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