mat3 - a 3x3 matrix

A mat3 represents a 3x3 matrix which can be used to store linear transformations (if you want to store translations or perspective transformations, you have to use a mat4). You can construct a mat3 by several ways:

# all components are set to zero
M = mat3()

[   0.0000,    0.0000,    0.0000]
[   0.0000,    0.0000,    0.0000]
[   0.0000,    0.0000,    0.0000]

# identity matrix
M = mat3(1.0)

[   1.0000,    0.0000,    0.0000]
[   0.0000,    1.0000,    0.0000]
[   0.0000,    0.0000,    1.0000]

# The elements on the diagonal are set to 2.5
M = mat3(2.5)

[   2.5000,    0.0000,    0.0000]
[   0.0000,    2.5000,    0.0000]
[   0.0000,    0.0000,    2.5000]

# All elements are explicitly set (values must be given in row-major order)
M = mat3(a,b,c,d,e,f,g,h,i)
M = mat3([a,b,c,d,e,f,g,h,i])

[ a, b, c]
[ d, e, f]
[ g, h, i]

# Create a copy of matrix N (which also has to be a mat3)
M = mat3(N)

# Specify the 3 columns of the matrix (as vec3's or sequences with 3 elements)
M = mat3(a,b,c)

[ a[0], b[0], c[0] ]
[ a[1], b[1], c[1] ]
[ a[2], b[2], c[2] ]

# All elements are explicitly set and are stored inside a string
M = mat3("1,2,3,4,5,6,7,8,9")

[   1.0000,    2.0000,    3.0000]
[   4.0000,    5.0000,    6.0000]
[   7.0000,    8.0000,    9.0000]

Mathematical operations:

The mathematical operators are supported with the following combination of types:

mat3  =  mat3 + mat3
mat3  =  mat3 - mat3
mat3  =  mat3 * mat3
vec3  =  mat3 * vec3
vec3  =  vec3 * mat3
mat3  = float * mat3
mat3  =  mat3 * float
mat3  =  mat3 / float
mat3  =  mat3 % float     # each component
mat3  = -mat3
vec3  =  mat3[i]          # get or set column i (as vec3)
float =  mat3[i,j]        # get or set element in row i and column j

Additionally, you can compare vectors with == and !=.

Methods:

getColumn(index): Return column index (0-based) as a vec3.

setColumn(index, value): Set column index (0-based) to value which has to be a sequence with 3 floats (this includes vec3).

getRow(index): Return row index (0-based) as a vec3.

setRow(index, value): Set row index (0-based) to value which has to be a sequence with 3 floats (this includes vec3).

toList([rowmajor]): Returns a list containing the matrix elements. By default the list is in column-major order. If you set the optional argument rowmajor to 1, you'll get the list in row-major order.

identity()

Returns the identity matrix.

[1 0 0]
[0 1 0]
[0 0 1]

transpose(): Returns the transpose of the matrix.

determinant(): Returns the determinant of the matrix.

inverse(): Returns the inverse of the matrix.

scaling(s)

Returns a scaling transformation. The scaling vector s must be a 3-sequence (e.g. a vec3).

[s.x 0   0  ]
[0   s.y 0  ]
[0   0   s.z]

rotation(angle, axis): Returns a rotation transformation. The angle must be given in radians, axis has to be a 3-sequence (e.g. a vec3).

scale(s): Concatenates a scaling transformation and returns self. The scaling vector s must be a 3-sequence (e.g. a vec3).

rotate(angle, axis): Concatenates a rotation transformation and returns self. The angle must be given in radians, axis has to be a 3-sequence (e.g. a vec3).

ortho(): Returns a matrix with orthogonal base vectors.

decompose(): Decomposes the matrix into a rotation and scaling part. The method returns a tuple (rotation, scaling). The scaling part is given as a vec3, the rotation is still a mat3.