| 1 | define(["dojo/_base/lang", "./_base"], function(lang, gfx3d){ |
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| 2 | |
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| 3 | // candidates for dojox.math: |
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| 4 | gfx3d.matrix = { |
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| 5 | _degToRad : function(degree){ return Math.PI * degree / 180; }, |
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| 6 | _radToDeg : function(radian){ return radian / Math.PI * 180; } |
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| 7 | }; |
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| 8 | |
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| 9 | gfx3d.matrix.Matrix3D = function(arg){ |
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| 10 | // summary: a 3D matrix object |
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| 11 | // description: Normalizes a 3D matrix-like object. If arrays is passed, |
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| 12 | // all objects of the array are normalized and multiplied sequentially. |
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| 13 | // arg: Object |
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| 14 | // a 3D matrix-like object, a number, or an array of such objects |
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| 15 | if(arg){ |
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| 16 | if(typeof arg == "number"){ |
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| 17 | this.xx = this.yy = this.zz = arg; |
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| 18 | }else if(arg instanceof Array){ |
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| 19 | if(arg.length > 0){ |
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| 20 | var m = gfx3d.matrix.normalize(arg[0]); |
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| 21 | // combine matrices |
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| 22 | for(var i = 1; i < arg.length; ++i){ |
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| 23 | var l = m; |
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| 24 | var r = gfx3d.matrix.normalize(arg[i]); |
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| 25 | m = new gfx3d.matrix.Matrix3D(); |
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| 26 | m.xx = l.xx * r.xx + l.xy * r.yx + l.xz * r.zx; |
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| 27 | m.xy = l.xx * r.xy + l.xy * r.yy + l.xz * r.zy; |
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| 28 | m.xz = l.xx * r.xz + l.xy * r.yz + l.xz * r.zz; |
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| 29 | m.yx = l.yx * r.xx + l.yy * r.yx + l.yz * r.zx; |
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| 30 | m.yy = l.yx * r.xy + l.yy * r.yy + l.yz * r.zy; |
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| 31 | m.yz = l.yx * r.xz + l.yy * r.yz + l.yz * r.zz; |
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| 32 | m.zx = l.zx * r.xx + l.zy * r.yx + l.zz * r.zx; |
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| 33 | m.zy = l.zx * r.xy + l.zy * r.yy + l.zz * r.zy; |
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| 34 | m.zz = l.zx * r.xz + l.zy * r.yz + l.zz * r.zz; |
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| 35 | m.dx = l.xx * r.dx + l.xy * r.dy + l.xz * r.dz + l.dx; |
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| 36 | m.dy = l.yx * r.dx + l.yy * r.dy + l.yz * r.dz + l.dy; |
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| 37 | m.dz = l.zx * r.dx + l.zy * r.dy + l.zz * r.dz + l.dz; |
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| 38 | } |
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| 39 | lang.mixin(this, m); |
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| 40 | } |
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| 41 | }else{ |
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| 42 | lang.mixin(this, arg); |
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| 43 | } |
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| 44 | } |
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| 45 | }; |
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| 46 | |
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| 47 | // the default (identity) matrix, which is used to fill in missing values |
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| 48 | 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}); |
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| 49 | |
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| 50 | lang.mixin(gfx3d.matrix, { |
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| 51 | // summary: class constants, and methods of dojox.gfx3d.matrix |
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| 52 | |
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| 53 | // matrix constants |
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| 54 | |
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| 55 | // identity: dojox.gfx3d.matrix.Matrix3D |
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| 56 | // an identity matrix constant: identity * (x, y, z) == (x, y, z) |
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| 57 | identity: new gfx3d.matrix.Matrix3D(), |
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| 58 | |
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| 59 | // matrix creators |
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| 60 | |
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| 61 | translate: function(a, b, c){ |
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| 62 | // summary: forms a translation matrix |
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| 63 | // description: The resulting matrix is used to translate (move) points by specified offsets. |
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| 64 | // a: Number: an x coordinate value |
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| 65 | // b: Number: a y coordinate value |
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| 66 | // c: Number: a z coordinate value |
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| 67 | if(arguments.length > 1){ |
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| 68 | return new gfx3d.matrix.Matrix3D({dx: a, dy: b, dz: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 69 | } |
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| 70 | // branch |
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| 71 | // a: Object: a point-like object, which specifies offsets for 3 dimensions |
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| 72 | // b: null |
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| 73 | return new gfx3d.matrix.Matrix3D({dx: a.x, dy: a.y, dz: a.z}); // dojox.gfx3d.matrix.Matrix3D |
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| 74 | }, |
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| 75 | scale: function(a, b, c){ |
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| 76 | // summary: forms a scaling matrix |
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| 77 | // description: The resulting matrix is used to scale (magnify) points by specified offsets. |
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| 78 | // a: Number: a scaling factor used for the x coordinate |
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| 79 | // b: Number: a scaling factor used for the y coordinate |
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| 80 | // c: Number: a scaling factor used for the z coordinate |
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| 81 | if(arguments.length > 1){ |
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| 82 | return new gfx3d.matrix.Matrix3D({xx: a, yy: b, zz: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 83 | } |
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| 84 | if(typeof a == "number"){ |
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| 85 | // branch |
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| 86 | // a: Number: a uniform scaling factor used for the all coordinates |
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| 87 | // b: null |
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| 88 | return new gfx3d.matrix.Matrix3D({xx: a, yy: a, zz: a}); // dojox.gfx3d.matrix.Matrix3D |
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| 89 | } |
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| 90 | // branch |
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| 91 | // a: Object: a point-like object, which specifies scale factors for 3 dimensions |
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| 92 | // b: null |
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| 93 | return new gfx3d.matrix.Matrix3D({xx: a.x, yy: a.y, zz: a.z}); // dojox.gfx3d.matrix.Matrix3D |
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| 94 | }, |
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| 95 | rotateX: function(angle){ |
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| 96 | // summary: forms a rotating matrix (about the x axis) |
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| 97 | // description: The resulting matrix is used to rotate points |
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| 98 | // around the origin of coordinates (0, 0) by specified angle. |
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| 99 | // angle: Number: an angle of rotation in radians (>0 for CW) |
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| 100 | var c = Math.cos(angle); |
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| 101 | var s = Math.sin(angle); |
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| 102 | return new gfx3d.matrix.Matrix3D({yy: c, yz: -s, zy: s, zz: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 103 | }, |
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| 104 | rotateXg: function(degree){ |
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| 105 | // summary: forms a rotating matrix (about the x axis) |
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| 106 | // description: The resulting matrix is used to rotate points |
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| 107 | // around the origin of coordinates (0, 0) by specified degree. |
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| 108 | // See dojox.gfx3d.matrix.rotateX() for comparison. |
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| 109 | // degree: Number: an angle of rotation in degrees (>0 for CW) |
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| 110 | return gfx3d.matrix.rotateX(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D |
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| 111 | }, |
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| 112 | rotateY: function(angle){ |
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| 113 | // summary: forms a rotating matrix (about the y axis) |
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| 114 | // description: The resulting matrix is used to rotate points |
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| 115 | // around the origin of coordinates (0, 0) by specified angle. |
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| 116 | // angle: Number: an angle of rotation in radians (>0 for CW) |
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| 117 | var c = Math.cos(angle); |
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| 118 | var s = Math.sin(angle); |
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| 119 | return new gfx3d.matrix.Matrix3D({xx: c, xz: s, zx: -s, zz: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 120 | }, |
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| 121 | rotateYg: function(degree){ |
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| 122 | // summary: forms a rotating matrix (about the y axis) |
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| 123 | // description: The resulting matrix is used to rotate points |
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| 124 | // around the origin of coordinates (0, 0) by specified degree. |
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| 125 | // See dojox.gfx3d.matrix.rotateY() for comparison. |
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| 126 | // degree: Number: an angle of rotation in degrees (>0 for CW) |
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| 127 | return gfx3d.matrix.rotateY(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D |
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| 128 | }, |
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| 129 | rotateZ: function(angle){ |
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| 130 | // summary: forms a rotating matrix (about the z axis) |
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| 131 | // description: The resulting matrix is used to rotate points |
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| 132 | // around the origin of coordinates (0, 0) by specified angle. |
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| 133 | // angle: Number: an angle of rotation in radians (>0 for CW) |
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| 134 | var c = Math.cos(angle); |
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| 135 | var s = Math.sin(angle); |
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| 136 | return new gfx3d.matrix.Matrix3D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 137 | }, |
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| 138 | rotateZg: function(degree){ |
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| 139 | // summary: forms a rotating matrix (about the z axis) |
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| 140 | // description: The resulting matrix is used to rotate points |
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| 141 | // around the origin of coordinates (0, 0) by specified degree. |
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| 142 | // See dojox.gfx3d.matrix.rotateZ() for comparison. |
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| 143 | // degree: Number: an angle of rotation in degrees (>0 for CW) |
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| 144 | return gfx3d.matrix.rotateZ(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D |
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| 145 | }, |
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| 146 | |
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| 147 | // camera transformation |
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| 148 | cameraTranslate: function(a, b, c){ |
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| 149 | // summary: forms a translation matrix |
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| 150 | // description: The resulting matrix is used to translate (move) points by specified offsets. |
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| 151 | // a: Number: an x coordinate value |
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| 152 | // b: Number: a y coordinate value |
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| 153 | // c: Number: a z coordinate value |
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| 154 | if(arguments.length > 1){ |
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| 155 | return new gfx3d.matrix.Matrix3D({dx: -a, dy: -b, dz: -c}); // dojox.gfx3d.matrix.Matrix3D |
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| 156 | } |
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| 157 | // branch |
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| 158 | // a: Object: a point-like object, which specifies offsets for 3 dimensions |
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| 159 | // b: null |
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| 160 | return new gfx3d.matrix.Matrix3D({dx: -a.x, dy: -a.y, dz: -a.z}); // dojox.gfx3d.matrix.Matrix3D |
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| 161 | }, |
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| 162 | cameraRotateX: function(angle){ |
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| 163 | // summary: forms a rotating matrix (about the x axis) in cameraTransform manner |
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| 164 | // description: The resulting matrix is used to rotate points |
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| 165 | // around the origin of coordinates (0, 0) by specified angle. |
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| 166 | // angle: Number: an angle of rotation in radians (>0 for CW) |
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| 167 | var c = Math.cos(-angle); |
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| 168 | var s = Math.sin(-angle); |
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| 169 | return new gfx3d.matrix.Matrix3D({yy: c, yz: -s, zy: s, zz: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 170 | }, |
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| 171 | cameraRotateXg: function(degree){ |
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| 172 | // summary: forms a rotating matrix (about the x axis)in cameraTransform manner |
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| 173 | // description: The resulting matrix is used to rotate points |
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| 174 | // around the origin of coordinates (0, 0) by specified degree. |
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| 175 | // See dojox.gfx3d.matrix.rotateX() for comparison. |
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| 176 | // degree: Number: an angle of rotation in degrees (>0 for CW) |
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| 177 | return gfx3d.matrix.rotateX(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D |
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| 178 | }, |
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| 179 | cameraRotateY: function(angle){ |
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| 180 | // summary: forms a rotating matrix (about the y axis) in cameraTransform manner |
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| 181 | // description: The resulting matrix is used to rotate points |
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| 182 | // around the origin of coordinates (0, 0) by specified angle. |
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| 183 | // angle: Number: an angle of rotation in radians (>0 for CW) |
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| 184 | var c = Math.cos(-angle); |
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| 185 | var s = Math.sin(-angle); |
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| 186 | return new gfx3d.matrix.Matrix3D({xx: c, xz: s, zx: -s, zz: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 187 | }, |
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| 188 | cameraRotateYg: function(degree){ |
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| 189 | // summary: forms a rotating matrix (about the y axis) in cameraTransform manner |
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| 190 | // description: The resulting matrix is used to rotate points |
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| 191 | // around the origin of coordinates (0, 0) by specified degree. |
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| 192 | // See dojox.gfx3d.matrix.rotateY() for comparison. |
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| 193 | // degree: Number: an angle of rotation in degrees (>0 for CW) |
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| 194 | return gfx3d.matrix.rotateY(dojox.gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D |
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| 195 | }, |
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| 196 | cameraRotateZ: function(angle){ |
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| 197 | // summary: forms a rotating matrix (about the z axis) in cameraTransform manner |
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| 198 | // description: The resulting matrix is used to rotate points |
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| 199 | // around the origin of coordinates (0, 0) by specified angle. |
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| 200 | // angle: Number: an angle of rotation in radians (>0 for CW) |
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| 201 | var c = Math.cos(-angle); |
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| 202 | var s = Math.sin(-angle); |
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| 203 | return new gfx3d.matrix.Matrix3D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx3d.matrix.Matrix3D |
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| 204 | }, |
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| 205 | cameraRotateZg: function(degree){ |
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| 206 | // summary: forms a rotating matrix (about the z axis) in cameraTransform manner |
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| 207 | // description: The resulting matrix is used to rotate points |
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| 208 | // around the origin of coordinates (0, 0) by specified degree. |
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| 209 | // See dojox.gfx3d.matrix.rotateZ() for comparison. |
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| 210 | // degree: Number: an angle of rotation in degrees (>0 for CW) |
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| 211 | return gfx3d.matrix.rotateZ(gfx3d.matrix._degToRad(degree)); // dojox.gfx3d.matrix.Matrix3D |
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| 212 | }, |
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| 213 | |
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| 214 | // ensure matrix 3D conformance |
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| 215 | normalize: function(matrix){ |
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| 216 | // summary: converts an object to a matrix, if necessary |
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| 217 | // description: Converts any 3D matrix-like object or an array of |
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| 218 | // such objects to a valid dojox.gfx3d.matrix.Matrix3D object. |
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| 219 | // matrix: Object: an object, which is converted to a matrix, if necessary |
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| 220 | return (matrix instanceof gfx3d.matrix.Matrix3D) ? matrix : new gfx3d.matrix.Matrix3D(matrix); // dojox.gfx3d.matrix.Matrix3D |
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| 221 | }, |
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| 222 | |
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| 223 | // common operations |
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| 224 | |
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| 225 | clone: function(matrix){ |
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| 226 | // summary: creates a copy of a 3D matrix |
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| 227 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix-like object to be cloned |
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| 228 | var obj = new gfx3d.matrix.Matrix3D(); |
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| 229 | for(var i in matrix){ |
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| 230 | if(typeof(matrix[i]) == "number" && typeof(obj[i]) == "number" && obj[i] != matrix[i]) obj[i] = matrix[i]; |
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| 231 | } |
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| 232 | return obj; // dojox.gfx3d.matrix.Matrix3D |
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| 233 | }, |
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| 234 | invert: function(matrix){ |
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| 235 | // summary: inverts a 2D matrix |
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| 236 | // matrix: dojox.gfx.matrix.Matrix3D: a 2D matrix-like object to be inverted |
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| 237 | var m = gfx3d.matrix.normalize(matrix); |
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| 238 | 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; |
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| 239 | var M = new gfx3d.matrix.Matrix3D({ |
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| 240 | xx: (m.yy * m.zz - m.yz * m.zy) / D, |
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| 241 | xy: (m.xz * m.zy - m.xy * m.zz) / D, |
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| 242 | xz: (m.xy * m.yz - m.xz * m.yy) / D, |
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| 243 | yx: (m.yz * m.zx - m.yx * m.zz) / D, |
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| 244 | yy: (m.xx * m.zz - m.xz * m.zx) / D, |
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| 245 | yz: (m.xz * m.yx - m.xx * m.yz) / D, |
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| 246 | zx: (m.yx * m.zy - m.yy * m.zx) / D, |
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| 247 | zy: (m.xy * m.zx - m.xx * m.zy) / D, |
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| 248 | zz: (m.xx * m.yy - m.xy * m.yx) / D, |
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| 249 | 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, |
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| 250 | 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, |
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| 251 | 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 |
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| 252 | }); |
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| 253 | return M; // dojox.gfx3d.matrix.Matrix3D |
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| 254 | }, |
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| 255 | _multiplyPoint: function(m, x, y, z){ |
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| 256 | // summary: applies a matrix to a point |
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| 257 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied |
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| 258 | // x: Number: an x coordinate of a point |
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| 259 | // y: Number: a y coordinate of a point |
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| 260 | // z: Number: a z coordinate of a point |
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| 261 | 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 |
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| 262 | }, |
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| 263 | multiplyPoint: function(matrix, /* Number||Point */ a, /* Number, optional */ b, /* Number, optional */ c){ |
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| 264 | // summary: applies a matrix to a point |
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| 265 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied |
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| 266 | // a: Number: an x coordinate of a point |
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| 267 | // b: Number: a y coordinate of a point |
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| 268 | // c: Number: a z coordinate of a point |
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| 269 | var m = gfx3d.matrix.normalize(matrix); |
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| 270 | if(typeof a == "number" && typeof b == "number" && typeof c == "number"){ |
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| 271 | return gfx3d.matrix._multiplyPoint(m, a, b, c); // Object |
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| 272 | } |
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| 273 | // branch |
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| 274 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied |
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| 275 | // a: Object: a point |
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| 276 | // b: null |
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| 277 | // c: null |
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| 278 | return gfx3d.matrix._multiplyPoint(m, a.x, a.y, a.z); // Object |
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| 279 | }, |
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| 280 | multiply: function(matrix){ |
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| 281 | // summary: combines matrices by multiplying them sequentially in the given order |
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| 282 | // matrix: dojox.gfx3d.matrix.Matrix3D...: a 3D matrix-like object, |
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| 283 | // all subsequent arguments are matrix-like objects too |
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| 284 | var m = gfx3d.matrix.normalize(matrix); |
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| 285 | // combine matrices |
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| 286 | for(var i = 1; i < arguments.length; ++i){ |
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| 287 | var l = m; |
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| 288 | var r = gfx3d.matrix.normalize(arguments[i]); |
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| 289 | m = new gfx3d.matrix.Matrix3D(); |
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| 290 | m.xx = l.xx * r.xx + l.xy * r.yx + l.xz * r.zx; |
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| 291 | m.xy = l.xx * r.xy + l.xy * r.yy + l.xz * r.zy; |
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| 292 | m.xz = l.xx * r.xz + l.xy * r.yz + l.xz * r.zz; |
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| 293 | m.yx = l.yx * r.xx + l.yy * r.yx + l.yz * r.zx; |
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| 294 | m.yy = l.yx * r.xy + l.yy * r.yy + l.yz * r.zy; |
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| 295 | m.yz = l.yx * r.xz + l.yy * r.yz + l.yz * r.zz; |
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| 296 | m.zx = l.zx * r.xx + l.zy * r.yx + l.zz * r.zx; |
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| 297 | m.zy = l.zx * r.xy + l.zy * r.yy + l.zz * r.zy; |
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| 298 | m.zz = l.zx * r.xz + l.zy * r.yz + l.zz * r.zz; |
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| 299 | m.dx = l.xx * r.dx + l.xy * r.dy + l.xz * r.dz + l.dx; |
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| 300 | m.dy = l.yx * r.dx + l.yy * r.dy + l.yz * r.dz + l.dy; |
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| 301 | m.dz = l.zx * r.dx + l.zy * r.dy + l.zz * r.dz + l.dz; |
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| 302 | } |
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| 303 | return m; // dojox.gfx3d.matrix.Matrix3D |
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| 304 | }, |
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| 305 | |
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| 306 | _project: function(m, x, y, z){ |
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| 307 | // summary: applies a matrix to a point |
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| 308 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied |
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| 309 | // x: Number: an x coordinate of a point |
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| 310 | // y: Number: a y coordinate of a point |
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| 311 | // z: Number: a z coordinate of a point |
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| 312 | return { // Object |
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| 313 | x: m.xx * x + m.xy * y + m.xz * z + m.dx, |
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| 314 | y: m.yx * x + m.yy * y + m.yz * z + m.dy, |
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| 315 | z: m.zx * x + m.zy * y + m.zz * z + m.dz}; |
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| 316 | }, |
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| 317 | project: function(matrix, /* Number||Point */ a, /* Number, optional */ b, /* Number, optional */ c){ |
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| 318 | // summary: applies a matrix to a point |
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| 319 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied |
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| 320 | // a: Number: an x coordinate of a point |
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| 321 | // b: Number: a y coordinate of a point |
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| 322 | // c: Number: a z coordinate of a point |
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| 323 | var m = gfx3d.matrix.normalize(matrix); |
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| 324 | if(typeof a == "number" && typeof b == "number" && typeof c == "number"){ |
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| 325 | return gfx3d.matrix._project(m, a, b, c); // Object |
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| 326 | } |
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| 327 | // branch |
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| 328 | // matrix: dojox.gfx3d.matrix.Matrix3D: a 3D matrix object to be applied |
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| 329 | // a: Object: a point |
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| 330 | // b: null |
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| 331 | // c: null |
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| 332 | return gfx3d.matrix._project(m, a.x, a.y, a.z); // Object |
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| 333 | } |
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| 334 | }); |
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| 335 | |
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| 336 | // propagate matrix up |
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| 337 | gfx3d.Matrix3D = gfx3d.matrix.Matrix3D; |
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| 338 | |
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| 339 | return gfx3d.matrix; |
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| 340 | }); |
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