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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;
}
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