shears
¶
Functions for working with shears
Terms used in function names:
 mat : array shape (3, 3) (3D nonhomogenous coordinates)
 aff : affine array shape (4, 4) (3D homogenous coordinates)
 striu : shears encoded by vector giving triangular portion above diagonal of NxN array (for ND transformation)
 sadn : shears encoded by angle scalar, direction vector, normal vector (with optional point vector)
aff2sadn (aff) 
Return shear angle, direction and plane normal from shear matrix. 
mat2sadn (mat) 
Return shear angle, direction and plane normal from shear matrix. 
sadn2aff (angle, direction, normal[, point]) 
Affine for shear by angle along vector direction on shear plane. 
sadn2mat (angle, direction, normal) 
Matrix for shear by angle along direction vector on shear plane. 
striu2mat (striu) 
Construct shear matrix from upper triangular vector 
aff2sadn¶

transforms3d.shears.
aff2sadn
(aff)¶ Return shear angle, direction and plane normal from shear matrix.
Parameters: mat : arraylike, shape (3,3)
shear matrix.
Returns: angle : scalar
angle to shear, in radians
direction : array, shape (3,)
direction along which to shear
normal : array, shape (3,)
vector normal to shear plane
point : array, shape (3,)
point that, with normal, defines shear plane.
Examples
>>> A = sadn2aff(0.5, [1, 0, 0], [0, 1, 0]) >>> angle, direction, normal, point = aff2sadn(A) >>> angle, direction, normal, point (0.5, array([1., 0., 0.]), array([ 0., 1., 0.]), array([ 0., 0., 0.])) >>> A_again = sadn2aff(angle, direction, normal, point) >>> np.allclose(A, A_again) True
mat2sadn¶

transforms3d.shears.
mat2sadn
(mat)¶ Return shear angle, direction and plane normal from shear matrix.
Parameters: mat : arraylike, shape (3,3)
shear matrix
Returns: angle : scalar
angle to shear, in radians
direction : array, shape (3,)
direction along which to shear
normal : array, shape (3,)
vector defining shear plane, where shear plane passes through origin
Examples
>>> M = sadn2mat(0.5, [1, 0, 0], [0, 1, 0]) >>> angle, direction, normal = mat2sadn(M) >>> angle, direction, normal (0.5, array([1., 0., 0.]), array([ 0., 1., 0.])) >>> M_again = sadn2mat(angle, direction, normal) >>> np.allclose(M, M_again) True
sadn2aff¶

transforms3d.shears.
sadn2aff
(angle, direction, normal, point=None)¶ Affine for shear by angle along vector direction on shear plane.
The shear plane is defined by a point and normal vector. The direction vector must be orthogonal to the plane’s normal vector.
A point P is transformed by the shear matrix into P” such that the vector PP” is parallel to the direction vector and its extent is given by the angle of PP’P”, where P’ is the orthogonal projection of P onto the shear plane.
Parameters: angle : scalar
angle to shear, in radians
direction : arraylike, shape (3,)
direction along which to shear
normal : arraylike, shape (3,)
vector normal to shearplane
point : None or arraylike, shape (3,), optional
point, that, with normal defines shear plane. Defaults to None, equivalent to shearplane through origin.
Returns: aff : array shape (4,4)
affine shearing matrix
Examples
>>> angle = (np.random.random()  0.5) * 4*math.pi >>> direct = np.random.random(3)  0.5 >>> normal = np.cross(direct, np.random.random(3)) >>> S = sadn2mat(angle, direct, normal) >>> np.allclose(1.0, np.linalg.det(S)) True
sadn2mat¶

transforms3d.shears.
sadn2mat
(angle, direction, normal)¶ Matrix for shear by angle along direction vector on shear plane.
The shear plane is defined by normal vector normal, and passes through the origin. The direction vector must be orthogonal to the plane’s normal vector.
A point P is transformed by the shear matrix into P” such that the vector PP” is parallel to the direction vector and its extent is given by the angle of PP’P”, where P’ is the orthogonal projection of P onto the shear plane.
Parameters: angle : scalar
angle to shear, in radians
direction : arraylike, shape (3,)
direction along which to shear
normal : arraylike, shape (3,)
vector defining shear plane, where shear plane passes through origin
Returns: mat : array shape (3,3)
shear matrix
Examples
>>> angle = (np.random.random()  0.5) * 4*math.pi >>> direct = np.random.random(3)  0.5 >>> normal = np.cross(direct, np.random.random(3)) >>> S = sadn2aff(angle, direct, normal) >>> np.allclose(1.0, np.linalg.det(S)) True
striu2mat¶

transforms3d.shears.
striu2mat
(striu)¶ Construct shear matrix from upper triangular vector
Parameters: striu : array, shape (N,)
vector giving triangle above diagonal of shear matrix.
Returns: SM : array, shape (N, N)
shear matrix
Notes
Shear lengths are triangular numbers.
See http://en.wikipedia.org/wiki/Triangular_number
Examples
>>> S = [0.1, 0.2, 0.3] >>> striu2mat(S) array([[ 1. , 0.1, 0.2], [ 0. , 1. , 0.3], [ 0. , 0. , 1. ]]) >>> striu2mat([1]) array([[ 1., 1.], [ 0., 1.]]) >>> striu2mat([1, 2]) Traceback (most recent call last): ... ValueError: 2 is a strange number of shear elements