Matrices¶
The geom
module defines matrices in two, three and four dimensions.
All matrices store the values in row-major order, meaning that, the matrix ((1,
2), (3,4)) stores the values as (1, 2, 3, 4). This is illustrated in
the following code examples:
m=geom.Mat2(1, 2, 3, 4)
print(m) # will print {{1,2},{3,4}}
print(m[(0,0)], m[(0,1)], m[(1,0)], m[(1,1)]) # will print 1, 2, 3, 4
Matrices support arithmetic via overloaded operators. The following operations are supported:
adding and subtracting two matrices
negation
multiplication of matrices
multiplying and dividing by scalar value
The Matrix Classes¶
- class Mat2¶
- class Mat2(d00, d01, d10, d11)
2x2 real-valued matrix. The first signature creates a new identity matrix. The second signature initializes the matrix in row-major order.
- static Identity()¶
Returns the 2x2 identity matrix
- class Mat3¶
- class Mat3(d00, d01, d02, d10, d11, d12, d20, d21, d22)
3x3 real-valued matrix. The first signature creates a new identity matrix. The second signature initializes the matrix in row-major order.
- static Identity()¶
Returns the 3x3 identity matrix
- class Mat4¶
- class Mat4(d00, d01, d02, d03, d10, d11, d12, d13, d20, d21, d22, d23, d30, d31, d32, d33)
4x4 real-valued matrix. The first signature creates a new identity matrix. The second signature initializes the matrix in row-major order.
- ExtractRotation()¶
Returns the 3x3 submatrix
- PasteRotation(mat)¶
Set the 3x3 submatrix of the top-left corner to mat
- ExtractTranslation()¶
Extract translation component from matrix. Only meaningful when matrix is a combination of rotation and translation matrices, otherwise the result is undefined.
- static Identity()¶
Returns the 4x4 identity matrix
Functions Operating on Matrices¶
- Equal(lhs, rhs, epsilon=geom.EPSILON)¶
Compares the two matrices lhs and rhs and returns True, if all of the element-wise differences are smaller than epsilon. lhs and rhs must be matrices of the same dimension.
- Transpose(mat)¶
Returns the transpose of mat
- Parameters:
mat – The matrix to be transposed
- Invert(mat)¶
Returns the inverse of mat
What happens when determinant is 0?
- CompMultiply(lhs, rhs)¶
Returns the component-wise product of lhs and rhs. lhs and rhs must be vectors of the same dimension.
- CompDivide(lhs, rhs)¶
Returns the component-wise quotient of lhs divided by rhs. lhs and rhs must be vectors of the same dimension.
- Minor(mat, i, j)¶
Returns the determinant of the 2x2 matrix generated from mat by removing the ith row and jth column.
- EulerTransformation(phi, theta, xi)¶
Returns a rotation matrix for the 3 euler angles phi, theta, and xi. The 3 angles are given in radians.