//>>built define("dojox/gfx3d/matrix", ["dojo/_base/lang", "./_base"], function(lang, gfx3d){ // candidates for dojox.math: gfx3d.matrix = { _degToRad : function(degree){ return Math.PI * degree / 180; }, _radToDeg : function(radian){ return radian / Math.PI * 180; } }; gfx3d.matrix.Matrix3D = function(arg){ // summary: a 3D matrix object // description: Normalizes a 3D matrix-like object. If arrays is passed, // all objects of the array are normalized and multiplied sequentially. // arg: Object // a 3D matrix-like object, a number, or an array of such objects if(arg){ if(typeof arg == "number"){ this.xx = this.yy = this.zz = arg; }else if(arg instanceof Array){ if(arg.length > 0){ var m = gfx3d.matrix.normalize(arg[0]); // combine matrices for(var i = 1; i < arg.length; ++i){ var l = m; var r = gfx3d.matrix.normalize(arg[i]); m = new gfx3d.matrix.Matrix3D(); m.xx = l.xx * r.xx + l.xy * r.yx + l.xz * r.zx; m.xy = l.xx * r.xy + l.xy * r.yy + l.xz * r.zy; m.xz = l.xx * r.xz + l.xy * r.yz + l.xz * r.zz; m.yx = l.yx * r.xx + l.yy * r.yx + l.yz * r.zx; m.yy = l.yx * r.xy + l.yy * r.yy + l.yz * r.zy; m.yz = l.yx * r.xz + l.yy * r.yz + l.yz * r.zz; m.zx = l.zx * r.xx + l.zy * r.yx + l.zz * r.zx; m.zy = l.zx * r.xy + l.zy * r.yy + l.zz * r.zy; m.zz = l.zx * r.xz + l.zy * r.yz + l.zz * r.zz; m.dx = l.xx * r.dx + l.xy * r.dy + l.xz * r.dz + l.dx; m.dy = l.yx * r.dx + l.yy * r.dy + l.yz * r.dz + l.dy; m.dz = l.zx * r.dx + l.zy * r.dy + l.zz * r.dz + l.dz; } lang.mixin(this, m); } }else{ lang.mixin(this, arg); } } }; // the default (identity) matrix, which is used to fill in missing values lang.extend(gfx3d.matrix.Matrix3D, {xx: 1, xy: 0, xz: 0, yx: 0, yy: 1, yz: 0, zx: 0, zy: 0, zz: 1, dx: 0, dy: 0, dz: 0}); lang.mixin(gfx3d.matrix, { // summary: class constants, and methods of dojox.gfx3d.matrix // matrix constants // identity: dojox.gfx3d.matrix.Matrix3D // an identity matrix constant: identity * (x, y, z) == (x, y, z) identity: new gfx3d.matrix.Matrix3D(), // matrix creators translate: function(a, b, c){ // summary: forms a translation matrix // description: The resulting matrix is used to translate (move) points by specified offsets. // a: Number: an x coordinate value // b: Number: a y coordinate value // c: Number: a z coordinate value if(arguments.length > 1){ return new gfx3d.matrix.Matrix3D({dx: a, dy: b, dz: c}); // dojox.gfx3d.matrix.Matrix3D } // branch // a: Object: a point-like object, which specifies offsets for 3 dimensions // b: null return new gfx3d.matrix.Matrix3D({dx: a.x, dy: a.y, dz: a.z}); // dojox.gfx3d.matrix.Matrix3D }, scale: function(a, b, c){ // summary: forms a scaling matrix // description: The resulting matrix is used to scale (magnify) points by specified offsets. // a: Number: a scaling factor used for the x coordinate // b: Number: a scaling factor used for the y coordinate // c: Number: a scaling factor used for the z coordinate if(arguments.length > 1){ return new gfx3d.matrix.Matrix3D({xx: a, yy: b, zz: c}); // dojox.gfx3d.matrix.Matrix3D } if(typeof a == "number"){ // branch // a: Number: a uniform scaling factor used for the all coordinates // b: null return new gfx3d.matrix.Matrix3D({xx: a, yy: a, zz: a}); // dojox.gfx3d.matrix.Matrix3D } // branch // a: Object: a point-like object, which specifies scale factors for 3 dimensions // b: null return new gfx3d.matrix.Matrix3D({xx: a.x, yy: a.y, zz: a.z}); // dojox.gfx3d.matrix.Matrix3D }, rotateX: function(angle){ // summary: forms a rotating matrix (about the x axis) // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified angle. // angle: Number: an angle of rotation in radians (>0 for CW) var c = Math.cos(angle); var s = Math.sin(angle); return new gfx3d.matrix.Matrix3D({yy: c, yz: -s, zy: s, zz: c}); // dojox.gfx3d.matrix.Matrix3D }, rotateXg: function(degree){ // summary: forms a rotating matrix (about the x axis) // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified degree. // See dojox.gfx3d.matrix.rotateX() for comparison. // degree: Number: an angle of rotation in degrees (>0 for CW) return gfx3d.matrix.rotateX(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D }, rotateY: function(angle){ // summary: forms a rotating matrix (about the y axis) // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified angle. // angle: Number: an angle of rotation in radians (>0 for CW) var c = Math.cos(angle); var s = Math.sin(angle); return new gfx3d.matrix.Matrix3D({xx: c, xz: s, zx: -s, zz: c}); // dojox.gfx3d.matrix.Matrix3D }, rotateYg: function(degree){ // summary: forms a rotating matrix (about the y axis) // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified degree. // See dojox.gfx3d.matrix.rotateY() for comparison. // degree: Number: an angle of rotation in degrees (>0 for CW) return gfx3d.matrix.rotateY(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D }, rotateZ: function(angle){ // summary: forms a rotating matrix (about the z axis) // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified angle. // angle: Number: an angle of rotation in radians (>0 for CW) var c = Math.cos(angle); var s = Math.sin(angle); return new gfx3d.matrix.Matrix3D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx3d.matrix.Matrix3D }, rotateZg: function(degree){ // summary: forms a rotating matrix (about the z axis) // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified degree. // See dojox.gfx3d.matrix.rotateZ() for comparison. // degree: Number: an angle of rotation in degrees (>0 for CW) return gfx3d.matrix.rotateZ(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D }, // camera transformation cameraTranslate: function(a, b, c){ // summary: forms a translation matrix // description: The resulting matrix is used to translate (move) points by specified offsets. // a: Number: an x coordinate value // b: Number: a y coordinate value // c: Number: a z coordinate value if(arguments.length > 1){ return new gfx3d.matrix.Matrix3D({dx: -a, dy: -b, dz: -c}); // dojox.gfx3d.matrix.Matrix3D } // branch // a: Object: a point-like object, which specifies offsets for 3 dimensions // b: null return new gfx3d.matrix.Matrix3D({dx: -a.x, dy: -a.y, dz: -a.z}); // dojox.gfx3d.matrix.Matrix3D }, cameraRotateX: function(angle){ // summary: forms a rotating matrix (about the x axis) in cameraTransform manner // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified angle. // angle: Number: an angle of rotation in radians (>0 for CW) var c = Math.cos(-angle); var s = Math.sin(-angle); return new gfx3d.matrix.Matrix3D({yy: c, yz: -s, zy: s, zz: c}); // dojox.gfx3d.matrix.Matrix3D }, cameraRotateXg: function(degree){ // summary: forms a rotating matrix (about the x axis)in cameraTransform manner // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified degree. // See dojox.gfx3d.matrix.rotateX() for comparison. // degree: Number: an angle of rotation in degrees (>0 for CW) return gfx3d.matrix.rotateX(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D }, cameraRotateY: function(angle){ // summary: forms a rotating matrix (about the y axis) in cameraTransform manner // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified angle. // angle: Number: an angle of rotation in radians (>0 for CW) var c = Math.cos(-angle); var s = Math.sin(-angle); return new gfx3d.matrix.Matrix3D({xx: c, xz: s, zx: -s, zz: c}); // dojox.gfx3d.matrix.Matrix3D }, cameraRotateYg: function(degree){ // summary: forms a rotating matrix (about the y axis) in cameraTransform manner // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified degree. // See dojox.gfx3d.matrix.rotateY() for comparison. // degree: Number: an angle of rotation in degrees (>0 for CW) return gfx3d.matrix.rotateY(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D }, cameraRotateZ: function(angle){ // summary: forms a rotating matrix (about the z axis) in cameraTransform manner // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified angle. // angle: Number: an angle of rotation in radians (>0 for CW) var c = Math.cos(-angle); var s = Math.sin(-angle); return new gfx3d.matrix.Matrix3D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx3d.matrix.Matrix3D }, cameraRotateZg: function(degree){ // summary: forms a rotating matrix (about the z axis) in cameraTransform manner // description: The resulting matrix is used to rotate points // around the origin of coordinates (0, 0) by specified degree. // See dojox.gfx3d.matrix.rotateZ() for comparison. // degree: Number: an angle of rotation in degrees (>0 for CW) return gfx3d.matrix.rotateZ(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D }, // ensure matrix 3D conformance normalize: function(matrix){ // summary: converts an object to a matrix, if necessary // description: Converts any 3D matrix-like object or an array of // such objects to a valid dojox.gfx3d.matrix.Matrix3D object. // matrix: Object: an object, which is converted to a matrix, if necessary return (matrix instanceof gfx3d.matrix.Matrix3D) ? matrix : new gfx3d.matrix.Matrix3D(matrix); // dojox.gfx3d.matrix.Matrix3D }, // common operations clone: function(matrix){ // summary: creates a copy of a 3D matrix // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix-like object to be cloned var obj = new gfx3d.matrix.Matrix3D(); for(var i in matrix){ if(typeof(matrix[i]) == "number" && typeof(obj[i]) == "number" && obj[i] != matrix[i]) obj[i] = matrix[i]; } return obj; // dojox.gfx3d.matrix.Matrix3D }, invert: function(matrix){ // summary: inverts a 2D matrix // matrix: dojox.gfx.matrix.Matrix3D: a 2D matrix-like object to be inverted var m = gfx3d.matrix.normalize(matrix); var D = m.xx * m.yy * m.zz + m.xy * m.yz * m.zx + m.xz * m.yx * m.zy - m.xx * m.yz * m.zy - m.xy * m.yx * m.zz - m.xz * m.yy * m.zx; var M = new gfx3d.matrix.Matrix3D({ xx: (m.yy * m.zz - m.yz * m.zy) / D, xy: (m.xz * m.zy - m.xy * m.zz) / D, xz: (m.xy * m.yz - m.xz * m.yy) / D, yx: (m.yz * m.zx - m.yx * m.zz) / D, yy: (m.xx * m.zz - m.xz * m.zx) / D, yz: (m.xz * m.yx - m.xx * m.yz) / D, zx: (m.yx * m.zy - m.yy * m.zx) / D, zy: (m.xy * m.zx - m.xx * m.zy) / D, zz: (m.xx * m.yy - m.xy * m.yx) / D, dx: -1 * (m.xy * m.yz * m.dz + m.xz * m.dy * m.zy + m.dx * m.yy * m.zz - m.xy * m.dy * m.zz - m.xz * m.yy * m.dz - m.dx * m.yz * m.zy) / D, dy: (m.xx * m.yz * m.dz + m.xz * m.dy * m.zx + m.dx * m.yx * m.zz - m.xx * m.dy * m.zz - m.xz * m.yx * m.dz - m.dx * m.yz * m.zx) / D, dz: -1 * (m.xx * m.yy * m.dz + m.xy * m.dy * m.zx + m.dx * m.yx * m.zy - m.xx * m.dy * m.zy - m.xy * m.yx * m.dz - m.dx * m.yy * m.zx) / D }); return M; // dojox.gfx3d.matrix.Matrix3D }, _multiplyPoint: function(m, x, y, z){ // summary: applies a matrix to a point // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied // x: Number: an x coordinate of a point // y: Number: a y coordinate of a point // z: Number: a z coordinate of a point return {x: m.xx * x + m.xy * y + m.xz * z + m.dx, y: m.yx * x + m.yy * y + m.yz * z + m.dy, z: m.zx * x + m.zy * y + m.zz * z + m.dz}; // Object }, multiplyPoint: function(matrix, /* Number||Point */ a, /* Number, optional */ b, /* Number, optional */ c){ // summary: applies a matrix to a point // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied // a: Number: an x coordinate of a point // b: Number: a y coordinate of a point // c: Number: a z coordinate of a point var m = gfx3d.matrix.normalize(matrix); if(typeof a == "number" && typeof b == "number" && typeof c == "number"){ return gfx3d.matrix._multiplyPoint(m, a, b, c); // Object } // branch // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied // a: Object: a point // b: null // c: null return gfx3d.matrix._multiplyPoint(m, a.x, a.y, a.z); // Object }, multiply: function(matrix){ // summary: combines matrices by multiplying them sequentially in the given order // matrix: dojox.gfx3d.matrix.Matrix3D...: a 3D matrix-like object, // all subsequent arguments are matrix-like objects too var m = gfx3d.matrix.normalize(matrix); // combine matrices for(var i = 1; i < arguments.length; ++i){ var l = m; var r = gfx3d.matrix.normalize(arguments[i]); m = new gfx3d.matrix.Matrix3D(); m.xx = l.xx * r.xx + l.xy * r.yx + l.xz * r.zx; m.xy = l.xx * r.xy + l.xy * r.yy + l.xz * r.zy; m.xz = l.xx * r.xz + l.xy * r.yz + l.xz * r.zz; m.yx = l.yx * r.xx + l.yy * r.yx + l.yz * r.zx; m.yy = l.yx * r.xy + l.yy * r.yy + l.yz * r.zy; m.yz = l.yx * r.xz + l.yy * r.yz + l.yz * r.zz; m.zx = l.zx * r.xx + l.zy * r.yx + l.zz * r.zx; m.zy = l.zx * r.xy + l.zy * r.yy + l.zz * r.zy; m.zz = l.zx * r.xz + l.zy * r.yz + l.zz * r.zz; m.dx = l.xx * r.dx + l.xy * r.dy + l.xz * r.dz + l.dx; m.dy = l.yx * r.dx + l.yy * r.dy + l.yz * r.dz + l.dy; m.dz = l.zx * r.dx + l.zy * r.dy + l.zz * r.dz + l.dz; } return m; // dojox.gfx3d.matrix.Matrix3D }, _project: function(m, x, y, z){ // summary: applies a matrix to a point // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied // x: Number: an x coordinate of a point // y: Number: a y coordinate of a point // z: Number: a z coordinate of a point return { // Object x: m.xx * x + m.xy * y + m.xz * z + m.dx, y: m.yx * x + m.yy * y + m.yz * z + m.dy, z: m.zx * x + m.zy * y + m.zz * z + m.dz}; }, project: function(matrix, /* Number||Point */ a, /* Number, optional */ b, /* Number, optional */ c){ // summary: applies a matrix to a point // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied // a: Number: an x coordinate of a point // b: Number: a y coordinate of a point // c: Number: a z coordinate of a point var m = gfx3d.matrix.normalize(matrix); if(typeof a == "number" && typeof b == "number" && typeof c == "number"){ return gfx3d.matrix._project(m, a, b, c); // Object } // branch // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied // a: Object: a point // b: null // c: null return gfx3d.matrix._project(m, a.x, a.y, a.z); // Object } }); // propagate matrix up gfx3d.Matrix3D = gfx3d.matrix.Matrix3D; return gfx3d.matrix; });