309 lines
9.9 KiB
JavaScript
309 lines
9.9 KiB
JavaScript
'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) {
|
|
/*jshint -W084 */
|
|
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
|
|
while (num = regNumericValues.exec(item)) {
|
|
num = Number(num);
|
|
if (current.data)
|
|
current.data.push(num);
|
|
else
|
|
current.data = [num];
|
|
}
|
|
}
|
|
}
|
|
});
|
|
|
|
return 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.reduce(function(a, b) {
|
|
return multiplyTransformMatrices(a, b);
|
|
})
|
|
};
|
|
|
|
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
|
|
* http://www.maths-informatique-jeux.com/blog/frederic/?post/2013/12/01/Decomposition-of-2D-transform-matrices
|
|
*
|
|
* @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.sqrt(data[0] * data[0] + data[1] * 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 || +(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.sqrt(data[0] * data[0] + data[2] * data[2]);
|
|
sy = (data[3] < 0 ? -1 : 1) * Math.sqrt(data[1] * data[1] + data[3] * data[3]);
|
|
transforms.push({ name: 'scale', data: [sx, sy] });
|
|
}
|
|
var rotate = [mth.acos(data[0] / sx, floatPrecision) * (data[1] * sy < 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} arc [a, b, rotation in deg]
|
|
* @param {Array} transform transformation matrix
|
|
* @return {Array} arc transformed input arc
|
|
*/
|
|
exports.transformArc = function(arc, transform) {
|
|
|
|
var a = arc[0],
|
|
b = arc[1],
|
|
rot = arc[2] * Math.PI / 180,
|
|
cos = Math.cos(rot),
|
|
sin = Math.sin(rot),
|
|
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;
|
|
}
|
|
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.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))
|
|
);
|
|
|
|
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.sqrt(term1 * term1 + term2 * term2)) * 180 / Math.PI;
|
|
}
|
|
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]
|
|
];
|
|
|
|
}
|