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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 * http://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} 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.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] ]; }