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MAINT: Unify calculation of normal vectors from polygons by eric-wieser · Pull Request #12136 · matplotlib/matplotlib · GitHub

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MAINT: Unify calculation of normal vectors from polygons #12136

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timhoffm merged 2 commits into from
Dec 6, 2018
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MAINT: Unify calculation of normal vectors from polygons #12136

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MAINT: Unify calculation of normal vectors from polygons
eric-wieser Sep 16, 2018
e8233aa
Merge branch 'master' into voxels-shading
eric-wieser Nov 27, 2018
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75 changes: 43 additions & 32 deletions lib/mpl_toolkits/mplot3d/axes3d.py
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Original file line number Diff line number Diff line change
Expand Up @@ -1684,28 +1684,14 @@ def plot_surface(self, X, Y, Z, *args, norm=None, vmin=None,
if fcolors is not None:
colset.append(fcolors[rs][cs])

def get_normals(polygons):
"""
Takes a list of polygons and return an array of their normals
"""
v1 = np.empty((len(polygons), 3))
v2 = np.empty((len(polygons), 3))
for poly_i, ps in enumerate(polygons):
# pick three points around the polygon at which to find the
# normal doesn't vectorize because polygons is jagged
i1, i2, i3 = 0, len(ps)//3, 2*len(ps)//3
v1[poly_i, :] = ps[i1, :] - ps[i2, :]
v2[poly_i, :] = ps[i2, :] - ps[i3, :]
return np.cross(v1, v2)

# note that the striding causes some polygons to have more coordinates
# than others
polyc = art3d.Poly3DCollection(polys, *args, **kwargs)

if fcolors is not None:
if shade:
colset = self._shade_colors(
colset, get_normals(polys), lightsource)
colset, self._generate_normals(polys), lightsource)
polyc.set_facecolors(colset)
polyc.set_edgecolors(colset)
elif cmap:
Expand All @@ -1719,7 +1705,7 @@ def get_normals(polygons):
else:
if shade:
colset = self._shade_colors(
color, get_normals(polys), lightsource)
color, self._generate_normals(polys), lightsource)
else:
colset = color
polyc.set_facecolors(colset)
Expand All @@ -1731,20 +1717,47 @@ def get_normals(polygons):

def _generate_normals(self, polygons):
"""
Generate normals for polygons by using the first three points.
This normal of course might not make sense for polygons with
more than three points not lying in a plane.
Takes a list of polygons and return an array of their normals.

Normals point towards the viewer for a face with its vertices in
counterclockwise order, following the right hand rule.
"""

normals = []
for verts in polygons:
v1 = np.array(verts[1]) - np.array(verts[0])
v2 = np.array(verts[2]) - np.array(verts[0])
normals.append(np.cross(v1, v2))
return normals
Uses three points equally spaced around the polygon.
This normal of course might not make sense for polygons with more than
three points not lying in a plane, but it's a plausible and fast
approximation.

Parameters
----------
polygons: list of (M_i, 3) array_like, or (..., M, 3) array_like

timhoffm Nov 27, 2018 •
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Choose a reason Spam Abuse Off Topic Outdated Duplicate Resolved Low Quality

Why the i index ?

eric-wieser Nov 27, 2018 •
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Choose a reason Spam Abuse Off Topic Outdated Duplicate Resolved Low Quality

Because the value of M can change between each list item - polygons[0] has shape (M_0, 3), polygons[1] has shape (M_1, 3), and it is likely that M_1 != M_0
A sequence of polygons to compute normals for, which can have
varying numbers of vertices. If the polygons all have the same
number of vertices and array is passed, then the operation will
be vectorized.

Returns
-------
normals: (..., 3) array_like
A normal vector estimated for the polygon.

"""
if isinstance(polygons, np.ndarray):
# optimization: polygons all have the same number of points, so can
# vectorize
n = polygons.shape[-2]
i1, i2, i3 = 0, n//3, 2*n//3
v1 = polygons[..., i1, :] - polygons[..., i2, :]
v2 = polygons[..., i2, :] - polygons[..., i3, :]

timhoffm Nov 28, 2018

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Choose a reason Spam Abuse Off Topic Outdated Duplicate Resolved Low Quality

Is there the sign change here intended? This is the convention of get_normals. _generate_normals had it the other way round. I know that there have been some orientation issues. But I don‘t know the state. Just want to make sure the sign change is notbslipping in unintendedly.

eric-wieser Nov 28, 2018

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Choose a reason Spam Abuse Off Topic Outdated Duplicate Resolved Low Quality

Sign change is only in v1 and v2, it cancels out in the cross product, so it doesn't affect the return value.

I picked the convention from get_normals because that was easiest. If you want me to flip both subtractions here, I can, but it won't make any difference.
else:
# The subtraction doesn't vectorize because polygons is jagged.
v1 = np.empty((len(polygons), 3))
v2 = np.empty((len(polygons), 3))
for poly_i, ps in enumerate(polygons):
n = len(ps)
i1, i2, i3 = 0, n//3, 2*n//3
v1[poly_i, :] = ps[i1, :] - ps[i2, :]
v2[poly_i, :] = ps[i2, :] - ps[i3, :]
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eric-wieser marked this conversation as resolved.
return np.cross(v1, v2)

def _shade_colors(self, color, normals, lightsource=None):
"""
Expand Down Expand Up @@ -1991,9 +2004,7 @@ def plot_trisurf(self, *args, color=None, norm=None, vmin=None, vmax=None,
polyc.set_norm(norm)
else:
if shade:
v1 = verts[:, 0, :] - verts[:, 1, :]
v2 = verts[:, 1, :] - verts[:, 2, :]
normals = np.cross(v1, v2)
normals = self._generate_normals(verts)
colset = self._shade_colors(color, normals, lightsource)
else:
colset = color
Expand Down Expand Up @@ -2040,9 +2051,9 @@ def _3d_extend_contour(self, cset, stride=5):
botverts[0][i2],
botverts[0][i1]])

v1 = np.array(topverts[0][i1]) - np.array(topverts[0][i2])
v2 = np.array(topverts[0][i1]) - np.array(botverts[0][i1])
normals.append(np.cross(v1, v2))
# all polygons have 4 vertices, so vectorize
polyverts = np.array(polyverts)
normals = self._generate_normals(polyverts)

colors = self._shade_colors(color, normals)
colors2 = self._shade_colors(color, normals)
Expand Down
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