_transforms.js•10.9 kB
'use strict';
const { toFixed } = require('../lib/svgo/tools');
/**
* @typedef {{ name: string, data: number[] }} TransformItem
* @typedef {{
* convertToShorts: boolean,
* floatPrecision: number,
* transformPrecision: number,
* matrixToTransform: boolean,
* shortTranslate: boolean,
* shortScale: boolean,
* shortRotate: boolean,
* removeUseless: boolean,
* collapseIntoOne: boolean,
* leadingZero: boolean,
* negativeExtraSpace: boolean,
* }} TransformParams
*/
const transformTypes = new Set([
'matrix',
'rotate',
'scale',
'skewX',
'skewY',
'translate',
]);
const regTransformSplit =
/\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/;
const regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;
/**
* Convert transform string to JS representation.
*
* @param {string} transformString
* @returns {TransformItem[]} Object representation of transform, or an empty array if it was malformed.
*/
exports.transform2js = (transformString) => {
/** @type {TransformItem[]} */
const transforms = [];
/** @type {?TransformItem} */
let currentTransform = null;
// split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
for (const item of transformString.split(regTransformSplit)) {
if (!item) {
continue;
}
if (transformTypes.has(item)) {
currentTransform = { name: item, data: [] };
transforms.push(currentTransform);
} else {
let num;
// then split it into [10, 50] and collect as context.data
while ((num = regNumericValues.exec(item))) {
num = Number(num);
if (currentTransform != null) {
currentTransform.data.push(num);
}
}
}
}
return currentTransform == null || currentTransform.data.length == 0
? []
: transforms;
};
/**
* Multiply transforms into one.
*
* @param {TransformItem[]} transforms
* @returns {TransformItem}
*/
exports.transformsMultiply = (transforms) => {
const matrixData = transforms.map((transform) => {
if (transform.name === 'matrix') {
return transform.data;
}
return transformToMatrix(transform);
});
const matrixTransform = {
name: 'matrix',
data:
matrixData.length > 0 ? matrixData.reduce(multiplyTransformMatrices) : [],
};
return matrixTransform;
};
/**
* Math utilities in radians.
*/
const mth = {
/**
* @param {number} deg
* @returns {number}
*/
rad: (deg) => {
return (deg * Math.PI) / 180;
},
/**
* @param {number} rad
* @returns {number}
*/
deg: (rad) => {
return (rad * 180) / Math.PI;
},
/**
* @param {number} deg
* @returns {number}
*/
cos: (deg) => {
return Math.cos(mth.rad(deg));
},
/**
* @param {number} val
* @param {number} floatPrecision
* @returns {number}
*/
acos: (val, floatPrecision) => {
return toFixed(mth.deg(Math.acos(val)), floatPrecision);
},
/**
* @param {number} deg
* @returns {number}
*/
sin: (deg) => {
return Math.sin(mth.rad(deg));
},
/**
* @param {number} val
* @param {number} floatPrecision
* @returns {number}
*/
asin: (val, floatPrecision) => {
return toFixed(mth.deg(Math.asin(val)), floatPrecision);
},
/**
* @param {number} deg
* @returns {number}
*/
tan: (deg) => {
return Math.tan(mth.rad(deg));
},
/**
* @param {number} val
* @param {number} floatPrecision
* @returns {number}
*/
atan: (val, floatPrecision) => {
return toFixed(mth.deg(Math.atan(val)), floatPrecision);
},
};
/**
* Decompose matrix into simple transforms.
*
* @param {TransformItem} transform
* @param {TransformParams} params
* @returns {TransformItem[]}
* @see https://frederic-wang.fr/decomposition-of-2d-transform-matrices.html
*/
exports.matrixToTransform = (transform, params) => {
const floatPrecision = params.floatPrecision;
const data = transform.data;
const transforms = [];
// [..., ..., ..., ..., tx, ty] → translate(tx, ty)
if (data[4] || data[5]) {
transforms.push({
name: 'translate',
data: data.slice(4, data[5] ? 6 : 5),
});
}
let sx = toFixed(Math.hypot(data[0], data[1]), params.transformPrecision);
let sy = toFixed(
(data[0] * data[3] - data[1] * data[2]) / sx,
params.transformPrecision,
);
const colsSum = data[0] * data[2] + data[1] * data[3];
const rowsSum = data[0] * data[1] + data[2] * data[3];
const scaleBefore = rowsSum !== 0 || sx === sy;
// [sx, 0, tan(a)·sy, sy, 0, 0] → skewX(a)·scale(sx, sy)
if (!data[1] && data[2]) {
transforms.push({
name: 'skewX',
data: [mth.atan(data[2] / sy, floatPrecision)],
});
// [sx, sx·tan(a), 0, sy, 0, 0] → skewY(a)·scale(sx, sy)
} else if (data[1] && !data[2]) {
transforms.push({
name: 'skewY',
data: [mth.atan(data[1] / data[0], floatPrecision)],
});
sx = data[0];
sy = data[3];
// [sx·cos(a), sx·sin(a), sy·-sin(a), sy·cos(a), x, y] → rotate(a[, cx, cy])·(scale or skewX) or
// [sx·cos(a), sy·sin(a), sx·-sin(a), sy·cos(a), x, y] → scale(sx, sy)·rotate(a[, cx, cy]) (if !scaleBefore)
} else if (!colsSum || (sx === 1 && sy === 1) || !scaleBefore) {
if (!scaleBefore) {
sx = Math.hypot(data[0], data[2]);
sy = Math.hypot(data[1], data[3]);
if (toFixed(data[0], params.transformPrecision) < 0) {
sx = -sx;
}
if (
data[3] < 0 ||
(Math.sign(data[1]) === Math.sign(data[2]) &&
toFixed(data[3], params.transformPrecision) === 0)
) {
sy = -sy;
}
transforms.push({ name: 'scale', data: [sx, sy] });
}
const angle = Math.min(Math.max(-1, data[0] / sx), 1);
const rotate = [
mth.acos(angle, floatPrecision) *
((scaleBefore ? 1 : sy) * data[1] < 0 ? -1 : 1),
];
if (rotate[0]) {
transforms.push({ name: 'rotate', data: rotate });
}
if (rowsSum && colsSum)
transforms.push({
name: 'skewX',
data: [mth.atan(colsSum / (sx * sx), floatPrecision)],
});
// rotate(a, cx, cy) can consume translate() within optional arguments cx, cy (rotation point)
if (rotate[0] && (data[4] || data[5])) {
transforms.shift();
const oneOverCos = 1 - data[0] / sx;
const sin = data[1] / (scaleBefore ? sx : sy);
const x = data[4] * (scaleBefore ? 1 : sy);
const y = data[5] * (scaleBefore ? 1 : sx);
const denom = (oneOverCos ** 2 + sin ** 2) * (scaleBefore ? 1 : sx * sy);
rotate.push(
(oneOverCos * x - sin * y) / denom,
(oneOverCos * y + sin * x) / denom,
);
}
// Too many transformations, return original matrix if it isn't just a scale/translate
} else if (data[1] || data[2]) {
return [transform];
}
if ((scaleBefore && (sx != 1 || sy != 1)) || !transforms.length) {
transforms.push({
name: 'scale',
data: sx == sy ? [sx] : [sx, sy],
});
}
return transforms;
};
/**
* Convert transform to the matrix data.
*
* @type {(transform: TransformItem) => number[] }
*/
const transformToMatrix = (transform) => {
if (transform.name === 'matrix') {
return transform.data;
}
switch (transform.name) {
case 'translate':
// [1, 0, 0, 1, tx, ty]
return [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
case 'scale':
// [sx, 0, 0, sy, 0, 0]
return [
transform.data[0],
0,
0,
transform.data[1] || transform.data[0],
0,
0,
];
case 'rotate':
// [cos(a), sin(a), -sin(a), cos(a), x, y]
var cos = mth.cos(transform.data[0]),
sin = mth.sin(transform.data[0]),
cx = transform.data[1] || 0,
cy = transform.data[2] || 0;
return [
cos,
sin,
-sin,
cos,
(1 - cos) * cx + sin * cy,
(1 - cos) * cy - sin * cx,
];
case 'skewX':
// [1, 0, tan(a), 1, 0, 0]
return [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
case 'skewY':
// [1, tan(a), 0, 1, 0, 0]
return [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
default:
throw Error(`Unknown transform ${transform.name}`);
}
};
/**
* 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}})
*
* @type {(
* cursor: [x: number, y: number],
* arc: number[],
* transform: number[]
* ) => number[]}
*/
exports.transformArc = (cursor, arc, transform) => {
const x = arc[5] - cursor[0];
const y = arc[6] - cursor[1];
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);
// skip if radius is 0
if (a > 0 && b > 0) {
let h =
Math.pow(x * cos + y * sin, 2) / (4 * a * a) +
Math.pow(y * cos - x * sin, 2) / (4 * b * b);
if (h > 1) {
h = Math.sqrt(h);
a *= h;
b *= h;
}
}
const ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0];
const m = multiplyTransformMatrices(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.hypot(m[0] - m[3], m[1] + m[2]) * Math.hypot(m[0] + m[3], m[1] - m[2]);
if (!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 sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol;
const rowsSum = m[0] * m[2] + m[1] * m[3];
const term1 = m[0] * sub + m[2] * rowsSum;
const term2 = m[1] * sub + 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.hypot(term1, term2)) *
180) /
Math.PI;
}
if (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;
};
/**
* Multiply transformation matrices.
*
* @type {(a: number[], b: number[]) => number[]}
*/
const multiplyTransformMatrices = (a, b) => {
return [
a[0] * b[0] + a[2] * b[1],
a[1] * b[0] + a[3] * b[1],
a[0] * b[2] + a[2] * b[3],
a[1] * b[2] + a[3] * b[3],
a[0] * b[4] + a[2] * b[5] + a[4],
a[1] * b[4] + a[3] * b[5] + a[5],
];
};