Matrix2D.js

/*
* Matrix2D
* Visit http://createjs.com/ for documentation, updates and examples.
*
* Copyright (c) 2010 gskinner.com, inc.
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/

/**
 * @module EaselJS
 */

// namespace:
this.createjs = this.createjs||{};

(function() {
	"use strict";


// constructor:
	/**
	 * Represents an affine transformation matrix, and provides tools for constructing and concatenating matrices.
	 *
	 * This matrix can be visualized as:
	 *
	 * 	[ a  c  tx
	 * 	  b  d  ty
	 * 	  0  0  1  ]
	 *
	 * Note the locations of b and c.
	 *
	 * @class Matrix2D
	 * @param {Number} [a=1] Specifies the a property for the new matrix.
	 * @param {Number} [b=0] Specifies the b property for the new matrix.
	 * @param {Number} [c=0] Specifies the c property for the new matrix.
	 * @param {Number} [d=1] Specifies the d property for the new matrix.
	 * @param {Number} [tx=0] Specifies the tx property for the new matrix.
	 * @param {Number} [ty=0] Specifies the ty property for the new matrix.
	 * @constructor
	 **/
	function Matrix2D(a, b, c, d, tx, ty) {
		this.setValues(a,b,c,d,tx,ty);
		
	// public properties:
		// assigned in the setValues method.
		/**
		 * Position (0, 0) in a 3x3 affine transformation matrix.
		 * @property a
		 * @type Number
		 **/
	
		/**
		 * Position (0, 1) in a 3x3 affine transformation matrix.
		 * @property b
		 * @type Number
		 **/
	
		/**
		 * Position (1, 0) in a 3x3 affine transformation matrix.
		 * @property c
		 * @type Number
		 **/
	
		/**
		 * Position (1, 1) in a 3x3 affine transformation matrix.
		 * @property d
		 * @type Number
		 **/
	
		/**
		 * Position (2, 0) in a 3x3 affine transformation matrix.
		 * @property tx
		 * @type Number
		 **/
	
		/**
		 * Position (2, 1) in a 3x3 affine transformation matrix.
		 * @property ty
		 * @type Number
		 **/
	}
	var p = Matrix2D.prototype;

	/**
	 * <strong>REMOVED</strong>. Removed in favor of using `MySuperClass_constructor`.
	 * See {{#crossLink "Utility Methods/extend"}}{{/crossLink}} and {{#crossLink "Utility Methods/promote"}}{{/crossLink}}
	 * for details.
	 *
	 * There is an inheritance tutorial distributed with EaselJS in /tutorials/Inheritance.
	 *
	 * @method initialize
	 * @protected
	 * @deprecated
	 */
	// p.initialize = function() {}; // searchable for devs wondering where it is.


// constants:
	/**
	 * Multiplier for converting degrees to radians. Used internally by Matrix2D.
	 * @property DEG_TO_RAD
	 * @static
	 * @final
	 * @type Number
	 * @readonly
	 **/
	Matrix2D.DEG_TO_RAD = Math.PI/180;


// static public properties:
	/**
	 * An identity matrix, representing a null transformation.
	 * @property identity
	 * @static
	 * @type Matrix2D
	 * @readonly
	 **/
	Matrix2D.identity = null; // set at bottom of class definition.
	

// public methods:
	/**
	 * Sets the specified values on this instance. 
	 * @method setValues
	 * @param {Number} [a=1] Specifies the a property for the new matrix.
	 * @param {Number} [b=0] Specifies the b property for the new matrix.
	 * @param {Number} [c=0] Specifies the c property for the new matrix.
	 * @param {Number} [d=1] Specifies the d property for the new matrix.
	 * @param {Number} [tx=0] Specifies the tx property for the new matrix.
	 * @param {Number} [ty=0] Specifies the ty property for the new matrix.
	 * @return {Matrix2D} This instance. Useful for chaining method calls.
	*/
	p.setValues = function(a, b, c, d, tx, ty) {
		// don't forget to update docs in the constructor if these change:
		this.a = (a == null) ? 1 : a;
		this.b = b || 0;
		this.c = c || 0;
		this.d = (d == null) ? 1 : d;
		this.tx = tx || 0;
		this.ty = ty || 0;
		return this;
	};

	/**
	 * Appends the specified matrix properties to this matrix. All parameters are required.
	 * This is the equivalent of multiplying `(this matrix) * (specified matrix)`.
	 * @method append
	 * @param {Number} a
	 * @param {Number} b
	 * @param {Number} c
	 * @param {Number} d
	 * @param {Number} tx
	 * @param {Number} ty
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.append = function(a, b, c, d, tx, ty) {
		var a1 = this.a;
		var b1 = this.b;
		var c1 = this.c;
		var d1 = this.d;
		if (a != 1 || b != 0 || c != 0 || d != 1) {
			this.a  = a1*a+c1*b;
			this.b  = b1*a+d1*b;
			this.c  = a1*c+c1*d;
			this.d  = b1*c+d1*d;
		}
		this.tx = a1*tx+c1*ty+this.tx;
		this.ty = b1*tx+d1*ty+this.ty;
		return this;
	};

	/**
	 * Prepends the specified matrix properties to this matrix.
	 * This is the equivalent of multiplying `(specified matrix) * (this matrix)`.
	 * All parameters are required.
	 * @method prepend
	 * @param {Number} a
	 * @param {Number} b
	 * @param {Number} c
	 * @param {Number} d
	 * @param {Number} tx
	 * @param {Number} ty
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.prepend = function(a, b, c, d, tx, ty) {
		var a1 = this.a;
		var c1 = this.c;
		var tx1 = this.tx;

		this.a  = a*a1+c*this.b;
		this.b  = b*a1+d*this.b;
		this.c  = a*c1+c*this.d;
		this.d  = b*c1+d*this.d;
		this.tx = a*tx1+c*this.ty+tx;
		this.ty = b*tx1+d*this.ty+ty;
		return this;
	};

	/**
	 * Appends the specified matrix to this matrix.
	 * This is the equivalent of multiplying `(this matrix) * (specified matrix)`.
	 * @method appendMatrix
	 * @param {Matrix2D} matrix
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.appendMatrix = function(matrix) {
		return this.append(matrix.a, matrix.b, matrix.c, matrix.d, matrix.tx, matrix.ty);
	};

	/**
	 * Prepends the specified matrix to this matrix.
	 * This is the equivalent of multiplying `(specified matrix) * (this matrix)`.
	 * For example, you could calculate the combined transformation for a child object using:
	 * 
	 * 	var o = myDisplayObject;
	 * 	var mtx = o.getMatrix();
	 * 	while (o = o.parent) {
	 * 		// prepend each parent's transformation in turn:
	 * 		o.prependMatrix(o.getMatrix());
	 * 	}
	 * @method prependMatrix
	 * @param {Matrix2D} matrix
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.prependMatrix = function(matrix) {
		return this.prepend(matrix.a, matrix.b, matrix.c, matrix.d, matrix.tx, matrix.ty);
	};

	/**
	 * Generates matrix properties from the specified display object transform properties, and appends them to this matrix.
	 * For example, you can use this to generate a matrix representing the transformations of a display object:
	 * 
	 * 	var mtx = new createjs.Matrix2D();
	 * 	mtx.appendTransform(o.x, o.y, o.scaleX, o.scaleY, o.rotation);
	 * @method appendTransform
	 * @param {Number} x
	 * @param {Number} y
	 * @param {Number} scaleX
	 * @param {Number} scaleY
	 * @param {Number} rotation
	 * @param {Number} skewX
	 * @param {Number} skewY
	 * @param {Number} regX Optional.
	 * @param {Number} regY Optional.
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.appendTransform = function(x, y, scaleX, scaleY, rotation, skewX, skewY, regX, regY) {
		if (rotation%360) {
			var r = rotation*Matrix2D.DEG_TO_RAD;
			var cos = Math.cos(r);
			var sin = Math.sin(r);
		} else {
			cos = 1;
			sin = 0;
		}

		if (skewX || skewY) {
			// TODO: can this be combined into a single append operation?
			skewX *= Matrix2D.DEG_TO_RAD;
			skewY *= Matrix2D.DEG_TO_RAD;
			this.append(Math.cos(skewY), Math.sin(skewY), -Math.sin(skewX), Math.cos(skewX), x, y);
			this.append(cos*scaleX, sin*scaleX, -sin*scaleY, cos*scaleY, 0, 0);
		} else {
			this.append(cos*scaleX, sin*scaleX, -sin*scaleY, cos*scaleY, x, y);
		}
		
		if (regX || regY) {
			// append the registration offset:
			this.tx -= regX*this.a+regY*this.c; 
			this.ty -= regX*this.b+regY*this.d;
		}
		return this;
	};

	/**
	 * Generates matrix properties from the specified display object transform properties, and prepends them to this matrix.
	 * For example, you could calculate the combined transformation for a child object using:
	 * 
	 * 	var o = myDisplayObject;
	 * 	var mtx = new createjs.Matrix2D();
	 * 	do  {
	 * 		// prepend each parent's transformation in turn:
	 * 		mtx.prependTransform(o.x, o.y, o.scaleX, o.scaleY, o.rotation, o.skewX, o.skewY, o.regX, o.regY);
	 * 	} while (o = o.parent);
	 * 	
	 * 	Note that the above example would not account for {{#crossLink "DisplayObject/transformMatrix:property"}}{{/crossLink}}
	 * 	values. See {{#crossLink "Matrix2D/prependMatrix"}}{{/crossLink}} for an example that does.
	 * @method prependTransform
	 * @param {Number} x
	 * @param {Number} y
	 * @param {Number} scaleX
	 * @param {Number} scaleY
	 * @param {Number} rotation
	 * @param {Number} skewX
	 * @param {Number} skewY
	 * @param {Number} regX Optional.
	 * @param {Number} regY Optional.
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.prependTransform = function(x, y, scaleX, scaleY, rotation, skewX, skewY, regX, regY) {
		if (rotation%360) {
			var r = rotation*Matrix2D.DEG_TO_RAD;
			var cos = Math.cos(r);
			var sin = Math.sin(r);
		} else {
			cos = 1;
			sin = 0;
		}

		if (regX || regY) {
			// prepend the registration offset:
			this.tx -= regX; this.ty -= regY;
		}
		if (skewX || skewY) {
			// TODO: can this be combined into a single prepend operation?
			skewX *= Matrix2D.DEG_TO_RAD;
			skewY *= Matrix2D.DEG_TO_RAD;
			this.prepend(cos*scaleX, sin*scaleX, -sin*scaleY, cos*scaleY, 0, 0);
			this.prepend(Math.cos(skewY), Math.sin(skewY), -Math.sin(skewX), Math.cos(skewX), x, y);
		} else {
			this.prepend(cos*scaleX, sin*scaleX, -sin*scaleY, cos*scaleY, x, y);
		}
		return this;
	};

	/**
	 * Applies a clockwise rotation transformation to the matrix.
	 * @method rotate
	 * @param {Number} angle The angle to rotate by, in degrees. To use a value in radians, multiply it by `180/Math.PI`.
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.rotate = function(angle) {
		angle = angle*Matrix2D.DEG_TO_RAD;
		var cos = Math.cos(angle);
		var sin = Math.sin(angle);

		var a1 = this.a;
		var b1 = this.b;

		this.a = a1*cos+this.c*sin;
		this.b = b1*cos+this.d*sin;
		this.c = -a1*sin+this.c*cos;
		this.d = -b1*sin+this.d*cos;
		return this;
	};

	/**
	 * Applies a skew transformation to the matrix.
	 * @method skew
	 * @param {Number} skewX The amount to skew horizontally in degrees. To use a value in radians, multiply it by `180/Math.PI`.
	 * @param {Number} skewY The amount to skew vertically in degrees.
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	*/
	p.skew = function(skewX, skewY) {
		skewX = skewX*Matrix2D.DEG_TO_RAD;
		skewY = skewY*Matrix2D.DEG_TO_RAD;
		this.append(Math.cos(skewY), Math.sin(skewY), -Math.sin(skewX), Math.cos(skewX), 0, 0);
		return this;
	};

	/**
	 * Applies a scale transformation to the matrix.
	 * @method scale
	 * @param {Number} x The amount to scale horizontally. E.G. a value of 2 will double the size in the X direction, and 0.5 will halve it.
	 * @param {Number} y The amount to scale vertically.
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.scale = function(x, y) {
		this.a *= x;
		this.b *= x;
		this.c *= y;
		this.d *= y;
		//this.tx *= x;
		//this.ty *= y;
		return this;
	};

	/**
	 * Translates the matrix on the x and y axes.
	 * @method translate
	 * @param {Number} x
	 * @param {Number} y
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.translate = function(x, y) {
		this.tx += this.a*x + this.c*y;
		this.ty += this.b*x + this.d*y;
		return this;
	};

	/**
	 * Sets the properties of the matrix to those of an identity matrix (one that applies a null transformation).
	 * @method identity
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.identity = function() {
		this.a = this.d = 1;
		this.b = this.c = this.tx = this.ty = 0;
		return this;
	};

	/**
	 * Inverts the matrix, causing it to perform the opposite transformation.
	 * @method invert
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	 **/
	p.invert = function() {
		var a1 = this.a;
		var b1 = this.b;
		var c1 = this.c;
		var d1 = this.d;
		var tx1 = this.tx;
		var n = a1*d1-b1*c1;

		this.a = d1/n;
		this.b = -b1/n;
		this.c = -c1/n;
		this.d = a1/n;
		this.tx = (c1*this.ty-d1*tx1)/n;
		this.ty = -(a1*this.ty-b1*tx1)/n;
		return this;
	};

	/**
	 * Returns true if the matrix is an identity matrix.
	 * @method isIdentity
	 * @return {Boolean}
	 **/
	p.isIdentity = function() {
		return this.tx === 0 && this.ty === 0 && this.a === 1 && this.b === 0 && this.c === 0 && this.d === 1;
	};
	
	/**
	 * Returns true if this matrix is equal to the specified matrix (all property values are equal).
	 * @method equals
	 * @param {Matrix2D} matrix The matrix to compare.
	 * @return {Boolean}
	 **/
	p.equals = function(matrix) {
		return this.tx === matrix.tx && this.ty === matrix.ty && this.a === matrix.a && this.b === matrix.b && this.c === matrix.c && this.d === matrix.d;
	};

	/**
	 * Transforms a point according to this matrix.
	 * @method transformPoint
	 * @param {Number} x The x component of the point to transform.
	 * @param {Number} y The y component of the point to transform.
	 * @param {Point | Object} [pt] An object to copy the result into. If omitted a generic object with x/y properties will be returned.
	 * @return {Point} This matrix. Useful for chaining method calls.
	 **/
	p.transformPoint = function(x, y, pt) {
		pt = pt||{};
		pt.x = x*this.a+y*this.c+this.tx;
		pt.y = x*this.b+y*this.d+this.ty;
		return pt;
	};

	/**
	 * Decomposes the matrix into transform properties (x, y, scaleX, scaleY, and rotation). Note that these values
	 * may not match the transform properties you used to generate the matrix, though they will produce the same visual
	 * results.
	 * @method decompose
	 * @param {Object} target The object to apply the transform properties to. If null, then a new object will be returned.
	 * @return {Object} The target, or a new generic object with the transform properties applied.
	*/
	p.decompose = function(target) {
		// TODO: it would be nice to be able to solve for whether the matrix can be decomposed into only scale/rotation even when scale is negative
		if (target == null) { target = {}; }
		target.x = this.tx;
		target.y = this.ty;
		target.scaleX = Math.sqrt(this.a * this.a + this.b * this.b);
		target.scaleY = Math.sqrt(this.c * this.c + this.d * this.d);

		var skewX = Math.atan2(-this.c, this.d);
		var skewY = Math.atan2(this.b, this.a);

		var delta = Math.abs(1-skewX/skewY);
		if (delta < 0.00001) { // effectively identical, can use rotation:
			target.rotation = skewY/Matrix2D.DEG_TO_RAD;
			if (this.a < 0 && this.d >= 0) {
				target.rotation += (target.rotation <= 0) ? 180 : -180;
			}
			target.skewX = target.skewY = 0;
		} else {
			target.skewX = skewX/Matrix2D.DEG_TO_RAD;
			target.skewY = skewY/Matrix2D.DEG_TO_RAD;
			target.rotation = 0;
		}
		return target;
	};
	
	/**
	 * Copies all properties from the specified matrix to this matrix.
	 * @method copy
	 * @param {Matrix2D} matrix The matrix to copy properties from.
	 * @return {Matrix2D} This matrix. Useful for chaining method calls.
	*/
	p.copy = function(matrix) {
		return this.setValues(matrix.a, matrix.b, matrix.c, matrix.d, matrix.tx, matrix.ty);
	};

	/**
	 * Returns a clone of the Matrix2D instance.
	 * @method clone
	 * @return {Matrix2D} a clone of the Matrix2D instance.
	 **/
	p.clone = function() {
		return new Matrix2D(this.a, this.b, this.c, this.d, this.tx, this.ty);
	};

	/**
	 * Returns a string representation of this object.
	 * @method toString
	 * @return {String} a string representation of the instance.
	 **/
	p.toString = function() {
		return "[Matrix2D (a="+this.a+" b="+this.b+" c="+this.c+" d="+this.d+" tx="+this.tx+" ty="+this.ty+")]";
	};

	// this has to be populated after the class is defined:
	Matrix2D.identity = new Matrix2D();


	createjs.Matrix2D = Matrix2D;
}());