From fcd3b65d1f1e8047323d2ef1bcddd506066fff57 Mon Sep 17 00:00:00 2001
From: Paul McCarthy <pauldmccarthy@gmail.com>
Date: Thu, 8 Oct 2020 14:12:50 +0100
Subject: [PATCH] ENH: decompose function has option to return shears, and
compose function accepts shears
---
fsl/transform/affine.py | 38 +++++++++++++++++++++++++++-----------
1 file changed, 27 insertions(+), 11 deletions(-)
diff --git a/fsl/transform/affine.py b/fsl/transform/affine.py
index 57007df77..47bdd4b37 100644
--- a/fsl/transform/affine.py
+++ b/fsl/transform/affine.py
@@ -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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