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

affarray-like shape (4,4)

4x4 affine transformation matrix.

Returns

factorscalar

zoom (scale) factor as for zfdir2mat

directionNone or array, shape (3,)

direction of zoom as for zfdir2mat. None if scaling is uniform.

originarray, 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

matarray-like shape (3,3)

3x3 zoom matrix

Returns

factorscalar

zoom (scale) factor as for zfdir2mat

directionNone 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

factorscalar

factor to zoom by (see direction)

directionNone 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.

originNone or array-like shape (3,)

point at which to apply implied zooms

Returns

affarray 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

factorscalar

factor to zoom by (see direction)

directionNone 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.

Returns

matarray 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)