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/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
"use strict";
/**
* Returns a matrix for the scaling given.
* Calling `scale()` or `scale(1) returns a new identity matrix.
*
* @param {Number} [sx = 1]
* the abscissa of the scaling vector.
* If unspecified, it will equal to `1`.
* @param {Number} [sy = sx]
* The ordinate of the scaling vector.
* If not present, its default value is `sx`, leading to a uniform scaling.
* @return {Array}
* The new matrix.
*/
const scale = (sx = 1, sy = sx) => [sx, 0, 0, 0, sy, 0, 0, 0, 1];
exports.scale = scale;
/**
* Returns a matrix for the translation given.
* Calling `translate()` or `translate(0) returns a new identity matrix.
*
* @param {Number} [tx = 0]
* The abscissa of the translating vector.
* If unspecified, it will equal to `0`.
* @param {Number} [ty = tx]
* The ordinate of the translating vector.
* If unspecified, it will equal to `tx`.
* @return {Array}
* The new matrix.
*/
const translate = (tx = 0, ty = tx) => [1, 0, tx, 0, 1, ty, 0, 0, 1];
exports.translate = translate;
/**
* Returns a matrix that reflects about the Y axis. For example, the point (x1, y1) would
* become (-x1, y1).
*
* @return {Array}
* The new matrix.
*/
const reflectAboutY = () => [-1, 0, 0, 0, 1, 0, 0, 0, 1];
exports.reflectAboutY = reflectAboutY;
/**
* Returns a matrix for the rotation given.
* Calling `rotate()` or `rotate(0)` returns a new identity matrix.
*
* @param {Number} [angle = 0]
* The angle, in radians, for which to return a corresponding rotation matrix.
* If unspecified, it will equal `0`.
* @return {Array}
* The new matrix.
*/
const rotate = (angle = 0) => {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
return [cos, sin, 0, -sin, cos, 0, 0, 0, 1];
};
exports.rotate = rotate;
/**
* Returns a new identity matrix.
*
* @return {Array}
* The new matrix.
*/
const identity = () => [1, 0, 0, 0, 1, 0, 0, 0, 1];
exports.identity = identity;
/**
* Multiplies two matrices and returns a new matrix with the result.
*
* @param {Array} M1
* The first operand.
* @param {Array} M2
* The second operand.
* @return {Array}
* The resulting matrix.
*/
const multiply = (M1, M2) => {
const c11 = M1[0] * M2[0] + M1[1] * M2[3] + M1[2] * M2[6];
const c12 = M1[0] * M2[1] + M1[1] * M2[4] + M1[2] * M2[7];
const c13 = M1[0] * M2[2] + M1[1] * M2[5] + M1[2] * M2[8];
const c21 = M1[3] * M2[0] + M1[4] * M2[3] + M1[5] * M2[6];
const c22 = M1[3] * M2[1] + M1[4] * M2[4] + M1[5] * M2[7];
const c23 = M1[3] * M2[2] + M1[4] * M2[5] + M1[5] * M2[8];
const c31 = M1[6] * M2[0] + M1[7] * M2[3] + M1[8] * M2[6];
const c32 = M1[6] * M2[1] + M1[7] * M2[4] + M1[8] * M2[7];
const c33 = M1[6] * M2[2] + M1[7] * M2[5] + M1[8] * M2[8];
return [c11, c12, c13, c21, c22, c23, c31, c32, c33];
};
exports.multiply = multiply;
/**
* Applies the given matrix to a point.
*
* @param {Array} M
* The matrix to apply.
* @param {Array} P
* The point's vector.
* @return {Array}
* The resulting point's vector.
*/
const apply = (M, P) => [
M[0] * P[0] + M[1] * P[1] + M[2],
M[3] * P[0] + M[4] * P[1] + M[5],
];
exports.apply = apply;
/**
* Returns `true` if the given matrix is a identity matrix.
*
* @param {Array} M
* The matrix to check
* @return {Boolean}
* `true` if the matrix passed is a identity matrix, `false` otherwise.
*/
const isIdentity = M =>
M[0] === 1 &&
M[1] === 0 &&
M[2] === 0 &&
M[3] === 0 &&
M[4] === 1 &&
M[5] === 0 &&
M[6] === 0 &&
M[7] === 0 &&
M[8] === 1;
exports.isIdentity = isIdentity;
/**
* Get the change of basis matrix and inverted change of basis matrix
* for the coordinate system based on the two given vectors, as well as
* the lengths of the two given vectors.
*
* @param {Array} u
* The first vector, serving as the "x axis" of the coordinate system.
* @param {Array} v
* The second vector, serving as the "y axis" of the coordinate system.
* @return {Object}
* { basis, invertedBasis, uLength, vLength }
* basis and invertedBasis are the change of basis matrices. uLength and
* vLength are the lengths of u and v.
*/
const getBasis = (u, v) => {
const uLength = Math.abs(Math.sqrt(u[0] ** 2 + u[1] ** 2));
const vLength = Math.abs(Math.sqrt(v[0] ** 2 + v[1] ** 2));
const basis = [
u[0] / uLength,
v[0] / vLength,
0,
u[1] / uLength,
v[1] / vLength,
0,
0,
0,
1,
];
const determinant = 1 / (basis[0] * basis[4] - basis[1] * basis[3]);
const invertedBasis = [
basis[4] / determinant,
-basis[1] / determinant,
0,
-basis[3] / determinant,
basis[0] / determinant,
0,
0,
0,
1,
];
return { basis, invertedBasis, uLength, vLength };
};
exports.getBasis = getBasis;
/**
* Convert the given matrix to a new coordinate system, based on the change of basis
* matrix.
*
* @param {Array} M
* The matrix to convert
* @param {Array} basis
* The change of basis matrix
* @param {Array} invertedBasis
* The inverted change of basis matrix
* @return {Array}
* The converted matrix.
*/
const changeMatrixBase = (M, basis, invertedBasis) => {
return multiply(invertedBasis, multiply(M, basis));
};
exports.changeMatrixBase = changeMatrixBase;
/**
* Returns the transformation matrix for the given node, relative to the ancestor passed
* as second argument; considering the ancestor transformation too.
* If no ancestor is specified, it will returns the transformation matrix relative to the
* node's parent element.
*
* @param {DOMNode} node
* The node.
* @param {DOMNode} ancestor
* The ancestor of the node given.
* @return {Array}
* The transformation matrix.
*/
function getNodeTransformationMatrix(node, ancestor = node.parentElement) {
const { a, b, c, d, e, f } = ancestor
.getTransformToParent()
.multiply(node.getTransformToAncestor(ancestor));
return [a, c, e, b, d, f, 0, 0, 1];
}
exports.getNodeTransformationMatrix = getNodeTransformationMatrix;
/**
* Returns the matrix to rotate, translate, and reflect (if needed) from the element's
* top-left origin into the actual writing mode and text direction applied to the element.
*
* @param {Object} size
* An element's untransformed content `width` and `height` (excluding any margin,
* borders, or padding).
* @param {Object} style
* The computed `writingMode` and `direction` properties for the element.
* @return {Array}
* The matrix with adjustments for writing mode and text direction, if any.
*/
function getWritingModeMatrix(size, style) {
let currentMatrix = identity();
const { width, height } = size;
const { direction, writingMode } = style;
switch (writingMode) {
case "horizontal-tb":
// This is the initial value. No further adjustment needed.
break;
case "vertical-rl":
currentMatrix = multiply(translate(width, 0), rotate(-Math.PI / 2));
break;
case "vertical-lr":
currentMatrix = multiply(reflectAboutY(), rotate(-Math.PI / 2));
break;
case "sideways-rl":
currentMatrix = multiply(translate(width, 0), rotate(-Math.PI / 2));
break;
case "sideways-lr":
currentMatrix = multiply(rotate(Math.PI / 2), translate(-height, 0));
break;
default:
console.error(`Unexpected writing-mode: ${writingMode}`);
}
switch (direction) {
case "ltr":
// This is the initial value. No further adjustment needed.
break;
case "rtl":
let rowLength = width;
if (writingMode != "horizontal-tb") {
rowLength = height;
}
currentMatrix = multiply(currentMatrix, translate(rowLength, 0));
currentMatrix = multiply(currentMatrix, reflectAboutY());
break;
default:
console.error(`Unexpected direction: ${direction}`);
}
return currentMatrix;
}
exports.getWritingModeMatrix = getWritingModeMatrix;
/**
* Convert from the matrix format used in this module:
* a, c, e,
* b, d, f,
* 0, 0, 1
* to the format used by the `matrix()` CSS transform function:
* a, b, c, d, e, f
*
* @param {Array} M
* The matrix in this module's 9 element format.
* @return {String}
* The matching 6 element CSS transform function.
*/
function getCSSMatrixTransform(M) {
const [a, c, e, b, d, f] = M;
return `matrix(${a}, ${b}, ${c}, ${d}, ${e}, ${f})`;
}
exports.getCSSMatrixTransform = getCSSMatrixTransform;