pyg4ometry.transformation¶

Functions¶

`rad2deg`(rad)	Convert rad in radians into degrees
`deg2rad`(deg)	Convert deg in degrees into radians
`grad2rad`(gradians)	Convert rad in gradians into radians
`tbxyz2axisangle`(rv)	Tait-Bryan x-y-z rotation to axis-angle representation
`matrix2axisangle`(matrix)	Convert 3x3 transformation matrix to axis angle representation
`axisangle2matrix`(axis, angle)	Convert axis angle to transformation matrix
`matrix2tbxyz`(matrix)	Convert rotation matrix to Tait-Bryan angles.
`axisangle2tbxyz`(axis, angle)	Convert axis and angle to tait bryan angles
`tbxyz2matrix`(angles)	Convert tait bryan angles to a single passive rotation matrix.
`tbzyx2matrix`(angles)	Convert Tait-Bryan angles to a single passive rotation matrix.
`matrix_from`(v_from, v_to)	Returns the rotation matrix that rotates v_from to parallel to
`_rodrigues_anti_parallel`(v_from, v_to)	v_from = vector FROM
`are_parallel`(vector_1, vector_2[, tolerance])	Check if vector vector_1 is parallel to vector vector_2 down to
`are_anti_parallel`(vector_1, vector_2[, tolerance])	Check if vector vector_1 is parallel to vector vector_2 down to
`reverse`(angles)	Invert the rotation represented by these angles.
`two_fold_orientation`(v1, v2, e1, e2)	matrix_from will align one vector with another, but there are

Module Contents¶

pyg4ometry.transformation.rad2deg(rad)¶

Convert rad in radians into degrees

Parameters:: rad (float) – Input in radians
Returns:: rad in degrees
Return type:: float

pyg4ometry.transformation.deg2rad(deg)¶

Convert deg in degrees into radians

Parameters:: deg (float) – Input in degrees
Returns:: deg in radians
Return type:: float

pyg4ometry.transformation.grad2rad(gradians)¶

Convert rad in gradians into radians

Parameters:: gradians (float) – Input in gradians
Returns:: gradians in radians
Return type:: float

pyg4ometry.transformation.tbxyz2axisangle(rv)¶

Tait-Bryan x-y-z rotation to axis-angle representation Algorithm from http://www.sedris.org/wg8home/Documents/WG80485.pdf

For converting rotation angles to an active axis/angle pair for use in pycsg. Order of rotation: x->y->z.

Parameters:: rv (float(3)) – rotation angles
Returns:: [axis,angle]
Return type:: list(list(3),float)

pyg4ometry.transformation.matrix2axisangle(matrix)¶

Convert 3x3 transformation matrix to axis angle representation

Parameters:: matrix (array(3,3)) – 3x3 rotation matrix array
Returns:: [axis,angle]
Return type:: list(list(3),float)

pyg4ometry.transformation.axisangle2matrix(axis, angle)¶

Convert axis angle to transformation matrix

Parameters:

axis (list/array(3)) – axis for rotation
angle (float) – rotation angle

Returns:

transformation matrix

Return type:

array(3,3)

pyg4ometry.transformation.matrix2tbxyz(matrix)¶

Convert rotation matrix to Tait-Bryan angles. Order of rotation is x -> y -> z.

Parameters:: matrix – active (positive angle = anti-clockwise rotation about that axis when looking at the axis) matrix.
Returns:: [x, y, z] Tait-Bryan angles in a list.
Return type:: list(3)

pyg4ometry.transformation.axisangle2tbxyz(axis, angle)¶

Convert axis and angle to tait bryan angles

Parameters:

axis (list/array(3)) – axis for rotation
angle (float) – rotation angle

Returns:

tait bryan angles (x-y-z)

Return type:

array(3)

pyg4ometry.transformation.tbxyz2matrix(angles)¶

Convert tait bryan angles to a single passive rotation matrix. rotation order = x -> y -> z.

Parameters:: angles – list of angles: x, y, z
Returns:: rotation matrix
Return type:: array(3,3)

pyg4ometry.transformation.tbzyx2matrix(angles)¶

Convert Tait-Bryan angles to a single passive rotation matrix. rotation order = x -> y -> z.

Parameters:: angles – list of angles: x, y, z
Returns:: rotation matrix
Return type:: array(3,3)

pyg4ometry.transformation.matrix_from(v_from, v_to)¶

Returns the rotation matrix that rotates v_from to parallel to v_to.

Useful for ensuring a given face points in a certain direction.

v_from and v_to should be array-like three-vectors.

pyg4ometry.transformation._rodrigues_anti_parallel(v_from, v_to)¶

v_from = vector FROM v_to = vector TO

source: http://en.citizendium.org/wiki/Rotation_matrix#Case_that_.22from.22_and_.22to.22_vectors_are_anti-parallel

pyg4ometry.transformation.are_parallel(vector_1, vector_2, tolerance=1e-10)¶

Check if vector vector_1 is parallel to vector vector_2 down to some tolerance.

Parameters:

vector_1 (array) – First input vector
vector_2 (array) – Second input vector
tolerance (float) – Tolerance for calculation

Returns:

if vectors are parallel

Return type:

bool

pyg4ometry.transformation.are_anti_parallel(vector_1, vector_2, tolerance=1e-10)¶

Check if vector vector_1 is parallel to vector vector_2 down to some tolerance.

Parameters:

vector_1 (array) – First input vector
vector_2 (array) – Second input vector
tolerance (float) – Tolerance for calculation

Returns:

if vectors are antiparallel

Return type:

bool

pyg4ometry.transformation.reverse(angles)¶: Invert the rotation represented by these angles.

pyg4ometry.transformation.two_fold_orientation(v1, v2, e1, e2)¶

matrix_from will align one vector with another, but there are an infinite number of such matrices that align two vectors. This further contrains the rotation by introducing a second pair of vectors.

v1 start v v2 end v e1 start e e2 end v