matrix.js

define(["dcl/dcl", "./_base", "dojo/_base/lang"], function (dcl, g, lang) {
	var m = g.matrix = {};

	var _degToRadCache = {};
	m._degToRad = function (degree) {
		return _degToRadCache[degree] || (_degToRadCache[degree] = (Math.PI * degree / 180));
	};
	m._radToDeg = function (radian) {
		return radian / Math.PI * 180;
	};

	m.Matrix2D = function (arg) {
		// summary:
		//		a 2D matrix object
		// description:
		//		Normalizes a 2D matrix-like object. If arrays is passed,
		//		all objects of the array are normalized and multiplied sequentially.
		// arg: Object
		//		a 2D matrix-like object, a number, or an array of such objects
		if (arg) {
			if (typeof arg === "number") {
				this.xx = this.yy = arg;
			} else if (arg instanceof Array) {
				if (arg.length > 0) {
					var matrix = m.normalize(arg[0]);
					// combine matrices
					for (var i = 1; i < arg.length; ++i) {
						var l = matrix, r = m.normalize(arg[i]);
						matrix = new m.Matrix2D();
						matrix.xx = l.xx * r.xx + l.xy * r.yx;
						matrix.xy = l.xx * r.xy + l.xy * r.yy;
						matrix.yx = l.yx * r.xx + l.yy * r.yx;
						matrix.yy = l.yx * r.xy + l.yy * r.yy;
						matrix.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
						matrix.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
					}
					dcl.mix(this, matrix);
				}
			} else {
				dcl.mix(this, arg);
			}
		}
	};

	// the default (identity) matrix, which is used to fill in missing values
	lang.extend(m.Matrix2D, {xx: 1, xy: 0, yx: 0, yy: 1, dx: 0, dy: 0});

	dcl.mix(m, {
		// summary:
		//		class constants, and methods of gfx/matrix

		// matrix constants

		// identity: gfx/matrix.Matrix2D
		//		an identity matrix constant: identity * (x, y) === (x, y)
		identity: new m.Matrix2D(),

		// flipX: gfx/matrix.Matrix2D
		//		a matrix, which reflects points at x = 0 line: flipX * (x, y) === (-x, y)
		flipX: new m.Matrix2D({xx: -1}),

		// flipY: gfx/matrix.Matrix2D
		//		a matrix, which reflects points at y = 0 line: flipY * (x, y) === (x, -y)
		flipY: new m.Matrix2D({yy: -1}),

		// flipXY: gfx/matrix.Matrix2D
		//		a matrix, which reflects points at the origin of coordinates: flipXY * (x, y) === (-x, -y)
		flipXY: new m.Matrix2D({xx: -1, yy: -1}),

		// matrix creators

		translate: function (a, b) {
			// summary:
			//		forms a translation matrix
			// description:
			//		The resulting matrix is used to translate (move) points by specified offsets.
			// a: Number|gfx.Point
			//		an x coordinate value, or a point-like object, which specifies offsets for both dimensions
			// b: Number?
			//		a y coordinate value
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 1) {
				return new m.Matrix2D({dx: a, dy: b}); // gfx/matrix.Matrix2D
			}
			// branch
			return new m.Matrix2D({dx: a.x, dy: a.y}); // gfx/matrix.Matrix2D
		},
		scale: function (a, b) {
			// summary:
			//		forms a scaling matrix
			// description:
			//		The resulting matrix is used to scale (magnify) points by specified offsets.
			// a: Number|gfx.Point
			//		a scaling factor used for the x coordinate, or
			//		a uniform scaling factor used for the both coordinates, or
			//		a point-like object, which specifies scale factors for both dimensions
			// b: Number?
			//		a scaling factor used for the y coordinate
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 1) {
				return new m.Matrix2D({xx: a, yy: b}); // gfx/matrix.Matrix2D
			}
			if (typeof a === "number") {
				return new m.Matrix2D({xx: a, yy: a}); // gfx/matrix.Matrix2D
			}
			return new m.Matrix2D({xx: a.x, yy: a.y}); // gfx/matrix.Matrix2D
		},
		rotate: function (angle) {
			// summary:
			//		forms a rotating matrix
			// 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)
			// returns: gfx/matrix.Matrix2D
			var c = Math.cos(angle);
			var s = Math.sin(angle);
			return new m.Matrix2D({xx: c, xy: -s, yx: s, yy: c}); // gfx/matrix.Matrix2D
		},
		rotateg: function (degree) {
			// summary:
			//		forms a rotating matrix
			// description:
			//		The resulting matrix is used to rotate points
			//		around the origin of coordinates (0, 0) by specified degree.
			//		See gfx/matrix.rotate() for comparison.
			// degree: Number
			//		an angle of rotation in degrees (>0 for CW)
			// returns: gfx/matrix.Matrix2D
			return m.rotate(m._degToRad(degree)); // gfx/matrix.Matrix2D
		},
		skewX: function (angle) {
			// summary:
			//		forms an x skewing matrix
			// description:
			//		The resulting matrix is used to skew points in the x dimension
			//		around the origin of coordinates (0, 0) by specified angle.
			// angle: Number
			//		a skewing angle in radians
			// returns: gfx/matrix.Matrix2D
			return new m.Matrix2D({xy: Math.tan(angle)}); // gfx/matrix.Matrix2D
		},
		skewXg: function (degree) {
			// summary:
			//		forms an x skewing matrix
			// description:
			//		The resulting matrix is used to skew points in the x dimension
			//		around the origin of coordinates (0, 0) by specified degree.
			//		See gfx/matrix.skewX() for comparison.
			// degree: Number
			//		a skewing angle in degrees
			// returns: gfx/matrix.Matrix2D
			return m.skewX(m._degToRad(degree)); // gfx/matrix.Matrix2D
		},
		skewY: function (angle) {
			// summary:
			//		forms a y skewing matrix
			// description:
			//		The resulting matrix is used to skew points in the y dimension
			//		around the origin of coordinates (0, 0) by specified angle.
			// angle: Number
			//		a skewing angle in radians
			// returns: gfx/matrix.Matrix2D
			return new m.Matrix2D({yx: Math.tan(angle)}); // gfx/matrix.Matrix2D
		},
		skewYg: function (degree) {
			// summary:
			//		forms a y skewing matrix
			// description:
			//		The resulting matrix is used to skew points in the y dimension
			//		around the origin of coordinates (0, 0) by specified degree.
			//		See gfx/matrix.skewY() for comparison.
			// degree: Number
			//		a skewing angle in degrees
			// returns: gfx/matrix.Matrix2D
			return m.skewY(m._degToRad(degree)); // gfx/matrix.Matrix2D
		},
		reflect: function (a, b) {
			// summary:
			//		forms a reflection matrix
			// description:
			//		The resulting matrix is used to reflect points around a vector,
			//		which goes through the origin.
			// a: gfx.Point|Number
			//		a point-like object, which specifies a vector of reflection, or an X value
			// b: Number?
			//		a Y value
			// returns: gfx/matrix.Matrix2D
			if (arguments.length === 1) {
				b = a.y;
				a = a.x;
			}
			// make a unit vector
			var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = 2 * a * b / n2;
			return new m.Matrix2D({xx: 2 * a2 / n2 - 1, xy: xy, yx: xy, yy: 2 * b2 / n2 - 1}); // gfx/matrix.Matrix2D
		},
		project: function (a, b) {
			// summary:
			//		forms an orthogonal projection matrix
			// description:
			//		The resulting matrix is used to project points orthogonally on a vector,
			//		which goes through the origin.
			// a: gfx.Point|Number
			//		a point-like object, which specifies a vector of projection, or
			//		an x coordinate value
			// b: Number?
			//		a y coordinate value
			// returns: gfx/matrix.Matrix2D
			if (arguments.length === 1) {
				b = a.y;
				a = a.x;
			}
			// make a unit vector
			var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = a * b / n2;
			return new m.Matrix2D({xx: a2 / n2, xy: xy, yx: xy, yy: b2 / n2}); // gfx/matrix.Matrix2D
		},

		// ensure matrix 2D conformance
		normalize: function (matrix) {
			// summary:
			//		converts an object to a matrix, if necessary
			// description:
			//		Converts any 2D matrix-like object or an array of
			//		such objects to a valid gfx/matrix.Matrix2D object.
			// matrix: Object
			//		an object, which is converted to a matrix, if necessary
			// returns: gfx/matrix.Matrix2D
			return (matrix instanceof m.Matrix2D) ? matrix : new m.Matrix2D(matrix); // gfx/matrix.Matrix2D
		},

		// common operations

		isIdentity: function (matrix) {
			// summary:
			//		returns whether the specified matrix is the identity.
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix object to be tested
			// returns: Boolean
			return matrix.xx === 1 && matrix.xy === 0 && matrix.yx === 0 && matrix.yy === 1 && matrix.dx === 0 &&
				matrix.dy === 0; // Boolean
		},
		clone: function (matrix) {
			// summary:
			//		creates a copy of a 2D matrix
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix-like object to be cloned
			// returns: gfx/matrix.Matrix2D
			var obj = new m.Matrix2D();
			for (var i in matrix) {
				if (typeof(matrix[i]) === "number" && typeof(obj[i]) === "number" && obj[i] !== matrix[i]) {
					obj[i] = matrix[i];
				}
			}
			return obj; // gfx/matrix.Matrix2D
		},
		invert: function (matrix) {
			// summary:
			//		inverts a 2D matrix
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix-like object to be inverted
			// returns: gfx/matrix.Matrix2D
			var M = m.normalize(matrix), D = M.xx * M.yy - M.xy * M.yx;
			M = new m.Matrix2D({
				xx: M.yy / D,
				xy: -M.xy / D,
				yx: -M.yx / D,
				yy: M.xx / D,
				dx: (M.xy * M.dy - M.yy * M.dx) / D,
				dy: (M.yx * M.dx - M.xx * M.dy) / D
			});
			return M; // gfx/matrix.Matrix2D
		},
		_multiplyPoint: function (matrix, x, y) {
			// summary:
			//		applies a matrix to a point
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix object to be applied
			// x: Number
			//		an x coordinate of a point
			// y: Number
			//		a y coordinate of a point
			// returns: gfx.Point
			return {x: matrix.xx * x + matrix.xy * y + matrix.dx, y: matrix.yx * x + matrix.yy * y + matrix.dy};
		},
		multiplyPoint: function (matrix, /* Number||Point */ a, /* Number? */ b) {
			// summary:
			//		applies a matrix to a point
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix object to be applied
			// a: Number|gfx.Point
			//		an x coordinate of a point, or a point
			// b: Number?
			//		a y coordinate of a point
			// returns: gfx.Point
			var M = m.normalize(matrix);
			if (typeof a === "number" && typeof b === "number") {
				return m._multiplyPoint(M, a, b); // gfx.Point
			}
			return m._multiplyPoint(M, a.x, a.y); // gfx.Point
		},
		multiplyRectangle: function (matrix, /*Rectangle*/ rect) {
			// summary:
			//		Applies a matrix to a rectangle.
			// description:
			//		The method applies the transformation on all corners of the
			//		rectangle and returns the smallest rectangle enclosing the 4 transformed
			//		points.
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix object to be applied.
			// rect: Rectangle
			//		the rectangle to transform.
			// returns: gfx.Rectangle
			var M = m.normalize(matrix);
			rect = rect || {x: 0, y: 0, width: 0, height: 0};
			if (m.isIdentity(M)) {
				return {x: rect.x, y: rect.y, width: rect.width, height: rect.height};
			} // dojo/gfx.Rectangle
			var p0 = m.multiplyPoint(M, rect.x, rect.y), p1 = m.multiplyPoint(M, rect.x,
				rect.y + rect.height), p2 = m.multiplyPoint(M, rect.x + rect.width, rect.y), p3 = m.multiplyPoint(M,
				rect.x + rect.width, rect.y + rect.height), minx = Math.min(p0.x, p1.x, p2.x,
				p3.x), miny = Math.min(p0.y, p1.y, p2.y, p3.y), maxx = Math.max(p0.x, p1.x, p2.x,
				p3.x), maxy = Math.max(p0.y, p1.y, p2.y, p3.y);
			return { // dojo/gfx.Rectangle
				x: minx,
				y: miny,
				width: maxx - minx,
				height: maxy - miny
			};
		},
		multiply: function (matrix) {
			// summary:
			//		combines matrices by multiplying them sequentially in the given order
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix-like object,
			//		all subsequent arguments are matrix-like objects too
			var M = m.normalize(matrix);
			// combine matrices
			for (var i = 1; i < arguments.length; ++i) {
				var l = M, r = m.normalize(arguments[i]);
				M = new m.Matrix2D();
				M.xx = l.xx * r.xx + l.xy * r.yx;
				M.xy = l.xx * r.xy + l.xy * r.yy;
				M.yx = l.yx * r.xx + l.yy * r.yx;
				M.yy = l.yx * r.xy + l.yy * r.yy;
				M.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
				M.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
			}
			return M; // gfx/matrix.Matrix2D
		},

		// high level operations

		_sandwich: function (matrix, x, y) {
			// summary:
			//		applies a matrix at a central point
			// matrix: gfx/matrix.Matrix2D
			//		a 2D matrix-like object, which is applied at a central point
			// x: Number
			//		an x component of the central point
			// y: Number
			//		a y component of the central point
			return m.multiply(m.translate(x, y), matrix, m.translate(-x, -y)); // gfx/matrix.Matrix2D
		},
		scaleAt: function (a, b, c, d) {
			// summary:
			//		scales a picture using a specified point as a center of scaling
			// description:
			//		Compare with gfx/matrix.scale().
			// a: Number
			//		a scaling factor used for the x coordinate, or a uniform scaling factor used for both coordinates
			// b: Number?
			//		a scaling factor used for the y coordinate
			// c: Number|Point
			//		an x component of a central point, or a central point
			// d: Number
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			switch (arguments.length) {
			case 4:
				// a and b are scale factor components, c and d are components of a point
				return m._sandwich(m.scale(a, b), c, d); // gfx/matrix.Matrix2D
			case 3:
				if (typeof c === "number") {
					return m._sandwich(m.scale(a), b, c); // gfx/matrix.Matrix2D
				}
				return m._sandwich(m.scale(a, b), c.x, c.y); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.scale(a), b.x, b.y); // gfx/matrix.Matrix2D
		},
		rotateAt: function (angle, a, b) {
			// summary:
			//		rotates a picture using a specified point as a center of rotation
			// description:
			//		Compare with gfx/matrix.rotate().
			// angle: Number
			//		an angle of rotation in radians (>0 for CW)
			// a: Number|gfx.Point
			//		an x component of a central point, or a central point
			// b: Number?
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 2) {
				return m._sandwich(m.rotate(angle), a, b); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.rotate(angle), a.x, a.y); // gfx/matrix.Matrix2D
		},
		rotategAt: function (degree, a, b) {
			// summary:
			//		rotates a picture using a specified point as a center of rotation
			// description:
			//		Compare with gfx/matrix.rotateg().
			// degree: Number
			//		an angle of rotation in degrees (>0 for CW)
			// a: Number|gfx.Point
			//		an x component of a central point, or a central point
			// b: Number?
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 2) {
				return m._sandwich(m.rotateg(degree), a, b); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.rotateg(degree), a.x, a.y); // gfx/matrix.Matrix2D
		},
		skewXAt: function (angle, a, b) {
			// summary:
			//		skews a picture along the x axis using a specified point as a center of skewing
			// description:
			//		Compare with gfx/matrix.skewX().
			// angle: Number
			//		a skewing angle in radians
			// a: Number|gfx.Point
			//		an x component of a central point, or a central point
			// b: Number?
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 2) {
				return m._sandwich(m.skewX(angle), a, b); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.skewX(angle), a.x, a.y); // gfx/matrix.Matrix2D
		},
		skewXgAt: function (degree, a, b) {
			// summary:
			//		skews a picture along the x axis using a specified point as a center of skewing
			// description:
			//		Compare with gfx/matrix.skewXg().
			// degree: Number
			//		a skewing angle in degrees
			// a: Number|gfx.Point
			//		an x component of a central point, or a central point
			// b: Number?
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 2) {
				return m._sandwich(m.skewXg(degree), a, b); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.skewXg(degree), a.x, a.y); // gfx/matrix.Matrix2D
		},
		skewYAt: function (angle, a, b) {
			// summary:
			//		skews a picture along the y axis using a specified point as a center of skewing
			// description:
			//		Compare with gfx/matrix.skewY().
			// angle: Number
			//		a skewing angle in radians
			// a: Number|gfx.Point
			//		an x component of a central point, or a central point
			// b: Number?
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 2) {
				return m._sandwich(m.skewY(angle), a, b); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.skewY(angle), a.x, a.y); // gfx/matrix.Matrix2D
		},
		skewYgAt: function (/* Number */ degree, /* Number||Point */ a, /* Number? */ b) {
			// summary:
			//		skews a picture along the y axis using a specified point as a center of skewing
			// description:
			//		Compare with gfx/matrix.skewYg().
			// degree: Number
			//		a skewing angle in degrees
			// a: Number|gfx.Point
			//		an x component of a central point, or a central point
			// b: Number?
			//		a y component of a central point
			// returns: gfx/matrix.Matrix2D
			if (arguments.length > 2) {
				return m._sandwich(m.skewYg(degree), a, b); // gfx/matrix.Matrix2D
			}
			return m._sandwich(m.skewYg(degree), a.x, a.y); // gfx/matrix.Matrix2D
		},

		//TODO: rect-to-rect mapping, scale-to-fit (isotropic and anisotropic versions)

	});
	// propagate Matrix2D up
	g.Matrix2D = m.Matrix2D;

	return m;
});