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'use strict';
var regTransformTypes = /matrix|translate|scale|rotate|skewX|skewY/,
regTransformSplit = /\s*(matrix|translate|scale|rotate|skewX|skewY)\s*\(\s*(.+?)\s*\)[\s,]*/,
regNumericValues = /[-+]?(?:\d*\.\d+|\d+\.?)(?:[eE][-+]?\d+)?/g;
/**
* Convert transform string to JS representation.
*
* @param {String} transformString input string
* @param {Object} params plugin params
* @return {Array} output array
*/
exports.transform2js = function (transformString) {
// JS representation of the transform data
var transforms = [],
// current transform context
current;
// split value into ['', 'translate', '10 50', '', 'scale', '2', '', 'rotate', '-45', '']
transformString.split(regTransformSplit).forEach(function (item) {
var num;
if (item) {
// if item is a translate function
if (regTransformTypes.test(item)) {
// then collect it and change current context
transforms.push((current = { name: item }));
// else if item is data
} else {
// then split it into [10, 50] and collect as context.data
// eslint-disable-next-line no-cond-assign
while ((num = regNumericValues.exec(item))) {
num = Number(num);
if (current.data) current.data.push(num);
else current.data = [num];
}
}
}
});
// return empty array if broken transform (no data)
return current && current.data ? transforms : [];
};
/**
* Multiply transforms into one.
*
* @param {Array} input transforms array
* @return {Array} output matrix array
*/
exports.transformsMultiply = function (transforms) {
// convert transforms objects to the matrices
transforms = transforms.map(function (transform) {
if (transform.name === 'matrix') {
return transform.data;
}
return transformToMatrix(transform);
});
// multiply all matrices into one
transforms = {
name: 'matrix',
data:
transforms.length > 0 ? transforms.reduce(multiplyTransformMatrices) : [],
};
return transforms;
};
/**
* Do math like a schoolgirl.
*
* @type {Object}
*/
var mth = (exports.mth = {
rad: function (deg) {
return (deg * Math.PI) / 180;
},
deg: function (rad) {
return (rad * 180) / Math.PI;
},
cos: function (deg) {
return Math.cos(this.rad(deg));
},
acos: function (val, floatPrecision) {
return +this.deg(Math.acos(val)).toFixed(floatPrecision);
},
sin: function (deg) {
return Math.sin(this.rad(deg));
},
asin: function (val, floatPrecision) {
return +this.deg(Math.asin(val)).toFixed(floatPrecision);
},
tan: function (deg) {
return Math.tan(this.rad(deg));
},
atan: function (val, floatPrecision) {
return +this.deg(Math.atan(val)).toFixed(floatPrecision);
},
});
/**
* Decompose matrix into simple transforms. See
* https://frederic-wang.fr/decomposition-of-2d-transform-matrices.html
*
* @param {Object} data matrix transform object
* @return {Object|Array} transforms array or original transform object
*/
exports.matrixToTransform = function (transform, params) {
var floatPrecision = params.floatPrecision,
data = transform.data,
transforms = [],
sx = +Math.hypot(data[0], data[1]).toFixed(params.transformPrecision),
sy = +((data[0] * data[3] - data[1] * data[2]) / sx).toFixed(
params.transformPrecision
),
colsSum = data[0] * data[2] + data[1] * data[3],
rowsSum = data[0] * data[1] + data[2] * data[3],
scaleBefore = rowsSum != 0 || sx == sy;
// [..., ..., ..., ..., tx, ty] → translate(tx, ty)
if (data[4] || data[5]) {
transforms.push({
name: 'translate',
data: data.slice(4, data[5] ? 6 : 5),
});
}
// [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 = (data[0] < 0 ? -1 : 1) * Math.hypot(data[0], data[2]);
sy = (data[3] < 0 ? -1 : 1) * Math.hypot(data[1], data[3]);
transforms.push({ name: 'scale', data: [sx, sy] });
}
var angle = Math.min(Math.max(-1, data[0] / sx), 1),
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();
var cos = data[0] / sx,
sin = data[1] / (scaleBefore ? sx : sy),
x = data[4] * (scaleBefore || sy),
y = data[5] * (scaleBefore || sx),
denom =
(Math.pow(1 - cos, 2) + Math.pow(sin, 2)) * (scaleBefore || sx * sy);
rotate.push(((1 - cos) * x - sin * y) / denom);
rotate.push(((1 - cos) * 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.
*
* @param {Object} transform transform object
* @return {Array} matrix data
*/
function transformToMatrix(transform) {
if (transform.name === 'matrix') return transform.data;
var matrix;
switch (transform.name) {
case 'translate':
// [1, 0, 0, 1, tx, ty]
matrix = [1, 0, 0, 1, transform.data[0], transform.data[1] || 0];
break;
case 'scale':
// [sx, 0, 0, sy, 0, 0]
matrix = [
transform.data[0],
0,
0,
transform.data[1] || transform.data[0],
0,
0,
];
break;
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;
matrix = [
cos,
sin,
-sin,
cos,
(1 - cos) * cx + sin * cy,
(1 - cos) * cy - sin * cx,
];
break;
case 'skewX':
// [1, 0, tan(a), 1, 0, 0]
matrix = [1, 0, mth.tan(transform.data[0]), 1, 0, 0];
break;
case 'skewY':
// [1, tan(a), 0, 1, 0, 0]
matrix = [1, mth.tan(transform.data[0]), 0, 1, 0, 0];
break;
}
return matrix;
}
/**
* 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} cursor [x, y]
* @param {Array} arc [a, b, rotation in deg]
* @param {Array} transform transformation matrix
* @return {Array} arc transformed input arc
*/
exports.transformArc = function (cursor, arc, transform) {
const x = arc[5] - cursor[0];
const y = arc[6] - cursor[1];
var a = arc[0],
b = arc[1],
rot = (arc[2] * Math.PI) / 180,
cos = Math.cos(rot),
sin = Math.sin(rot),
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;
}
var ellipse = [a * cos, a * sin, -b * sin, b * cos, 0, 0],
m = multiplyTransformMatrices(transform, ellipse),
// Decompose the new ellipse matrix
lastCol = m[2] * m[2] + m[3] * m[3],
squareSum = m[0] * m[0] + m[1] * m[1] + lastCol,
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 {
var majorAxisSqr = (squareSum + root) / 2,
minorAxisSqr = (squareSum - root) / 2,
major = Math.abs(majorAxisSqr - lastCol) > 1e-6,
sub = (major ? majorAxisSqr : minorAxisSqr) - lastCol,
rowsSum = m[0] * m[2] + m[1] * m[3],
term1 = m[0] * sub + m[2] * rowsSum,
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.
*
* @param {Array} a matrix A data
* @param {Array} b matrix B data
* @return {Array} result
*/
function 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],
];
}