analytics/webcontent/dojo16/dojox/gfx3d/matrix.js

/*
	Copyright (c) 2004-2012, The Dojo Foundation All Rights Reserved.
	Available via Academic Free License >= 2.1 OR the modified BSD license.
	see: http://dojotoolkit.org/license for details
*/


if(!dojo._hasResource["dojox.gfx3d.matrix"]){ //_hasResource checks added by build. Do not use _hasResource directly in your code.
dojo._hasResource["dojox.gfx3d.matrix"] = true;
dojo.provide("dojox.gfx3d.matrix");

// candidates for dojox.math:
dojox.gfx3d.matrix._degToRad = function(degree){ return Math.PI * degree / 180; };
dojox.gfx3d.matrix._radToDeg = function(radian){ return radian / Math.PI * 180; };

dojox.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 = dojox.gfx3d.matrix.normalize(arg[0]);
				// combine matrices
				for(var i = 1; i < arg.length; ++i){
					var l = m;
					var r = dojox.gfx3d.matrix.normalize(arg[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;
				}
				dojo.mixin(this, m);
			}
		}else{
			dojo.mixin(this, arg);
		}
	}
};

// the default (identity) matrix, which is used to fill in missing values
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});

dojo.mixin(dojox.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 dojox.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 dojox.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 dojox.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 dojox.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 dojox.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 dojox.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 dojox.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 dojox.gfx3d.matrix.rotateX(dojox.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 dojox.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 dojox.gfx3d.matrix.rotateY(dojox.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 dojox.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 dojox.gfx3d.matrix.rotateZ(dojox.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 dojox.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 dojox.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 dojox.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 dojox.gfx3d.matrix.rotateX(dojox.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 dojox.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 dojox.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 dojox.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 dojox.gfx3d.matrix.rotateZ(dojox.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 dojox.gfx3d.matrix.Matrix3D) ? matrix : new dojox.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 dojox.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 = dojox.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 dojox.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 = dojox.gfx3d.matrix.normalize(matrix);
		if(typeof a == "number" && typeof b == "number" && typeof c == "number"){
			return dojox.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 dojox.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 = 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;

}