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Matrices
================================================================================
.. currentmodule:: ost.geom
The :mod:`~ost.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:
.. code-block:: python
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()
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.
.. staticmethod:: Identity()
Returns the 2x2 identity matrix
.. class:: Mat3()
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.
.. staticmethod:: Identity()
Returns the 3x3 identity matrix
.. class:: Mat4()
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.
.. method:: ExtractRotation()
Returns the 3x3 submatrix
.. method:: PasteRotation(mat)
Set the 3x3 submatrix of the top-left corner to `mat`
.. method:: ExtractTranslation()
Extract translation component from matrix. Only meaningful when matrix
is a combination of rotation and translation matrices, otherwise the result
is undefined.
.. PasteTranslation(trans)
Set the translation component of the matrix to `trans`
:param trans: The translation
:type trans: :class:`Vec3`
.. staticmethod:: Identity()
Returns the 4x4 identity matrix
Functions Operating on Matrices
--------------------------------------------------------------------------------
.. function:: 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.
:param lhs: First matrix
:type lhs: :class:`Mat2`, :class:`Mat3` or :class:`Mat4`
:param rhs: Second matrix
:type rhs: :class:`Mat2`, :class:`Mat3` or :class:`Mat4`
.. function:: Transpose(mat)
Returns the transpose of `mat`
:param mat: The matrix to be transposed
:type lhs: :class:`Mat2`, :class:`Mat3` or :class:`Mat4`
.. function:: Invert(mat)
Returns the inverse of `mat`
:param mat: The matrix to be inverted
:type mat: :class:`Mat2`, :class:`Mat3` or :class:`Mat4`
What happens when determinant is 0?
.. function:: CompMultiply(lhs, rhs)
Returns the component-wise product of `lhs` and `rhs`. `lhs` and
`rhs` must be vectors of the same dimension.
:param lhs: The lefthand-side vector
:type lhs: :class:`~Vec2`, :class:`~Vec3` or
:class:`~Vec4`
:param rhs: The righthand-side vector
:type rhs: :class:`~Vec2`, :class:`~Vec3` or
:class:`~Vec4`
.. function:: CompDivide(lhs, rhs)
Returns the component-wise quotient of `lhs` divided by `rhs`. `lhs`
and `rhs` must be vectors of the same dimension.
:param lhs: The lefthand-side vector
:type lhs: :class:`~Vec2`, :class:`~Vec3` or
:class:`~Vec4`
:param rhs: The righthand-side vector
:type rhs: :class:`~Vec2`, :class:`~Vec3` or
:class:`~Vec4`
.. function:: Det(mat)
Returns the determinant of `mat`
:param mat: A matrix
:type mat: :class:`~Mat2`, :class:`~Mat3` or :class:`~Mat4`
.. function:: Minor(mat, i, j)
Returns the determinant of the 2x2 matrix generated from `mat` by
removing the ith row and jth column.
.. function:: EulerTransformation(phi, theta, xi)
Returns a rotation matrix for the 3 euler angles `phi`, `theta`, and
`xi`. The 3 angles are given in radians.
.. function:: AxisRotation(axis, angle)
Returns a rotation matrix that represents a rotation of `angle`
around the `axis`.
:param axis: The rotation axis. Will be normalized
:type axis: :class:`Vec3`
:param angle: Rotation angle (radians) in clockwise direction when
looking down the axis.
.. function:: OrthogonalVector(vec)
Get arbitrary vector orthogonal to `vec`. The returned vector is of length
1, except when `vec` is a zero vector. In that case, the returned vector is
(0, 0, 0).
:param vec: A vector of arbitrary length
:type vec: :class:`Vec3`
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