zooms
¶
Functions for working with zooms (scales)
Terms used in function names:
 mat : array shape (3, 3) (3D nonhomogenous coordinates)
 aff : affine array shape (4, 4) (3D homogenous coordinates)
 zfdir : zooms encoded by factor scalar and direction vector
aff2zfdir (aff) 
Return scaling factor, direction and origin from scaling matrix. 
mat2zfdir (mat) 
Return scaling factor and direction from zoom (scaling) matrix 
zfdir2aff (factor[, direction, origin]) 
Return affine to scale by factor around origin in direction. 
zfdir2mat (factor[, direction]) 
Return matrix to scale by factor around origin in direction. 
aff2zfdir¶

transforms3d.zooms.
aff2zfdir
(aff)¶ Return scaling factor, direction and origin from scaling matrix.
Parameters: aff : arraylike shape (4,4)
4x4 affine transformation matrix.
Returns: factor : scalar
zoom (scale) factor as for
zfdir2mat
direction : None or array, shape (3,)
direction of zoom as for
zfdir2mat
. None if scaling is uniform.origin : array, shape (3,)
origin of zooms
Examples
>>> factor = np.random.random() * 10  5 >>> direct = np.random.random(3)  0.5 >>> origin = np.random.random(3)  0.5 >>> S0 = zfdir2aff(factor) >>> f2, d2, o2 = aff2zfdir(S0) >>> np.allclose(S0, zfdir2aff(f2, d2, o2)) True >>> S0 = zfdir2aff(factor, direct) >>> f2, d2, o2 = aff2zfdir(S0) >>> np.allclose(S0, zfdir2aff(f2, d2, o2)) True >>> S0 = zfdir2aff(factor, direct, origin)
mat2zfdir¶

transforms3d.zooms.
mat2zfdir
(mat)¶ Return scaling factor and direction from zoom (scaling) matrix
Parameters: mat : arraylike shape (3,3)
3x3 zoom matrix
Returns: factor : scalar
zoom (scale) factor as for
zfdir2mat
direction : None or array, shape (3,)
direction of zoom as for
zfdir2mat
. None if scaling is uniform.Examples
Roundtrip may not generate same factor, direction, but the generated transformation matrices will be the same
>>> factor = np.random.random() * 10  5 >>> S0 = zfdir2mat(factor, None) >>> f2, d2 = mat2zfdir(S0) >>> S1 = zfdir2mat(f2, d2) >>> np.allclose(S0, S1) True >>> direct = np.random.random(3)  0.5 >>> S0 = zfdir2mat(factor, direct) >>> f2, d2 = mat2zfdir(S0) >>> S1 = zfdir2mat(f2, d2) >>> np.allclose(S0, S1) True
zfdir2aff¶

transforms3d.zooms.
zfdir2aff
(factor, direction=None, origin=None)¶ Return affine to scale by factor around origin in direction.
Use factor 1 for point symmetry.
Parameters: factor : scalar
factor to zoom by (see direction)
direction : None or arraylike shape (3,)
If None, simply apply uniform scaling by factor. Otherwise, apply scaling along direction given by vector direction. We convert direction to a unit vector before application.
origin : None or arraylike shape (3,)
point at which to apply implied zooms
Returns: aff : array shape (4,4)
4x4 transformation matrix implementing zooms
Examples
>>> v = (np.random.rand(3, 5)  0.5) * 20.0 >>> S = zfdir2aff(1.234)[:3,:3] >>> np.allclose(np.dot(S, v), 1.234*v) True >>> factor = np.random.random() * 10  5 >>> direct = np.random.random(3)  0.5 >>> origin = np.random.random(3)  0.5 >>> S = zfdir2aff(factor, None, origin) >>> S = zfdir2aff(factor, direct, origin)
zfdir2mat¶

transforms3d.zooms.
zfdir2mat
(factor, direction=None)¶ Return matrix to scale by factor around origin in direction.
Use factor == 1 for point symmetry.
Parameters: factor : scalar
factor to zoom by (see direction)
direction : None or arraylike shape (3,), optional
If None, simply apply uniform scaling by factor. Otherwise, apply scaling along direction given by vector direction. We convert direction to a unit vector before application.
Returns: mat : array shape (3,3)
3x3 transformation matrix implementing zooms
Examples
>>> v = (np.random.rand(3, 5)  0.5) * 20.0 >>> S = zfdir2mat(1.234) >>> np.allclose(np.dot(S, v), 1.234*v) True >>> factor = np.random.random() * 10  5 >>> direct = np.random.random(3)  0.5 >>> S = zfdir2mat(factor, direct)