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, animation, converting to and from a SVG/DOM matrix, creating matrix from triangles 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, or when you need cross-browser compatibility.

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

For browsers which support DOMMatrix and/or SVGMatrix it can be used as a supplementary framework to increase flexibility such as working directly with transformed points, perform addition transformation, interpolate animation and so forth.

Targets first and most client side use, but can be used directly in a node.js environment as well.

No dependencies.

There is now also included a "light" version with the essentials only.

Install

Using NPM

$ npm install transformation-matrix-js

Usage

Browser

Just include the script and create a new instance:

var matrix = new Matrix([context] [,domElement]);

You can supply an optional canvas 2D context and/or DOM element as arguments which will be synchronized with the transformations that are applied to the matrix object.

Node

Using it with Node: use npm to install the package first (see above), then

var Matrix = require("transformation-matrix-js").Matrix;
var m = new Matrix();

Quick overview

Constructor

var m = new Matrix( [context] [,element] );

Can optionally synchronize a canvas 2D context and/or a DOM element.

Static methods (alternatives to the constructor):

Matrix.from( a, b, c, d, e, f );        // create a matrix from various sources
Matrix.from( DOMMatrix | SVGMatrix | CSSMatrix);
Matrix.fromTriangles( t1, t2 );   		// returns matrix needed to produce t2 from t1
Matrix.fromSVGTransformList( tList );	// create new matrix from a SVG transform list

Methods:

applyToArray(points)
applyToContext(context)
applyToElement(element [, use3D])    // auto-detects browser prefix if any
applyToObject(obj)
applyToPoint(x, y)
applyToTypedArray(points [, use64])
clone(noContext)
concat(cm)
decompose([useLU])                   // breaks down the transform into individual components
determinant()
divide(m)
divideScalar(d)
flipX()
flipY()
interpolate(m2, t [, context [, dom]])
interpolateAnim(m2, t [, context [, dom]]) // decomposed interpolation (prevents flipping)
inverse([cloneContext][, cloneElement])    // get inverse matrix
isEqual(m)
isIdentity()
isInvertible()
isValid()
multiply(m)
reflectVector(x, y)
reset()
rotate(angle)
rotateDeg(angle)
rotateFromVector(x, y)
scale(sx, sy)
scaleFromVector(x, y)               // uniform scale based on input vector (hypotenuse)
scaleU(f)							// uniform scale
scaleX(sx)
scaleY(sy)
setTransform(a, b, c, d, e, f)
shear(sx, sy)
shearX(sx)
shearY(sy)
skew(ax, ay)
skewDeg(ax, ay)
skewX(ax)
skewY(ay)
toArray()
toCSS()
toCSS3D()
toCSV()
toJSON()
toString()
toDOMMatrix()                       // creates a DOMMatrix from current transforms
toSVGMatrix()						// creates a SVGMatrix from current transforms
toTypedArray([use64])
transform(a2, b2, c2, d2, e2, f2)
translate(tx, ty)
translateX(tx)
translateY(ty)

Properties:

a									// scale x
b									// shear y
c									// shear x
d									// scale y
e									// translate x
f									// translate y

Examples

Apply to a point:

tPoint = m.applyToPoint( x, y );

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

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

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

m.applyToContext( myContext );

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

invMatrix = m.inverse();

or

var invMatrix;

if (m.isInvertible()) {             // check if we can inverse
    invMatrix = m.inverse();
}

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

im = m.interpolate( m2, t );   		// t = [0.0, 1.0]
im = m.interpolateAnim( m2, t );

The former does a naive interpolation which works fine with translate and scale. The latter is better suited when there is rotation involved to avoid "flipping" utilizing decomposition.

Check if there is any transforms applied:

state = m.isIdentity();        		// true if identity

Check if two matrices are identical:

state = m.isEqual( matrix2 );      	// true if equal

Reset matrix to an identity matrix:

m.reset();

Methods are chainable:

// rotate, then translate
m.rotateDeg(45).translate(100, 200);

To synchronize a DOM element you can either specify the DOM element in the constructor or synchronize manually (auto-detects browser prefix):

m.applyToElement( domElement );

See documentation for full overview and usage.