(); // simplex = [b, a]
      } else {
        // region 5
        set(direction, AO);
        simplex.splice(0, 2); // simplex = [a]
      }
    } else if (dot(ABC, AO) > 0) {
      Eif (dot(AC, AO) > 0) {
        // region 6
        set(direction, ABC);
        simplex.splice(1, 1); // simplex = [c, a]
      } else {
        // region 5 (again)
        set(direction, AO);
        simplex.splice(0, 2); // simplex = [a]
      }
    } else {
      return true; // region 7
    }
  }
  return false;
}
 
function minus(v: number[]) {
  return [-v[0], -v[1]];
}
 
function sub(v1: number[], v2: number[]) {
  return [v1[0] - v2[0], v1[1] - v2[1]];
}
 
function dot(v1: number[], v2: number[]) {
  return v1[0] * v2[0] + v1[1] * v2[1];
}
 
function orth(v: number[], from: number[]) {
  const o = [-v[1], v[0]];
  return dot(o, minus(from)) < 0 ? minus(o) : o;
}
 
interface MinMax {
  maxX: number;
  maxY: number;
  minX: number;
  minY: number;
}
 
function gatherPoints(
  points: Array<number[][] & Partial<MinMax>> & Partial<MinMax>,
  item: PathItem,
  index: number,
  path: PathItem[],
) {
  let subPath = points.length && points[points.length - 1];
  const prev = index && path[index - 1];
  let basePoint = subPath.length && subPath[subPath.length - 1];
  const data = item.data;
  let ctrlPoint = basePoint;
 
  switch (item.instruction) {
    case 'M':
      points.push((subPath = []));
      break;
    case 'H':
      addPoint(subPath, [data[0], basePoint[1]]);
      break;
    case 'V':
      addPoint(subPath, [basePoint[0], data[0]]);
      break;
    case 'Q':
      addPoint(subPath, data.slice(0, 2));
      prevCtrlPoint = [data[2] - data[0], data[3] - data[1]]; // Save control point for shorthand
      break;
    case 'T':
      if (prev.instruction === 'Q' || prev.instruction === 'T') {
        ctrlPoint = [
          basePoint[0] + prevCtrlPoint[0],
          basePoint[1] + prevCtrlPoint[1],
        ];
        addPoint(subPath, ctrlPoint);
        prevCtrlPoint = [data[0] - ctrlPoint[0], data[1] - ctrlPoint[1]];
      }
      break;
    case 'C':
      // Approximate quibic Bezier curve with middle points between control points
      addPoint(subPath, [
        0.5 * (basePoint[0] + data[0]),
        0.5 * (basePoint[1] + data[1]),
      ]);
      addPoint(subPath, [0.5 * (data[0] + data[2]), 0.5 * (data[1] + data[3])]);
      addPoint(subPath, [0.5 * (data[2] + data[4]), 0.5 * (data[3] + data[5])]);
      prevCtrlPoint = [data[4] - data[2], data[5] - data[3]]; // Save control point for shorthand
      break;
    case 'S':
      Eif (prev.instruction === 'C' || prev.instruction === 'S') {
        addPoint(subPath, [
          basePoint[0] + 0.5 * prevCtrlPoint[0],
          basePoint[1] + 0.5 * prevCtrlPoint[1],
        ]);
        ctrlPoint = [
          basePoint[0] + prevCtrlPoint[0],
          basePoint[1] + prevCtrlPoint[1],
        ];
      }
      addPoint(subPath, [
        0.5 * (ctrlPoint[0] + data[0]),
        0.5 * (ctrlPoint[1] + data[1]),
      ]);
      addPoint(subPath, [0.5 * (data[0] + data[2]), 0.5 * (data[1] + data[3])]);
      prevCtrlPoint = [data[2] - data[0], data[3] - data[1]];
      break;
    case 'A':
      // Convert the arc to bezier curves and use the same approximation
      const curves = a2c.apply(0, basePoint.concat(data));
      for (let cData; (cData = curves.splice(0, 6).map(toAbsolute)).length; ) {
        addPoint(subPath, [
          0.5 * (basePoint[0] + cData[0]),
          0.5 * (basePoint[1] + cData[1]),
        ]);
        addPoint(subPath, [
          0.5 * (cData[0] + cData[2]),
          0.5 * (cData[1] + cData[3]),
        ]);
        addPoint(subPath, [
          0.5 * (cData[2] + cData[4]),
          0.5 * (cData[3] + cData[5]),
        ]);
        if (curves.length) {
          addPoint(subPath, (basePoint = cData.slice(-2)));
        }
      }
      break;
  }
  // Save final command coordinates
  if (data && data.length >= 2) {
    addPoint(subPath, data.slice(-2));
  }
  return points;
 
  function toAbsolute(n: number, i: number) {
    return n + basePoint[i % 2];
  }
 
  // Writes data about the extreme points on each axle
  function addPoint(p: number[][] & Partial<MinMax>, point: number[]) {
    if (!p.length || point[1] > p[p.maxY][1]) {
      p.maxY = p.length;
      points.maxY = points.length ? Math.max(point[1], points.maxY) : point[1];
    }
    if (!p.length || point[0] > p[p.maxX][0]) {
      p.maxX = p.length;
      points.maxX = points.length ? Math.max(point[0], points.maxX) : point[0];
    }
    if (!p.length || point[1] < p[p.minY][1]) {
      p.minY = p.length;
      points.minY = points.length ? Math.min(point[1], points.minY) : point[1];
    }
    if (!p.length || point[0] < p[p.minX][0]) {
      p.minX = p.length;
      points.minX = points.length ? Math.min(point[0], points.minX) : point[0];
    }
    p.push(point);
  }
}
 
/**
 * Forms a convex hull from set of points of every subpath using monotone chain convex hull algorithm.
 * http://en.wikibooks.org/wiki/Algorithm_Implementation/Geometry/Convex_hull/Monotone_chain
 *
 * @param points An array of [X, Y] coordinates
 */
function convexHull(points: number[][]) {
  points.sort((a, b) => (a[0] === b[0] ? a[1] - b[1] : a[0] - b[0]));
 
  const lower = [];
  let minY = 0;
  let bottom = 0;
  for (let i = 0; i < points.length; i++) {
    while (
      lower.length >= 2 &&
      cross(lower[lower.length - 2], lower[lower.length - 1], points[i]) <= 0
    ) {
      lower.pop();
    }
    if (points[i][1] < points[minY][1]) {
      minY = i;
      bottom = lower.length;
    }
    lower.push(points[i]);
  }
 
  const upper = [];
  let maxY = points.length - 1;
  let top = 0;
  for (let i = points.length; i--; ) {
    while (
      upper.length >= 2 &&
      cross(upper[upper.length - 2], upper[upper.length - 1], points[i]) <= 0
    ) {
      upper.pop();
    }
    if (points[i][1] > points[maxY][1]) {
      maxY = i;
      top = upper.length;
    }
    upper.push(points[i]);
  }
 
  // last points are equal to starting points of the other part
  upper.pop();
  lower.pop();
 
  const hull: any = lower.concat(upper);
  hull.minX = 0; // by sorting
  hull.maxX = lower.length;
  hull.minY = bottom;
  hull.maxY = (lower.length + top) % hull.length;
  return hull;
}
 
function cross(o: number[], a: number[], b: number[]) {
  return (a[0] - o[0]) * (b[1] - o[1]) - (a[1] - o[1]) * (b[0] - o[0]);
}
 
/*
 * Based on code from Snap.svg (Apache 2 license). http://snapsvg.io/
 * Thanks to Dmitry Baranovskiy for his great work!
 */
function a2c(
  x1: number,
  y1: number,
  rx: number,
  ry: number,
  angle: number,
  large_arc_flag: number,
  sweep_flag: number,
  x2: number,
  y2: number,
  recursive: number[],
) {
  // For more information of where this Math came from visit:
  // http://www.w3.org/TR/SVG11/implnote.html#ArcImplementationNotes
  const _120 = Math.PI * 120 / 180;
  const rad = Math.PI / 180 * (+angle || 0);
  let res: number[] = [];
  const rotateX = (x: number, y: number, r: number) =>
    x * Math.cos(r) - y * Math.sin(r);
  const rotateY = (x: number, y: number, r: number) =>
    x * Math.sin(r) + y * Math.cos(r);
  let f1: number;
  let f2: number;
  let cx: number;
  let cy: number;
  if (!recursive) {
    x1 = rotateX(x1, y1, -rad);
    y1 = rotateY(x1, y1, -rad);
    x2 = rotateX(x2, y2, -rad);
    y2 = rotateY(x2, y2, -rad);
    const x = (x1 - x2) / 2;
    const y = (y1 - y2) / 2;
    let h = x * x / (rx * rx) + y * y / (ry * ry);
    Iif (h > 1) {
      h = Math.sqrt(h);
      rx = h * rx;
      ry = h * ry;
    }
    const rx2 = rx * rx;
    const ry2 = ry * ry;
    const k =
      (large_arc_flag === sweep_flag ? -1 : 1) *
      Math.sqrt(
        Math.abs(
          (rx2 * ry2 - rx2 * y * y - ry2 * x * x) / (rx2 * y * y + ry2 * x * x),
        ),
      );
    cx = k * rx * y / ry + (x1 + x2) / 2;
    cy = k * -ry * x / rx + (y1 + y2) / 2;
    f1 = Math.asin(+((y1 - cy) / ry).toFixed(9));
    f2 = Math.asin(+((y2 - cy) / ry).toFixed(9));
 
    f1 = x1 < cx ? Math.PI - f1 : f1;
    f2 = x2 < cx ? Math.PI - f2 : f2;
    Eif (f1 < 0) {
      f1 = Math.PI * 2 + f1;
    }
    Iif (f2 < 0) {
      f2 = Math.PI * 2 + f2;
    }
    Eif (sweep_flag && f1 > f2) {
      f1 = f1 - Math.PI * 2;
    }
    Iif (!sweep_flag && f2 > f1) {
      f2 = f2 - Math.PI * 2;
    }
  } else {
    f1 = recursive[0];
    f2 = recursive[1];
    cx = recursive[2];
    cy = recursive[3];
  }
  let df = f2 - f1;
  if (Math.abs(df) > _120) {
    const f2old = f2;
    const x2old = x2;
    const y2old = y2;
    f2 = f1 + _120 * (sweep_flag && f2 > f1 ? 1 : -1);
    x2 = cx + rx * Math.cos(f2);
    y2 = cy + ry * Math.sin(f2);
    res = a2c(x2, y2, rx, ry, angle, 0, sweep_flag, x2old, y2old, [
      f2,
      f2old,
      cx,
      cy,
    ]);
  }
  df = f2 - f1;
  const c1 = Math.cos(f1);
  const s1 = Math.sin(f1);
  const c2 = Math.cos(f2);
  const s2 = Math.sin(f2);
  const t = Math.tan(df / 4);
  const hx = 4 / 3 * rx * t;
  const hy = 4 / 3 * ry * t;
  const m = [
    -hx * s1,
    hy * c1,
    x2 + hx * s2 - x1,
    y2 - hy * c2 - y1,
    x2 - x1,
    y2 - y1,
  ];
  if (recursive) {
    return m.concat(res);
  } else {
    res = m.concat(res);
    const newRes: number[] = [];
    for (let i = 0, n = res.length; i < n; i++) {
      newRes[i] =
        i % 2
          ? rotateY(res[i - 1], res[i], rad)
          : rotateX(res[i], res[i + 1], rad);
    }
    return newRes;
  }
}
 
/**
 * Applies transformation to an arc. To do so, we represent ellipse as a matrix, multiply it
 * by the transformation matrix and use a singular value decomposition to represent in a form
 * rotate(θ)·scale(a b)·rotate(φ). This gives us new ellipse params a, b and θ.
 * SVD is being done with the formulae provided by Wolffram|Alpha (svd {{m0, m2}, {m1, m3}})
 *
 * @param {Array} arc [a, b, rotation in deg]
 * @param {Array} transform transformation matrix
 * @return {Array} arc transformed input arc
 */
function transformArc(arc: number[], transform: Matrix) {
  let a = arc[0];
  let b = arc[1];
  const rot = arc[2] * Math.PI / 180;
  const cos = Math.cos(rot);
  const sin = Math.sin(rot);
  let h =
    Math.pow(arc[5] * cos + arc[6] * sin, 2) / (4 * a * a) +
    Math.pow(arc[6] * cos - arc[5] * sin, 2) / (4 * b * b);
  if (h > 1) {
    h = Math.sqrt(h);
    a *= h;
    b *= h;
  }
  const ellipse: Matrix = [a * cos, a * sin, -b * sin, b * cos, 0, 0];
  const m = flattenMatrices(transform, ellipse);
  // Decompose the new ellipse matrix.
  const lastCol = m[2] * m[2] + m[3] * m[3];
  const squareSum = m[0] * m[0] + m[1] * m[1] + lastCol;
  const root = Math.sqrt(
    (Math.pow(m[0] - m[3], 2) + Math.pow(m[1] + m[2], 2)) *
      (Math.pow(m[0] + m[3], 2) + Math.pow(m[1] - m[2], 2)),
  );
 
  Eif (!root) {
    // circle
    arc[0] = arc[1] = Math.sqrt(squareSum / 2);
    arc[2] = 0;
  } else {
    const majorAxisSqr = (squareSum + root) / 2;
    const minorAxisSqr = (squareSum - root) / 2;
    const major = Math.abs(majorAxisSqr - lastCol) > 1e-6;
    const s = (major ? majorAxisSqr : minorAxisSqr) - lastCol;
    const rowsSum = m[0] * m[2] + m[1] * m[3];
    const term1 = m[0] * s + m[2] * rowsSum;
    const term2 = m[1] * s + m[3] * rowsSum;
    arc[0] = Math.sqrt(majorAxisSqr);
    arc[1] = Math.sqrt(minorAxisSqr);
    arc[2] =
      ((major ? term2 < 0 : term1 > 0) ? -1 : 1) *
      Math.acos(
        (major ? term1 : term2) / Math.sqrt(term1 * term1 + term2 * term2),
      ) *
      180 /
      Math.PI;
  }
 
  Iif (transform[0] < 0 !== transform[3] < 0) {
    // Flip the sweep flag if coordinates are being flipped horizontally XOR vertically
    arc[4] = 1 - arc[4];
  }
 
  return arc;
}