Mat23

2D Matrix class representing affine transformations:

[ a  b  tx ]
[ c  d  ty ]
[ 0  0  1  ]

Note that in AS3, flash.geom.Matrix has 'b' and 'c' swapped! so if you are converting between flash.geom.Matrix and nape.geom.Mat23 you should use the methods provided to avoid any mistakes with this.

Static Members #

Construct a Mat23 representing a clockwise rotation.

[ cos angle  -sin angle  0 ]
[ sin angle   cos angle  0 ]

Construct a Mat23 representing a translation

[ 1  0  tx ]
[ 0  1  ty ]

Construct a Mat23 representing a scaling

[ sx  0  0 ]
[ 0  sy  0 ]

Instance Members #

@private

The (1,1) entry in Mat23:

[ a  .  . ]
[ .  .  . ]

@default 1

The (1,2) entry in Mat23:

[ .  b  . ]
[ .  .  . ]

@default 0

The (2,1) entry in Mat23:

[ .  .  . ]
[ c  .  . ]

@default 0

The (2,2) entry in Mat23:

[ .  .  . ]
[ .  d  . ]

@default 1

The (1,3) entry in Mat23 which represents x translation

[ .  .  tx ]
[ .  .  .  ]

@default 0

The (2,3) entry in Mat23 which represents y translation

[ .  .  .  ]
[ .  .  ty ]

@default 0

(readonly) The determinant of this matrix.

This represents the factor of change in area for a region of the plane after transformation by matrix.

A determinant of 0 signifies that the matrix is not invertible.

A negative determinant signifies that for example, a clockwise wound polygon would be transformed into a counter-clockwise polygon.

@default 1

Produce copy of this Mat23

Set values of matrix from another.

Set values of matrix from numbers.

So that: mat.setAs(...) is semantically equivalent to: mat.set(new Mat23(...))

Reset matrix to identity.

Equivalent to calling setAs with default argument values.

Determine if the matrix is singular. This check is based on computing the condition number of the matrix by the Frobenius norm, and comparing against 2 / epsilon.

If matrix is singular, then inversion of the matrix cannot be performed

Compute the inverse of this matrix, returning the inverse in a new Mat23 object.

The inverse is such that mat.concat(mat.inverse()) is the identity matrix, as well as mat.inverse().concat(mat)

Compute the transpose of this matrix, returning the transpose in a new Mat23 object.

Technically speaking, we cannot transpose a matrix if the tx/ty values are non-zero as the implicit bottom row of matrix must be (0, 0, 1) so the tx/ty values of output matrix are set so that should the main 2x2 block of the matrix be orthogonal (Representing a rotation), then the transpose will be able to act as the matrix inverse.

var mat = Mat23.rotation(..).concat(Mat23.translation(...));
trace(mat.concat(mat.transpose())); // Identity matrix
trace(mat.concat(mat.inverse())); // Identity matrix

If the main 2x2 block of matrix is 'not' orthogonal, then the transpose will not be equal to the inverse.

Concatenate matrices (left-multiplication), returning new Mat23.

mat1.concat(mat2) is the transformation that first performs transformation represented by mat1, followed by transformation represented by mat2.

Transform a Vec2 by this matrix in new Vec2.

The Vec2 object will be allocated form the global object pool.

Perform inverse transformation with Vec2, returning new Vec2.

The matrix inverse will be performed implicitly and should this method be called many times for the same Mat23, it would be better to instead compute the matrix inverse only once.

The new Vec2 will be allocated from the global object pool.

@private

Determine if matrix is equiorthogonal

This is a term I invented after failing to find an existing name. It describes that this matrix maps circles into other circles (of not necessarigly the same radius). In otherwords the matrix can be decomposed into a rotation, translation and scaling of equal x/y factors.

This property is required for any Mat23 that is used to transform a Circle, or any Body containing a Circle, or to transform a Debug view.

This is a weaker property than orthogonality which describes a mapping to a circle of equal radius.

Mathematically speaking a matrix is equiorthogonal iff. transpose(M) * M = kI for some non-zero scalar k.

Determine if matrix is orthogonal

This property describes a matrix which maps circles into other circles of equal radius. In otherwords the matrix can be decomposed into a rotation and a translation.

Mathematically speaking a matrix is orthogonal iff. transpose(M) * M = I.

Equiorthogonalise matrix.

We do this by finding the 'nearest' orthogonal matrix; scaling the basis vectors of matrix to their mean length and applying an equal and opposite rotation to each basis vector to make them perpendicular.

Orthogonalise matrix.

We do this by finding the 'nearest' orthogonal matrix; normalising the basis vectors of matrix and applying an equal and opposite rotation to each basis vector to make them perpendicular.

Construct new Mat23.

[ a  b  tx ]
[ c  d  ty ]

Private Members #

Metadata #