2D Affine Transformation Matrix

An affine transformation matrix (3x3) class for JavaScript that performs various transformations such as rotate, scale, translate, skew, shear, add, subtract, multiply, divide, inverse, decomposing and more (full HTML documentation is included).

It's primarily intended for situations where you need to track or create transforms and want to apply it permanently/manually to your own points and polygons.

The matrix can optionally synchronize a canvas 2D context object so the transformations on the canvas matches pixel perfect the local transformations of the Matrix object.

Using toCSS() can synchronize a DOM element as well.

No dependencies.

Now also includes a vector reflection method (see included demo for example usage):

Install

Download zip and extract to folder.

git via HTTPS:

$ git clone https://github.com/epistemex/transformation-matrix-js.git

git via SSH:

$ git clone git@github.com:epistemex/transformation-matrix-js.git

Using Bower:

$ bower install transformation-matrix-js

Usage

Just include the script and create a new instance like:

var matrix = new Matrix([context]);

You can supply an optional context as argument which in case will be synchronized with the transformations that are applied to the matrix object.

Some of the methods:

*NEW matrix.interpolateAnim();      // decomposed interpolation

matrix.toString();
matrix.toJSON();
matrix.toCSS();
matrix.toArray();
matrix.rotate(angle);    		    // angle in radians
matrix.rotateDeg(angle);   		    // angle in degrees
matrix.rotateFromVector(x, y);      // use a vector to set angle
matrix.translate(x, y);
matrix.translateX(x);
matrix.translateY(y);
matrix.scale(sx, sy);
matrix.scaleX(sx);
matrix.scaleY(sy);
matrix.scaleU(f);                    // scale both x and y
matrix.shear(sx, sy);
matrix.shearX(sx);
matrix.shearY(sy);
matrix.skew(ax, ay);                // angle in radians
matrix.skewX(ax);
matrix.skewY(ay);
matrix.transform(a, b, c, d, e, f);
matrix.setTransform(a, b, c, d, e, f);
matrix.divide();                    // divide matrix on another matrix
matrix.divideScalar();              // divide matrix by scalar value
matrix.inverse();
matrix.decompose([lu]);             // BETA decompose matrix using QR or LU
matrix.determinant();               // get determinant of current matrix
matrix.reset();
matrix.clone();
matrix.isInvertible();
matrix.isValid();
matrix.reflectVector(x, y)         // BETA reflects vector on normal (=current x-axis);
matrix.concat(childMatrix)

Get current transform matrix property values:

var a = matrix.a;	// scale x
var b = matrix.b;	// shear y
var c = matrix.c;	// shear x
var d = matrix.d;	// scale y
var e = matrix.e;	// translate x
var f = matrix.f;	// translate y

(also see decompose()).

Apply to a point:

var tPoint = matrix.applyToPoint(x, y);

Apply to an Array with point objects or point pair values:

var tPoints = matrix.applyToArray([{x: x1, y: y1}, {x: x2, y: y2}, ...]);
var tPoints = matrix.applyToArray([x1, y1, x2, y2, ...]);
var tPoints = matrix.applyToTypedArray(...);

or apply to a canvas context (other than optionally referenced in constructor):

matrix.applyToContext(myContext);

Get inverse transformation matrix (the matrix you need to apply to get back to a identity matrix from whatever the matrix contains):

var invmatrix = matrix.inverse();

or

var invmatrix;

if (matrix.isInvertible()) {                  // check if we can inverse
    invmatrix = matrix.inverse();
}

You can interpolate between current and a new matrix. The function returns a new matrix:

var imatrix = matrix.interpolate(matrix2, t);  // t = [0.0, 1.0]
var imatrix = matrix.interpolateAnim(matrix2, t);

The former does a naive interpolation which works fine with translate and scale. The latter is better suited when there is for example rotation involved to avoid "flipping" (and is what the browsers are using) utilizing decomposition.

Check if there is any transforms applied:

var status = matrix.isIdentity();              // true if identity

Check if two matrices are identical:

var status = matrix.isEqual(matrix2);          // true if equal

Reset matrix to an identity matrix:

matrix.reset();

Methods are also chain-able:

matrix.rotateDeg(45).translate(100, 120);     // rotate, then translate

For CSS you could do:

elem.style.transform = matrix.toCSS();        // some browsers may need prefix

See documentation for full overview and usage.

License

Released under MIT license. You can use this class in both commercial and non-commercial projects provided that full header (minified and developer versions) is included.

© 2014-2015 Epistmex