| /* |
| * Add some helpers for matrices. This is ported from SkMatrix.cpp and others |
| * to save complexity and overhead of going back and forth between C++ and JS layers. |
| * I would have liked to use something like DOMMatrix, except it |
| * isn't widely supported (would need polyfills) and it doesn't |
| * have a mapPoints() function (which could maybe be tacked on here). |
| * If DOMMatrix catches on, it would be worth re-considering this usage. |
| */ |
| |
| CanvasKit.Matrix = {}; |
| function sdot() { // to be called with an even number of scalar args |
| var acc = 0; |
| for (var i=0; i < arguments.length-1; i+=2) { |
| acc += arguments[i] * arguments[i+1]; |
| } |
| return acc; |
| } |
| |
| // Private general matrix functions used in both 3x3s and 4x4s. |
| // Return a square identity matrix of size n. |
| var identityN = function(n) { |
| var size = n*n; |
| var m = new Array(size); |
| while(size--) { |
| m[size] = size%(n+1) === 0 ? 1.0 : 0.0; |
| } |
| return m; |
| }; |
| |
| // Stride, a function for compactly representing several ways of copying an array into another. |
| // Write vector `v` into matrix `m`. `m` is a matrix encoded as an array in row-major |
| // order. Its width is passed as `width`. `v` is an array with length < (m.length/width). |
| // An element of `v` is copied into `m` starting at `offset` and moving `colStride` cols right |
| // each row. |
| // |
| // For example, a width of 4, offset of 3, and stride of -1 would put the vector here. |
| // _ _ 0 _ |
| // _ 1 _ _ |
| // 2 _ _ _ |
| // _ _ _ 3 |
| // |
| var stride = function(v, m, width, offset, colStride) { |
| for (var i=0; i<v.length; i++) { |
| m[i * width + // column |
| (i * colStride + offset + width) % width // row |
| ] = v[i]; |
| } |
| return m; |
| }; |
| |
| CanvasKit.Matrix.identity = function() { |
| return identityN(3); |
| }; |
| |
| // Return the inverse (if it exists) of this matrix. |
| // Otherwise, return null. |
| CanvasKit.Matrix.invert = function(m) { |
| // Find the determinant by the sarrus rule. https://en.wikipedia.org/wiki/Rule_of_Sarrus |
| var det = m[0]*m[4]*m[8] + m[1]*m[5]*m[6] + m[2]*m[3]*m[7] |
| - m[2]*m[4]*m[6] - m[1]*m[3]*m[8] - m[0]*m[5]*m[7]; |
| if (!det) { |
| Debug('Warning, uninvertible matrix'); |
| return null; |
| } |
| // Return the inverse by the formula adj(m)/det. |
| // adj (adjugate) of a 3x3 is the transpose of it's cofactor matrix. |
| // a cofactor matrix is a matrix where each term is +-det(N) where matrix N is the 2x2 formed |
| // by removing the row and column we're currently setting from the source. |
| // the sign alternates in a checkerboard pattern with a `+` at the top left. |
| // that's all been combined here into one expression. |
| return [ |
| (m[4]*m[8] - m[5]*m[7])/det, (m[2]*m[7] - m[1]*m[8])/det, (m[1]*m[5] - m[2]*m[4])/det, |
| (m[5]*m[6] - m[3]*m[8])/det, (m[0]*m[8] - m[2]*m[6])/det, (m[2]*m[3] - m[0]*m[5])/det, |
| (m[3]*m[7] - m[4]*m[6])/det, (m[1]*m[6] - m[0]*m[7])/det, (m[0]*m[4] - m[1]*m[3])/det, |
| ]; |
| }; |
| |
| // Maps the given points according to the passed in matrix. |
| // Results are done in place. |
| // See SkMatrix.h::mapPoints for the docs on the math. |
| CanvasKit.Matrix.mapPoints = function(matrix, ptArr) { |
| if (IsDebug && (ptArr.length % 2)) { |
| throw 'mapPoints requires an even length arr'; |
| } |
| for (var i = 0; i < ptArr.length; i+=2) { |
| var x = ptArr[i], y = ptArr[i+1]; |
| // Gx+Hy+I |
| var denom = matrix[6]*x + matrix[7]*y + matrix[8]; |
| // Ax+By+C |
| var xTrans = matrix[0]*x + matrix[1]*y + matrix[2]; |
| // Dx+Ey+F |
| var yTrans = matrix[3]*x + matrix[4]*y + matrix[5]; |
| ptArr[i] = xTrans/denom; |
| ptArr[i+1] = yTrans/denom; |
| } |
| return ptArr; |
| }; |
| |
| function isnumber(val) { return !isNaN(val); } |
| |
| // generalized iterative algorithm for multiplying two matrices. |
| function multiply(m1, m2, size) { |
| |
| if (IsDebug && (!m1.every(isnumber) || !m2.every(isnumber))) { |
| throw 'Some members of matrices are NaN m1='+m1+', m2='+m2+''; |
| } |
| if (IsDebug && (m1.length !== m2.length)) { |
| throw 'Undefined for matrices of different sizes. m1.length='+m1.length+', m2.length='+m2.length; |
| } |
| if (IsDebug && (size*size !== m1.length)) { |
| throw 'Undefined for non-square matrices. array size was '+size; |
| } |
| |
| var result = Array(m1.length); |
| for (var r = 0; r < size; r++) { |
| for (var c = 0; c < size; c++) { |
| // accumulate a sum of m1[r,k]*m2[k, c] |
| var acc = 0; |
| for (var k = 0; k < size; k++) { |
| acc += m1[size * r + k] * m2[size * k + c]; |
| } |
| result[r * size + c] = acc; |
| } |
| } |
| return result; |
| } |
| |
| // Accept an integer indicating the size of the matrices being multiplied (3 for 3x3), and any |
| // number of matrices following it. |
| function multiplyMany(size, listOfMatrices) { |
| if (IsDebug && (listOfMatrices.length < 2)) { |
| throw 'multiplication expected two or more matrices'; |
| } |
| var result = multiply(listOfMatrices[0], listOfMatrices[1], size); |
| var next = 2; |
| while (next < listOfMatrices.length) { |
| result = multiply(result, listOfMatrices[next], size); |
| next++; |
| } |
| return result; |
| } |
| |
| // Accept any number 3x3 of matrices as arguments, multiply them together. |
| // Matrix multiplication is associative but not commutative. the order of the arguments |
| // matters, but it does not matter that this implementation multiplies them left to right. |
| CanvasKit.Matrix.multiply = function() { |
| return multiplyMany(3, arguments); |
| }; |
| |
| // Return a matrix representing a rotation by n radians. |
| // px, py optionally say which point the rotation should be around |
| // with the default being (0, 0); |
| CanvasKit.Matrix.rotated = function(radians, px, py) { |
| px = px || 0; |
| py = py || 0; |
| var sinV = Math.sin(radians); |
| var cosV = Math.cos(radians); |
| return [ |
| cosV, -sinV, sdot( sinV, py, 1 - cosV, px), |
| sinV, cosV, sdot(-sinV, px, 1 - cosV, py), |
| 0, 0, 1, |
| ]; |
| }; |
| |
| CanvasKit.Matrix.scaled = function(sx, sy, px, py) { |
| px = px || 0; |
| py = py || 0; |
| var m = stride([sx, sy], identityN(3), 3, 0, 1); |
| return stride([px-sx*px, py-sy*py], m, 3, 2, 0); |
| }; |
| |
| CanvasKit.Matrix.skewed = function(kx, ky, px, py) { |
| px = px || 0; |
| py = py || 0; |
| var m = stride([kx, ky], identityN(3), 3, 1, -1); |
| return stride([-kx*px, -ky*py], m, 3, 2, 0); |
| }; |
| |
| CanvasKit.Matrix.translated = function(dx, dy) { |
| return stride(arguments, identityN(3), 3, 2, 0); |
| }; |
| |
| // Functions for manipulating vectors. |
| // Loosely based off of SkV3 in SkM44.h but skia also has SkVec2 and Skv4. This combines them and |
| // works on vectors of any length. |
| CanvasKit.Vector = {}; |
| CanvasKit.Vector.dot = function(a, b) { |
| if (IsDebug && (a.length !== b.length)) { |
| throw 'Cannot perform dot product on arrays of different length ('+a.length+' vs '+b.length+')'; |
| } |
| return a.map(function(v, i) { return v*b[i] }).reduce(function(acc, cur) { return acc + cur; }); |
| }; |
| CanvasKit.Vector.lengthSquared = function(v) { |
| return CanvasKit.Vector.dot(v, v); |
| }; |
| CanvasKit.Vector.length = function(v) { |
| return Math.sqrt(CanvasKit.Vector.lengthSquared(v)); |
| }; |
| CanvasKit.Vector.mulScalar = function(v, s) { |
| return v.map(function(i) { return i*s }); |
| }; |
| CanvasKit.Vector.add = function(a, b) { |
| return a.map(function(v, i) { return v+b[i] }); |
| }; |
| CanvasKit.Vector.sub = function(a, b) { |
| return a.map(function(v, i) { return v-b[i]; }); |
| }; |
| CanvasKit.Vector.dist = function(a, b) { |
| return CanvasKit.Vector.length(CanvasKit.Vector.sub(a, b)); |
| }; |
| CanvasKit.Vector.normalize = function(v) { |
| return CanvasKit.Vector.mulScalar(v, 1/CanvasKit.Vector.length(v)); |
| }; |
| CanvasKit.Vector.cross = function(a, b) { |
| if (IsDebug && (a.length !== 3 || a.length !== 3)) { |
| throw 'Cross product is only defined for 3-dimensional vectors (a.length='+a.length+', b.length='+b.length+')'; |
| } |
| return [ |
| a[1]*b[2] - a[2]*b[1], |
| a[2]*b[0] - a[0]*b[2], |
| a[0]*b[1] - a[1]*b[0], |
| ]; |
| }; |
| |
| // Functions for creating and manipulating (row-major) 4x4 matrices. Accepted in place of |
| // SkM44 in canvas methods, for the same reasons as the 3x3 matrices above. |
| // ported from C++ code in SkM44.cpp |
| CanvasKit.M44 = {}; |
| // Create a 4x4 identity matrix |
| CanvasKit.M44.identity = function() { |
| return identityN(4); |
| }; |
| |
| // Anything named vec below is an array of length 3 representing a vector/point in 3D space. |
| // Create a 4x4 matrix representing a translate by the provided 3-vec |
| CanvasKit.M44.translated = function(vec) { |
| return stride(vec, identityN(4), 4, 3, 0); |
| }; |
| // Create a 4x4 matrix representing a scaling by the provided 3-vec |
| CanvasKit.M44.scaled = function(vec) { |
| return stride(vec, identityN(4), 4, 0, 1); |
| }; |
| // Create a 4x4 matrix representing a rotation about the provided axis 3-vec. |
| // axis does not need to be normalized. |
| CanvasKit.M44.rotated = function(axisVec, radians) { |
| return CanvasKit.M44.rotatedUnitSinCos( |
| CanvasKit.Vector.normalize(axisVec), Math.sin(radians), Math.cos(radians)); |
| }; |
| // Create a 4x4 matrix representing a rotation about the provided normalized axis 3-vec. |
| // Rotation is provided redundantly as both sin and cos values. |
| // This rotate can be used when you already have the cosAngle and sinAngle values |
| // so you don't have to atan(cos/sin) to call roatated() which expects an angle in radians. |
| // this does no checking! Behavior for invalid sin or cos values or non-normalized axis vectors |
| // is incorrect. Prefer rotated(). |
| CanvasKit.M44.rotatedUnitSinCos = function(axisVec, sinAngle, cosAngle) { |
| var x = axisVec[0]; |
| var y = axisVec[1]; |
| var z = axisVec[2]; |
| var c = cosAngle; |
| var s = sinAngle; |
| var t = 1 - c; |
| return [ |
| t*x*x + c, t*x*y - s*z, t*x*z + s*y, 0, |
| t*x*y + s*z, t*y*y + c, t*y*z - s*x, 0, |
| t*x*z - s*y, t*y*z + s*x, t*z*z + c, 0, |
| 0, 0, 0, 1 |
| ]; |
| }; |
| // Create a 4x4 matrix representing a camera at eyeVec, pointed at centerVec. |
| CanvasKit.M44.lookat = function(eyeVec, centerVec, upVec) { |
| var f = CanvasKit.Vector.normalize(CanvasKit.Vector.sub(centerVec, eyeVec)); |
| var u = CanvasKit.Vector.normalize(upVec); |
| var s = CanvasKit.Vector.normalize(CanvasKit.Vector.cross(f, u)); |
| |
| var m = CanvasKit.M44.identity(); |
| // set each column's top three numbers |
| stride(s, m, 4, 0, 0); |
| stride(CanvasKit.Vector.cross(s, f), m, 4, 1, 0); |
| stride(CanvasKit.Vector.mulScalar(f, -1), m, 4, 2, 0); |
| stride(eyeVec, m, 4, 3, 0); |
| |
| var m2 = CanvasKit.M44.invert(m); |
| if (m2 === null) { |
| return CanvasKit.M44.identity(); |
| } |
| return m2; |
| }; |
| // Create a 4x4 matrix representing a perspective. All arguments are scalars. |
| // angle is in radians. |
| CanvasKit.M44.perspective = function(near, far, angle) { |
| if (IsDebug && (far <= near)) { |
| throw 'far must be greater than near when constructing M44 using perspective.'; |
| } |
| var dInv = 1 / (far - near); |
| var halfAngle = angle / 2; |
| var cot = Math.cos(halfAngle) / Math.sin(halfAngle); |
| return [ |
| cot, 0, 0, 0, |
| 0, cot, 0, 0, |
| 0, 0, (far+near)*dInv, 2*far*near*dInv, |
| 0, 0, -1, 1, |
| ]; |
| }; |
| // Returns the number at the given row and column in matrix m. |
| CanvasKit.M44.rc = function(m, r, c) { |
| return m[r*4+c]; |
| }; |
| // Accepts any number of 4x4 matrix arguments, multiplies them left to right. |
| CanvasKit.M44.multiply = function() { |
| return multiplyMany(4, arguments); |
| }; |
| |
| // Invert the 4x4 matrix if it is invertible and return it. if not, return null. |
| // taken from SkM44.cpp (altered to use row-major order) |
| // m is not altered. |
| CanvasKit.M44.invert = function(m) { |
| if (IsDebug && !m.every(isnumber)) { |
| throw 'some members of matrix are NaN m='+m; |
| } |
| |
| var a00 = m[0]; |
| var a01 = m[4]; |
| var a02 = m[8]; |
| var a03 = m[12]; |
| var a10 = m[1]; |
| var a11 = m[5]; |
| var a12 = m[9]; |
| var a13 = m[13]; |
| var a20 = m[2]; |
| var a21 = m[6]; |
| var a22 = m[10]; |
| var a23 = m[14]; |
| var a30 = m[3]; |
| var a31 = m[7]; |
| var a32 = m[11]; |
| var a33 = m[15]; |
| |
| var b00 = a00 * a11 - a01 * a10; |
| var b01 = a00 * a12 - a02 * a10; |
| var b02 = a00 * a13 - a03 * a10; |
| var b03 = a01 * a12 - a02 * a11; |
| var b04 = a01 * a13 - a03 * a11; |
| var b05 = a02 * a13 - a03 * a12; |
| var b06 = a20 * a31 - a21 * a30; |
| var b07 = a20 * a32 - a22 * a30; |
| var b08 = a20 * a33 - a23 * a30; |
| var b09 = a21 * a32 - a22 * a31; |
| var b10 = a21 * a33 - a23 * a31; |
| var b11 = a22 * a33 - a23 * a32; |
| |
| // calculate determinate |
| var det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06; |
| var invdet = 1.0 / det; |
| |
| // bail out if the matrix is not invertible |
| if (det === 0 || invdet === Infinity) { |
| Debug('Warning, uninvertible matrix'); |
| return null; |
| } |
| |
| b00 *= invdet; |
| b01 *= invdet; |
| b02 *= invdet; |
| b03 *= invdet; |
| b04 *= invdet; |
| b05 *= invdet; |
| b06 *= invdet; |
| b07 *= invdet; |
| b08 *= invdet; |
| b09 *= invdet; |
| b10 *= invdet; |
| b11 *= invdet; |
| |
| // store result in row major order |
| var tmp = [ |
| a11 * b11 - a12 * b10 + a13 * b09, |
| a12 * b08 - a10 * b11 - a13 * b07, |
| a10 * b10 - a11 * b08 + a13 * b06, |
| a11 * b07 - a10 * b09 - a12 * b06, |
| |
| a02 * b10 - a01 * b11 - a03 * b09, |
| a00 * b11 - a02 * b08 + a03 * b07, |
| a01 * b08 - a00 * b10 - a03 * b06, |
| a00 * b09 - a01 * b07 + a02 * b06, |
| |
| a31 * b05 - a32 * b04 + a33 * b03, |
| a32 * b02 - a30 * b05 - a33 * b01, |
| a30 * b04 - a31 * b02 + a33 * b00, |
| a31 * b01 - a30 * b03 - a32 * b00, |
| |
| a22 * b04 - a21 * b05 - a23 * b03, |
| a20 * b05 - a22 * b02 + a23 * b01, |
| a21 * b02 - a20 * b04 - a23 * b00, |
| a20 * b03 - a21 * b01 + a22 * b00, |
| ]; |
| |
| |
| if (!tmp.every(function(val) { return !isNaN(val) && val !== Infinity && val !== -Infinity; })) { |
| Debug('inverted matrix contains infinities or NaN '+tmp); |
| return null; |
| } |
| return tmp; |
| }; |
| |
| CanvasKit.M44.transpose = function(m) { |
| return [ |
| m[0], m[4], m[8], m[12], |
| m[1], m[5], m[9], m[13], |
| m[2], m[6], m[10], m[14], |
| m[3], m[7], m[11], m[15], |
| ]; |
| }; |
| |
| // Return the inverse of an SkM44. throw an error if it's not invertible |
| CanvasKit.M44.mustInvert = function(m) { |
| var m2 = CanvasKit.M44.invert(m); |
| if (m2 === null) { |
| throw 'Matrix not invertible'; |
| } |
| return m2; |
| }; |
| |
| // returns a matrix that sets up a 3D perspective view from a given camera. |
| // |
| // area - a rect describing the viewport. (0, 0, canvas_width, canvas_height) suggested |
| // zscale - a scalar describing the scale of the z axis. min(width, height)/2 suggested |
| // cam - an object with the following attributes |
| // const cam = { |
| // 'eye' : [0, 0, 1 / Math.tan(Math.PI / 24) - 1], // a 3D point locating the camera |
| // 'coa' : [0, 0, 0], // center of attention - the 3D point the camera is looking at. |
| // 'up' : [0, 1, 0], // a unit vector pointing in the camera's up direction, because eye and |
| // // coa alone leave roll unspecified. |
| // 'near' : 0.02, // near clipping plane |
| // 'far' : 4, // far clipping plane |
| // 'angle': Math.PI / 12, // field of view in radians |
| // }; |
| CanvasKit.M44.setupCamera = function(area, zscale, cam) { |
| var camera = CanvasKit.M44.lookat(cam['eye'], cam['coa'], cam['up']); |
| var perspective = CanvasKit.M44.perspective(cam['near'], cam['far'], cam['angle']); |
| var center = [(area[0] + area[2])/2, (area[1] + area[3])/2, 0]; |
| var viewScale = [(area[2] - area[0])/2, (area[3] - area[1])/2, zscale]; |
| var viewport = CanvasKit.M44.multiply( |
| CanvasKit.M44.translated(center), |
| CanvasKit.M44.scaled(viewScale)); |
| return CanvasKit.M44.multiply( |
| viewport, perspective, camera, CanvasKit.M44.mustInvert(viewport)); |
| }; |
| |
| // An ColorMatrix is a 4x4 color matrix that transforms the 4 color channels |
| // with a 1x4 matrix that post-translates those 4 channels. |
| // For example, the following is the layout with the scale (S) and post-transform |
| // (PT) items indicated. |
| // RS, 0, 0, 0 | RPT |
| // 0, GS, 0, 0 | GPT |
| // 0, 0, BS, 0 | BPT |
| // 0, 0, 0, AS | APT |
| // |
| // Much of this was hand-transcribed from SkColorMatrix.cpp, because it's easier to |
| // deal with a Float32Array of length 20 than to try to expose the SkColorMatrix object. |
| |
| var rScale = 0; |
| var gScale = 6; |
| var bScale = 12; |
| var aScale = 18; |
| |
| var rPostTrans = 4; |
| var gPostTrans = 9; |
| var bPostTrans = 14; |
| var aPostTrans = 19; |
| |
| CanvasKit.ColorMatrix = {}; |
| CanvasKit.ColorMatrix.identity = function() { |
| var m = new Float32Array(20); |
| m[rScale] = 1; |
| m[gScale] = 1; |
| m[bScale] = 1; |
| m[aScale] = 1; |
| return m; |
| }; |
| |
| CanvasKit.ColorMatrix.scaled = function(rs, gs, bs, as) { |
| var m = new Float32Array(20); |
| m[rScale] = rs; |
| m[gScale] = gs; |
| m[bScale] = bs; |
| m[aScale] = as; |
| return m; |
| }; |
| |
| var rotateIndices = [ |
| [6, 7, 11, 12], |
| [0, 10, 2, 12], |
| [0, 1, 5, 6], |
| ]; |
| // axis should be 0, 1, 2 for r, g, b |
| CanvasKit.ColorMatrix.rotated = function(axis, sine, cosine) { |
| var m = CanvasKit.ColorMatrix.identity(); |
| var indices = rotateIndices[axis]; |
| m[indices[0]] = cosine; |
| m[indices[1]] = sine; |
| m[indices[2]] = -sine; |
| m[indices[3]] = cosine; |
| return m; |
| }; |
| |
| // m is a ColorMatrix (i.e. a Float32Array), and this sets the 4 "special" |
| // params that will translate the colors after they are multiplied by the 4x4 matrix. |
| CanvasKit.ColorMatrix.postTranslate = function(m, dr, dg, db, da) { |
| m[rPostTrans] += dr; |
| m[gPostTrans] += dg; |
| m[bPostTrans] += db; |
| m[aPostTrans] += da; |
| return m; |
| }; |
| |
| // concat returns a new ColorMatrix that is the result of multiplying outer*inner |
| CanvasKit.ColorMatrix.concat = function(outer, inner) { |
| var m = new Float32Array(20); |
| var index = 0; |
| for (var j = 0; j < 20; j += 5) { |
| for (var i = 0; i < 4; i++) { |
| m[index++] = outer[j + 0] * inner[i + 0] + |
| outer[j + 1] * inner[i + 5] + |
| outer[j + 2] * inner[i + 10] + |
| outer[j + 3] * inner[i + 15]; |
| } |
| m[index++] = outer[j + 0] * inner[4] + |
| outer[j + 1] * inner[9] + |
| outer[j + 2] * inner[14] + |
| outer[j + 3] * inner[19] + |
| outer[j + 4]; |
| } |
| |
| return m; |
| }; |