Commit f339b54d authored by Paul McCarthy's avatar Paul McCarthy 🚵
Browse files

ENH: decompose function has option to return shears, and compose function

accepts shears
parent c2bf208e
......@@ -120,7 +120,7 @@ def scaleOffsetXform(scales, offsets):
return xform
def compose(scales, offsets, rotations, origin=None):
def compose(scales, offsets, rotations, origin=None, shears=None):
"""Compose a transformation matrix out of the given scales, offsets
and axis rotations.
......@@ -133,6 +133,8 @@ def compose(scales, offsets, rotations, origin=None):
:arg origin: Origin of rotation - must be scaled by the ``scales``.
If not provided, the rotation origin is ``(0, 0, 0)``.
:arg shears: Sequence of three shear values
"""
preRotate = np.eye(4)
......@@ -154,6 +156,7 @@ def compose(scales, offsets, rotations, origin=None):
scale = np.eye(4, dtype=np.float64)
offset = np.eye(4, dtype=np.float64)
rotate = np.eye(4, dtype=np.float64)
shear = np.eye(4, dtype=np.float64)
scale[ 0, 0] = scales[ 0]
scale[ 1, 1] = scales[ 1]
......@@ -164,10 +167,15 @@ def compose(scales, offsets, rotations, origin=None):
rotate[:3, :3] = rotations
return concat(offset, postRotate, rotate, preRotate, scale)
if shears is not None:
shear[0, 1] = shears[0]
shear[0, 2] = shears[1]
shear[1, 2] = shears[2]
return concat(offset, postRotate, rotate, preRotate, scale, shear)
def decompose(xform, angles=True):
def decompose(xform, angles=True, shears=False):
"""Decomposes the given transformation matrix into separate offsets,
scales, and rotations, according to the algorithm described in:
......@@ -175,8 +183,7 @@ def decompose(xform, angles=True):
320-323 in *Graphics Gems II*, James Arvo (editor), Academic Press, 1991,
ISBN: 0120644819.
It is assumed that the given transform has no perspective components. Any
shears in the affine are discarded.
It is assumed that the given transform has no perspective components.
:arg xform: A ``(3, 3)`` or ``(4, 4)`` affine transformation matrix.
......@@ -184,6 +191,8 @@ def decompose(xform, angles=True):
as axis-angles, in radians. Otherwise, the rotation matrix
is returned.
:arg shears: Defaults to ``False``. If ``True``, shears are returned.
:returns: The following:
- A sequence of three scales
......@@ -191,6 +200,7 @@ def decompose(xform, angles=True):
was a ``(3, 3)`` matrix)
- A sequence of three rotations, in radians. Or, if
``angles is False``, a rotation matrix.
- If ``shears is True``, a sequence of three shears.
"""
# The inline comments in the code below are taken verbatim from
......@@ -199,7 +209,7 @@ def decompose(xform, angles=True):
# The next step is to extract the translations. This is trivial;
# we find t_x = M_{4,1}, t_y = M_{4,2}, and t_z = M_{4,3}. At this
# point we are left with a 3*3 matrix M' = M_{1..3,1..3}.
xform = xform.T
xform = np.array(xform).T
if xform.shape == (4, 4):
translations = xform[ 3, :3]
......@@ -214,7 +224,7 @@ def decompose(xform, angles=True):
# The process of finding the scaling factors and shear parameters
# is interleaved. First, find s_x = |M'_1|.
sx = np.sqrt(np.dot(M1, M1))
M1 /= sx
M1 = M1 / sx
# Then, compute an initial value for the xy shear factor,
# s_xy = M'_1 * M'_2. (this is too large by the y scaling factor).
......@@ -231,7 +241,7 @@ def decompose(xform, angles=True):
# The second row is normalized, and s_xy is divided by s_y to
# get its final value.
M2 = M2 / sy
sxy = sxy / sy
sxy = sxy / sx
# The xz and yz shear factors are computed as in the preceding,
sxz = np.dot(M1, M3)
......@@ -246,8 +256,8 @@ def decompose(xform, angles=True):
# the third row is normalized, and the xz and yz shear factors are
# rescaled.
M3 = M3 / sz
sxz = sxz / sz
syz = sxz / sz
sxz = sxz / sx
syz = syz / sy
# The resulting matrix now is a pure rotation matrix, except that it
# might still include a scale factor of -1. If the determinant of the
......@@ -267,7 +277,13 @@ def decompose(xform, angles=True):
if angles: rotations = rotMatToAxisAngles(R.T)
else: rotations = R.T
return np.array([sx, sy, sz]), translations, rotations
retval = [np.array([sx, sy, sz]), translations, rotations]
if shears:
retval.append(np.array((sxy, sxz, syz)))
return tuple(retval)
def rotMatToAffine(rotmat, origin=None):
......
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