# zooms¶

Functions for working with zooms (scales)

Terms used in function names:

• mat : array shape (3, 3) (3D non-homogenous 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 : array-like shape (4,4) 4x4 affine transformation matrix. 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 : array-like shape (3,3) 3x3 zoom matrix 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 array-like 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 array-like shape (3,) point at which to apply implied zooms 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 array-like 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. 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)