Matrix functions¶

Matrix33¶

3x3 Matrix which supports rotation, translation, scale and skew.

Matrices are laid out in row-major format and can be loaded directly into OpenGL. To convert to column-major format, transpose the array using the numpy.array.T method.

pyrr.matrix33.apply_to_vector(*args, **kwargs)[source]¶

Apply a matrix to a vector.

The matrix’s rotation are applied to the vector. Supports multiple matrices and vectors.

Parameters:	mat (numpy.array) – The rotation / translation matrix. Can be a list of matrices. vec (numpy.array) – The vector to modify. Can be a numpy.array of vectors. ie. numpy.array([[x1,…], [x2,…], …])
Return type:	numpy.array
Returns:	The vectors rotated by the specified matrix.

pyrr.matrix33.create_direction_scale(direction, scale)[source]¶

Creates a matrix which can apply a directional scaling to a set of vectors.

An example usage for this is to flatten a mesh against a single plane.

Parameters:	direction (numpy.array) – a numpy.array of shape (3,) of the direction to scale. scale (float) – a float value for the scaling along the specified direction. A scale of 0.0 will flatten the vertices into a single plane with the direction being the plane’s normal.
Return type:	numpy.array
Returns:	The scaling matrix.

pyrr.matrix33.create_from_axis_rotation(*args, **kwargs)[source]¶

Creates a matrix from the specified theta rotation around an axis.

Parameters:	axis (numpy.array) – A (3,) vector specifying the axis of rotation. theta (float) – A rotation specified in radians.
Return type:	numpy.array
Returns:	A matrix with shape (3,3).

pyrr.matrix33.create_from_eulers(*args, **kwargs)[source]¶

Creates a matrix from the specified Euler rotations.

Parameters:	eulers (numpy.array) – A set of euler rotations in the format specified by the euler modules.
Return type:	numpy.array
Returns:	A matrix with shape (3,3) with the euler’s rotation.

pyrr.matrix33.create_from_inverse_of_quaternion(*args, **kwargs)[source]¶

Creates a matrix with the inverse rotation of a quaternion.

Parameters:	quat (numpy.array) – The quaternion to make the matrix from (shape 4).
Return type:	numpy.array
Returns:	A matrix with shape (3,3) that respresents the inverse of the quaternion.

pyrr.matrix33.create_from_matrix44(mat, dtype=None)[source]¶

Creates a Matrix33 from a Matrix44.

Return type:	numpy.array
Returns:	A matrix with shape (3,3) with the input matrix rotation.

pyrr.matrix33.create_from_quaternion(*args, **kwargs)[source]¶

Creates a matrix with the same rotation as a quaternion.

Parameters:	quat – The quaternion to create the matrix from.
Return type:	numpy.array
Returns:	A matrix with shape (3,3) with the quaternion’s rotation.

pyrr.matrix33.create_from_scale(scale, dtype=None)[source]¶

Creates an identity matrix with the scale set.

Parameters:	scale (numpy.array) – The scale to apply as a vector (shape 3).
Return type:	numpy.array
Returns:	A matrix with shape (3,3) with the scale set to the specified vector.

pyrr.matrix33.create_from_x_rotation(theta, dtype=None)[source]¶

Creates a matrix with the specified rotation about the X axis.

Parameters:	theta (float) – The rotation, in radians, about the X-axis.
Return type:	numpy.array
Returns:	A matrix with the shape (3,3) with the specified rotation about the X-axis.

pyrr.matrix33.create_from_y_rotation(theta, dtype=None)[source]¶

Creates a matrix with the specified rotation about the Y axis.

Parameters:	theta (float) – The rotation, in radians, about the Y-axis.
Return type:	numpy.array
Returns:	A matrix with the shape (3,3) with the specified rotation about the Y-axis.

pyrr.matrix33.create_from_z_rotation(theta, dtype=None)[source]¶

Creates a matrix with the specified rotation about the Z axis.

Parameters:	theta (float) – The rotation, in radians, about the Z-axis.
Return type:	numpy.array
Returns:	A matrix with the shape (3,3) with the specified rotation about the Z-axis.

pyrr.matrix33.create_identity(dtype=None)[source]¶

Creates a new matrix33 and sets it to an identity matrix.

Return type:	numpy.array
Returns:	A matrix representing an identity matrix with shape (3,3).

pyrr.matrix33.inverse(mat)[source]¶

Returns the inverse of the matrix.

This is essentially a wrapper around numpy.linalg.inv.

Parameters:	m (numpy.array) – A matrix.
Return type:	numpy.array
Returns:	The inverse of the specified matrix.

pyrr.matrix33.multiply(m1, m2)[source]¶

Multiply two matricies, m1 . m2.

This is essentially a wrapper around numpy.dot( m1, m2 )

Parameters:	m1 (numpy.array) – The first matrix. Can be a list of matrices. m2 (numpy.array) – The second matrix. Can be a list of matrices.
Return type:	numpy.array
Returns:	A matrix that results from multiplying m1 by m2.

Matrix44¶

4x4 Matrix which supports rotation, translation, scale and skew.

Matrices are laid out in row-major format and can be loaded directly into OpenGL. To convert to column-major format, transpose the array using the numpy.array.T method.

pyrr.matrix44.apply_to_vector(*args, **kwargs)[source]¶

Apply a matrix to a vector.

The matrix’s rotation and translation are applied to the vector. Supports multiple matrices and vectors.

Parameters:	mat (numpy.array) – The rotation / translation matrix. Can be a list of matrices. vec (numpy.array) – The vector to modify. Can be a numpy.array of vectors. ie. numpy.array([[x1,…], [x2,…], …])
Return type:	numpy.array
Returns:	The vectors rotated by the specified matrix.

pyrr.matrix44.create_from_axis_rotation(*args, **kwargs)[source]¶

Creates a matrix from the specified rotation theta around an axis.

Parameters:	axis (numpy.array) – A (3,) vector. theta (float) – A rotation in radians.
Return type:	numpy.array
Returns:	A matrix with shape (4,4).

pyrr.matrix44.create_from_eulers(*args, **kwargs)[source]¶

Creates a matrix from the specified Euler rotations.

Parameters:	eulers (numpy.array) – A set of euler rotations in the format specified by the euler modules.
Return type:	numpy.array
Returns:	A matrix with shape (4,4) with the euler’s rotation.

pyrr.matrix44.create_from_inverse_of_quaternion(*args, **kwargs)[source]¶

Creates a matrix with the inverse rotation of a quaternion.

This can be used to go from object space to inertial space.

Parameters:	quat (numpy.array) – The quaternion to make the matrix from (shape 4).
Return type:	numpy.array
Returns:	A matrix with shape (4,4) that respresents the inverse of the quaternion.

pyrr.matrix44.create_from_matrix33(mat, dtype=None)[source]¶

Creates a Matrix44 from a Matrix33.

The translation will be 0,0,0.

Return type:	numpy.array
Returns:	A matrix with shape (4,4) with the input matrix rotation.

pyrr.matrix44.create_from_quaternion(*args, **kwargs)[source]¶

Creates a matrix with the same rotation as a quaternion.

Parameters:	quat – The quaternion to create the matrix from.
Return type:	numpy.array
Returns:	A matrix with shape (4,4) with the quaternion’s rotation.

pyrr.matrix44.create_from_scale(scale, dtype=None)[source]¶

Creates an identity matrix with the scale set.

Parameters:	scale (numpy.array) – The scale to apply as a vector (shape 3).
Return type:	numpy.array
Returns:	A matrix with shape (4,4) with the scale set to the specified vector.

pyrr.matrix44.create_from_translation(*args, **kwargs)[source]¶

Creates an identity matrix with the translation set.

Parameters:	vec (numpy.array) – The translation vector (shape 3 or 4).
Return type:	numpy.array
Returns:	A matrix with shape (4,4) that represents a matrix with the translation set to the specified vector.

pyrr.matrix44.create_from_x_rotation(theta, dtype=None)[source]¶

Creates a matrix with the specified rotation about the X axis.

Parameters:	theta (float) – The rotation, in radians, about the X-axis.
Return type:	numpy.array
Returns:	A matrix with the shape (4,4) with the specified rotation about the X-axis.

pyrr.matrix44.create_from_y_rotation(theta, dtype=None)[source]¶

Creates a matrix with the specified rotation about the Y axis.

Parameters:	theta (float) – The rotation, in radians, about the Y-axis.
Return type:	numpy.array
Returns:	A matrix with the shape (4,4) with the specified rotation about the Y-axis.

pyrr.matrix44.create_from_z_rotation(theta, dtype=None)[source]¶

Creates a matrix with the specified rotation about the Z axis.

Parameters:	theta (float) – The rotation, in radians, about the Z-axis.
Return type:	numpy.array
Returns:	A matrix with the shape (4,4) with the specified rotation about the Z-axis.

pyrr.matrix44.create_identity(dtype=None)[source]¶

Creates a new matrix44 and sets it to an identity matrix.

Return type:	numpy.array
Returns:	A matrix representing an identity matrix with shape (4,4).

pyrr.matrix44.create_look_at(eye, target, up, dtype=None)[source]¶

Creates a look at matrix according to OpenGL standards.

Parameters:	eye (numpy.array) – Position of the camera in world coordinates. target (numpy.array) – The position in world coordinates that the camera is looking at. up (numpy.array) – The up vector of the camera.
Return type:	numpy.array
Returns:	A look at matrix that can be used as a viewMatrix

pyrr.matrix44.create_matrix33_view(mat)[source]¶

Returns a view into the matrix in Matrix33 format.

This is different from matrix33.create_from_matrix44, in that changes to the returned matrix will also alter the original matrix.

Return type:	numpy.array
Returns:	A view into the matrix in the format of a matrix33 (shape (3,3)).

pyrr.matrix44.create_orthogonal_projection(left, right, bottom, top, near, far, dtype=None)[source]¶

Creates an orthogonal projection matrix.

Parameters:	left (float) – The left of the near plane relative to the plane’s centre. right (float) – The right of the near plane relative to the plane’s centre. top (float) – The top of the near plane relative to the plane’s centre. bottom (float) – The bottom of the near plane relative to the plane’s centre. near (float) – The distance of the near plane from the camera’s origin. It is recommended that the near plane is set to 1.0 or above to avoid rendering issues at close range. far (float) – The distance of the far plane from the camera’s origin.
Return type:	numpy.array
Returns:	A projection matrix representing the specified orthogonal perspective.

pyrr.matrix44.create_orthogonal_projection_matrix(left, right, bottom, top, near, far, dtype=None)[source]¶

Creates an orthogonal projection matrix.

Parameters:	left (float) – The left of the near plane relative to the plane’s centre. right (float) – The right of the near plane relative to the plane’s centre. top (float) – The top of the near plane relative to the plane’s centre. bottom (float) – The bottom of the near plane relative to the plane’s centre. near (float) – The distance of the near plane from the camera’s origin. It is recommended that the near plane is set to 1.0 or above to avoid rendering issues at close range. far (float) – The distance of the far plane from the camera’s origin.
Return type:	numpy.array
Returns:	A projection matrix representing the specified orthogonal perspective.

pyrr.matrix44.create_perspective_projection(fovy, aspect, near, far, dtype=None)[source]¶

Creates perspective projection matrix.

Parameters:	fovy (float) – field of view in y direction in degrees aspect (float) – aspect ratio of the view (width / height) near (float) – distance from the viewer to the near clipping plane (only positive) far (float) – distance from the viewer to the far clipping plane (only positive)
Return type:	numpy.array
Returns:	A projection matrix representing the specified perpective.

pyrr.matrix44.create_perspective_projection_from_bounds(left, right, bottom, top, near, far, dtype=None)[source]¶

Creates a perspective projection matrix using the specified near plane dimensions.

Parameters:	left (float) – The left of the near plane relative to the plane’s centre. right (float) – The right of the near plane relative to the plane’s centre. top (float) – The top of the near plane relative to the plane’s centre. bottom (float) – The bottom of the near plane relative to the plane’s centre. near (float) – The distance of the near plane from the camera’s origin. It is recommended that the near plane is set to 1.0 or above to avoid rendering issues at close range. far (float) – The distance of the far plane from the camera’s origin.
Return type:	numpy.array
Returns:	A projection matrix representing the specified perspective.

pyrr.matrix44.create_perspective_projection_matrix(fovy, aspect, near, far, dtype=None)[source]¶

Creates perspective projection matrix.

Parameters:	fovy (float) – field of view in y direction in degrees aspect (float) – aspect ratio of the view (width / height) near (float) – distance from the viewer to the near clipping plane (only positive) far (float) – distance from the viewer to the far clipping plane (only positive)
Return type:	numpy.array
Returns:	A projection matrix representing the specified perpective.

pyrr.matrix44.create_perspective_projection_matrix_from_bounds(left, right, bottom, top, near, far, dtype=None)[source]¶

Creates a perspective projection matrix using the specified near plane dimensions.

Parameters:	left (float) – The left of the near plane relative to the plane’s centre. right (float) – The right of the near plane relative to the plane’s centre. top (float) – The top of the near plane relative to the plane’s centre. bottom (float) – The bottom of the near plane relative to the plane’s centre. near (float) – The distance of the near plane from the camera’s origin. It is recommended that the near plane is set to 1.0 or above to avoid rendering issues at close range. far (float) – The distance of the far plane from the camera’s origin.
Return type:	numpy.array
Returns:	A projection matrix representing the specified perspective.

pyrr.matrix44.decompose(m)[source]¶

Decomposes an affine transformation matrix into its scale, rotation and translation components.

Parameters:	m (numpy.array) – A matrix.
Returns:	tuple (scale, rotation, translation) numpy.array scale vector3 numpy.array rotation quaternion numpy.array translation vector3

pyrr.matrix44.inverse(m)[source]¶

Returns the inverse of the matrix.

This is essentially a wrapper around numpy.linalg.inv.

Parameters:	m (numpy.array) – A matrix.
Return type:	numpy.array
Returns:	The inverse of the specified matrix.

pyrr.matrix44.multiply(m1, m2)[source]¶

Multiply two matricies, m1 . m2.

This is essentially a wrapper around numpy.dot(m1, m2)

Parameters:	m1 (numpy.array) – The first matrix. Can be a list of matrices. m2 (numpy.array) – The second matrix. Can be a list of matrices.
Return type:	numpy.array
Returns:	A matrix that results from multiplying m1 by m2.