使用 Python 的 matplotlib 3D API 的轮廓问题
Problems With Contours Using Python's matplotlib 3D API
我正在尝试做类似于文档中的 this 3D 示例的操作，但使用的是点云而不是光滑表面。该示例将 2D 轮廓投影到三个坐标平面中的每一个平面上。这表明我能够在 xy 平面上做到这一点。
当我尝试在其他两个平面上做同样的事情时，我得到一个奇怪的轮廓塌陷成一条细条，
或者在 matplotlib.
的内部我无法触及的异常方式
Traceback (most recent call last):
File ".../matplotlib/backends/backend_qt5.py", line 519, in _draw_idle
self.draw()
File ".../matplotlib/backends/backend_agg.py", line 433, in draw
self.figure.draw(self.renderer)
File ".../matplotlib/artist.py", line 55, in draw_wrapper
return draw(artist, renderer, *args, **kwargs)
File ".../matplotlib/figure.py", line 1475, in draw
renderer, self, artists, self.suppressComposite)
File ".../matplotlib/image.py", line 141, in _draw_list_compositing_images
a.draw(renderer)
File ".../mpl_toolkits/mplot3d/axes3d.py", line 281, in draw
reverse=True)):
File ".../mpl_toolkits/mplot3d/axes3d.py", line 280, in <lambda>
key=lambda col: col.do_3d_projection(renderer),
File ".../mpl_toolkits/mplot3d/art3d.py", line 226, in do_3d_projection
self._segments3d]
File ".../mpl_toolkits/mplot3d/art3d.py", line 225, in <listcomp>
proj3d.proj_trans_points(points, renderer.M) for points in
File ".../mpl_toolkits/mplot3d/proj3d.py", line 188, in proj_trans_points
xs, ys, zs = zip(*points)
ValueError: not enough values to unpack (expected 3, got 0)
这是问题的一个例子。这个版本有效。取消注释 plot() 函数中对 ax.contour() 的一个或两个调用以查看奇怪的轮廓，或者更可能是异常。
import math
import sys
import matplotlib as mpl
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d
import numpy as np
import scipy.spatial
#np.random.seed(4)
numPts = 1000 # number of points in cloud
scatter = False # adds scatter plot to show point cloud
def main():
(pts, f) = mkData() # create the point cloud
tris = mkTris(pts) # triangulate it
plot(pts, tris, f) # plot it
def plot(pts, tris, f):
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
cmap = plt.get_cmap("coolwarm")
collec = ax.plot_trisurf(tris, pts[:, 2], cmap=cmap)
colors = np.mean(f[tris.triangles], axis=1)
collec.set_array(colors)
collec.autoscale()
(xr, yr, zr, xMin, yMin, zMin, zMax) = resample(ax, tris, f)
ax.set_zlim(zMin, zMax) # default always includes zero for some reason
#
# Uncomment one or both of these lines to see the problem.
#
ax.contour(xr, yr, zr, 10, zdir="z", cmap=cmap, offset=zMin)
#ax.contour(xr, yr, zr, 10, zdir="x", cmap=cmap, offset=xMin)
#ax.contour(xr, yr, zr, 10, zdir="y", cmap=cmap, offset=yMin)
if scatter:
ax.scatter(pts[:, 0], pts[:, 1], pts[:, 2], alpha=0.1)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
fig.colorbar(collec, shrink=0.5, aspect=5)
plt.show()
def mkData():
"""
Create a random point cloud near a random plane, and define a function on
the plane for colors and contours.
"""
offset = 1 # generate points near a unit square, xy-plane
pts = 2 * np.random.rand(numPts, 3) - 1
pts[:, 2] = offset * (2 * np.random.rand(numPts) - 1)
x = 2 * np.ravel(pts[:, 0])
y = 2 * np.ravel(pts[:, 1])
f = x * np.exp(-x**2 - y**2) # just some function for colors, contours
width = 100 # scale unit square to a larger rectangle
height = 20
pts[:, 0] *= width
pts[:, 1] *= height
(e1, e2, e3) =[2 * np.pi * np.random.rand() for _ in range(3)]
(c1, s1) = (math.cos(e1), math.sin(e1)) # rotate scaled rectangle
(c2, s2) = (math.cos(e2), math.sin(e2))
(c3, s3) = (math.cos(e3), math.sin(e3))
Ta2b = np.array(( # do not have scipy.spatial.transform
[ c1 *c2, s2, -s1 * c2],
[s1 * s3 - c1 * s2 * c3, c2 * c3, c1 *s3 + s1 * s2 * c3],
[s1 * c3 + c1 * s2 * s3, -c2 * s3, c1 *c3 - s1 * s2 * s3]))
pts = (Ta2b @ pts.T).T
dist = 500 # translate away from the origin
Ra2bNb = dist * (2 * np.random.rand(3, 1) - 1)
pts += Ra2bNb.T
return (pts, f)
def mkTris(pts): # triangulate the point cloud
u = np.ravel(pts[:, 0])
v = np.ravel(pts[:, 1])
try:
return mpl.tri.Triangulation(u, v)
except (ValueError, RuntimeError) as ex:
sys.exit(f"Unable to compute triangulation: {ex}.")
def resample(ax, tris, f): # resample triangulation onto a regular grid
(xMin, xMax) = ax.get_xlim()
(yMin, yMax) = ax.get_ylim()
(zMin, zMax) = ax.get_zlim()
x = np.linspace(xMin, xMax, 30)
y = np.linspace(yMin, yMax, 30)
(xm, ym)=np.meshgrid(x, y)
interp = mpl.tri.triinterpolate.LinearTriInterpolator(tris, f)
zm = interp(xm, ym)
return (xm, ym, zm, xMin, yMin, zMin, zMax)
if __name__ == "__main__":
main()
这是 matplotlib 2.2.2 和 3.1.1。感谢您提供的任何帮助，以获取所有三个平面上的轮廓，例如演示。
吉姆
一位matplotlib开发者指出重采样是错误的。修复后，这是更正后的情节。
对于看到数据 edge-on 的坐标平面，如本例中的 yz 平面，轮廓看起来有点不稳定。这是预料之中的，因为数据可以接近 multi-valued。 xz 平面轮廓看起来也很参差不齐。我怀疑这两个问题都可以通过分别对每个平面进行三角测量和轮廓绘制来改善，而不是像这里所做的那样支持 xy 平面。
这是固定的测试脚本。唯一重要的变化是 plot() 和 resample()。
import math
import sys
import matplotlib as mpl
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d
import numpy as np
import scipy.spatial
#np.random.seed(4)
numPts = 1000 # number of points in cloud
numGrid = 120 # number of points in meshgrid used in resample for contours
scatter = False # adds scatter plot to show point cloud
def main():
(pts, f) = mkData() # create the point cloud
tris = mkTris(pts) # triangulate it
plot(pts, tris, f) # plot it
def plot(pts, tris, f):
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
cmap = plt.get_cmap("coolwarm")
collec = ax.plot_trisurf(tris, pts[:, 2], cmap=cmap)
colors = np.mean(f[tris.triangles], axis=1)
collec.set_array(colors)
collec.autoscale()
(xr, yr, zr, fr, xMin, xMax, yMin, yMax, zMin, zMax) = resample(ax, tris,
pts, f)
ax.set_xlim(xMin, xMax) # default always includes zero for some reason
ax.set_ylim(yMin, yMax)
ax.set_zlim(zMin, zMax)
ax.contour(xr, yr, fr, 10, zdir="z", cmap=cmap, offset=zMin)
ax.contour(fr, yr, zr, 10, zdir="x", cmap=cmap, offset=xMin)
ax.contour(xr, fr, zr, 10, zdir="y", cmap=cmap, offset=yMax)
if scatter:
ax.scatter(pts[:, 0], pts[:, 1], pts[:, 2], alpha=0.1)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
fig.colorbar(collec, shrink=0.5, aspect=5)
plt.show()
def mkData():
"""
Create a random point cloud near a random plane, and define a function on
the plane for colors and contours.
"""
offset = 1 # generate points near a unit square, xy-plane
pts = 2 * np.random.rand(numPts, 3) - 1
pts[:, 2] = offset * (2 * np.random.rand(numPts) - 1)
x = 2 * np.ravel(pts[:, 0])
y = 2 * np.ravel(pts[:, 1])
f = x * np.exp(-x**2 - y**2) # just some function for colors, contours
width = 100 # scale unit square to a larger rectangle
height = 20
pts[:, 0] *= width
pts[:, 1] *= height
(e1, e2, e3) =[2 * np.pi * np.random.rand() for _ in range(3)]
(c1, s1) = (math.cos(e1), math.sin(e1)) # rotate scaled rectangle
(c2, s2) = (math.cos(e2), math.sin(e2))
(c3, s3) = (math.cos(e3), math.sin(e3))
Ta2b = np.array(( # do not have scipy.spatial.transform
[ c1 *c2, s2, -s1 * c2],
[s1 * s3 - c1 * s2 * c3, c2 * c3, c1 *s3 + s1 * s2 * c3],
[s1 * c3 + c1 * s2 * s3, -c2 * s3, c1 *c3 - s1 * s2 * s3]))
pts = (Ta2b @ pts.T).T
dist = 500 # translate away from the origin
Ra2bNb = dist * (2 * np.random.rand(3, 1) - 1)
pts += Ra2bNb.T
return (pts, f)
def mkTris(pts):
"Triangulate the point cloud."
u = np.ravel(pts[:, 0])
v = np.ravel(pts[:, 1])
try:
return mpl.tri.Triangulation(u, v)
except (ValueError, RuntimeError) as ex:
sys.exit(f"Unable to compute triangulation: {ex}.")
def resample(ax, tris, pts, f):
"Resample the triangulation onto a regular grid for contours."
(xMin, xMax) = ax.get_xlim()
(yMin, yMax) = ax.get_ylim()
(zMin, zMax) = ax.get_zlim()
x = np.linspace(xMin, xMax, numGrid)
y = np.linspace(yMin, yMax, numGrid)
(xm, ym)=np.meshgrid(x, y)
fInterp = mpl.tri.CubicTriInterpolator(tris, f)
fm = fInterp(xm, ym)
zInterp = mpl.tri.CubicTriInterpolator(tris, pts[:,2])
zm = zInterp(xm, ym)
return (xm, ym, zm, fm, xMin, xMax, yMin, yMax, zMin, zMax)
if __name__ == "__main__":
main()
我正在尝试做类似于文档中的 this 3D 示例的操作，但使用的是点云而不是光滑表面。该示例将 2D 轮廓投影到三个坐标平面中的每一个平面上。这表明我能够在 xy 平面上做到这一点。
当我尝试在其他两个平面上做同样的事情时，我得到一个奇怪的轮廓塌陷成一条细条，
或者在 matplotlib.
的内部我无法触及的异常方式Traceback (most recent call last):
File ".../matplotlib/backends/backend_qt5.py", line 519, in _draw_idle
self.draw()
File ".../matplotlib/backends/backend_agg.py", line 433, in draw
self.figure.draw(self.renderer)
File ".../matplotlib/artist.py", line 55, in draw_wrapper
return draw(artist, renderer, *args, **kwargs)
File ".../matplotlib/figure.py", line 1475, in draw
renderer, self, artists, self.suppressComposite)
File ".../matplotlib/image.py", line 141, in _draw_list_compositing_images
a.draw(renderer)
File ".../mpl_toolkits/mplot3d/axes3d.py", line 281, in draw
reverse=True)):
File ".../mpl_toolkits/mplot3d/axes3d.py", line 280, in <lambda>
key=lambda col: col.do_3d_projection(renderer),
File ".../mpl_toolkits/mplot3d/art3d.py", line 226, in do_3d_projection
self._segments3d]
File ".../mpl_toolkits/mplot3d/art3d.py", line 225, in <listcomp>
proj3d.proj_trans_points(points, renderer.M) for points in
File ".../mpl_toolkits/mplot3d/proj3d.py", line 188, in proj_trans_points
xs, ys, zs = zip(*points)
ValueError: not enough values to unpack (expected 3, got 0)
这是问题的一个例子。这个版本有效。取消注释 plot() 函数中对 ax.contour() 的一个或两个调用以查看奇怪的轮廓，或者更可能是异常。
import math
import sys
import matplotlib as mpl
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d
import numpy as np
import scipy.spatial
#np.random.seed(4)
numPts = 1000 # number of points in cloud
scatter = False # adds scatter plot to show point cloud
def main():
(pts, f) = mkData() # create the point cloud
tris = mkTris(pts) # triangulate it
plot(pts, tris, f) # plot it
def plot(pts, tris, f):
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
cmap = plt.get_cmap("coolwarm")
collec = ax.plot_trisurf(tris, pts[:, 2], cmap=cmap)
colors = np.mean(f[tris.triangles], axis=1)
collec.set_array(colors)
collec.autoscale()
(xr, yr, zr, xMin, yMin, zMin, zMax) = resample(ax, tris, f)
ax.set_zlim(zMin, zMax) # default always includes zero for some reason
#
# Uncomment one or both of these lines to see the problem.
#
ax.contour(xr, yr, zr, 10, zdir="z", cmap=cmap, offset=zMin)
#ax.contour(xr, yr, zr, 10, zdir="x", cmap=cmap, offset=xMin)
#ax.contour(xr, yr, zr, 10, zdir="y", cmap=cmap, offset=yMin)
if scatter:
ax.scatter(pts[:, 0], pts[:, 1], pts[:, 2], alpha=0.1)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
fig.colorbar(collec, shrink=0.5, aspect=5)
plt.show()
def mkData():
"""
Create a random point cloud near a random plane, and define a function on
the plane for colors and contours.
"""
offset = 1 # generate points near a unit square, xy-plane
pts = 2 * np.random.rand(numPts, 3) - 1
pts[:, 2] = offset * (2 * np.random.rand(numPts) - 1)
x = 2 * np.ravel(pts[:, 0])
y = 2 * np.ravel(pts[:, 1])
f = x * np.exp(-x**2 - y**2) # just some function for colors, contours
width = 100 # scale unit square to a larger rectangle
height = 20
pts[:, 0] *= width
pts[:, 1] *= height
(e1, e2, e3) =[2 * np.pi * np.random.rand() for _ in range(3)]
(c1, s1) = (math.cos(e1), math.sin(e1)) # rotate scaled rectangle
(c2, s2) = (math.cos(e2), math.sin(e2))
(c3, s3) = (math.cos(e3), math.sin(e3))
Ta2b = np.array(( # do not have scipy.spatial.transform
[ c1 *c2, s2, -s1 * c2],
[s1 * s3 - c1 * s2 * c3, c2 * c3, c1 *s3 + s1 * s2 * c3],
[s1 * c3 + c1 * s2 * s3, -c2 * s3, c1 *c3 - s1 * s2 * s3]))
pts = (Ta2b @ pts.T).T
dist = 500 # translate away from the origin
Ra2bNb = dist * (2 * np.random.rand(3, 1) - 1)
pts += Ra2bNb.T
return (pts, f)
def mkTris(pts): # triangulate the point cloud
u = np.ravel(pts[:, 0])
v = np.ravel(pts[:, 1])
try:
return mpl.tri.Triangulation(u, v)
except (ValueError, RuntimeError) as ex:
sys.exit(f"Unable to compute triangulation: {ex}.")
def resample(ax, tris, f): # resample triangulation onto a regular grid
(xMin, xMax) = ax.get_xlim()
(yMin, yMax) = ax.get_ylim()
(zMin, zMax) = ax.get_zlim()
x = np.linspace(xMin, xMax, 30)
y = np.linspace(yMin, yMax, 30)
(xm, ym)=np.meshgrid(x, y)
interp = mpl.tri.triinterpolate.LinearTriInterpolator(tris, f)
zm = interp(xm, ym)
return (xm, ym, zm, xMin, yMin, zMin, zMax)
if __name__ == "__main__":
main()
这是 matplotlib 2.2.2 和 3.1.1。感谢您提供的任何帮助，以获取所有三个平面上的轮廓，例如演示。
吉姆
一位matplotlib开发者指出重采样是错误的。修复后，这是更正后的情节。
对于看到数据 edge-on 的坐标平面，如本例中的 yz 平面，轮廓看起来有点不稳定。这是预料之中的，因为数据可以接近 multi-valued。 xz 平面轮廓看起来也很参差不齐。我怀疑这两个问题都可以通过分别对每个平面进行三角测量和轮廓绘制来改善，而不是像这里所做的那样支持 xy 平面。
这是固定的测试脚本。唯一重要的变化是 plot() 和 resample()。
import math
import sys
import matplotlib as mpl
import matplotlib.pyplot as plt
import mpl_toolkits.mplot3d
import numpy as np
import scipy.spatial
#np.random.seed(4)
numPts = 1000 # number of points in cloud
numGrid = 120 # number of points in meshgrid used in resample for contours
scatter = False # adds scatter plot to show point cloud
def main():
(pts, f) = mkData() # create the point cloud
tris = mkTris(pts) # triangulate it
plot(pts, tris, f) # plot it
def plot(pts, tris, f):
fig = plt.figure()
ax = fig.add_subplot(111, projection="3d")
cmap = plt.get_cmap("coolwarm")
collec = ax.plot_trisurf(tris, pts[:, 2], cmap=cmap)
colors = np.mean(f[tris.triangles], axis=1)
collec.set_array(colors)
collec.autoscale()
(xr, yr, zr, fr, xMin, xMax, yMin, yMax, zMin, zMax) = resample(ax, tris,
pts, f)
ax.set_xlim(xMin, xMax) # default always includes zero for some reason
ax.set_ylim(yMin, yMax)
ax.set_zlim(zMin, zMax)
ax.contour(xr, yr, fr, 10, zdir="z", cmap=cmap, offset=zMin)
ax.contour(fr, yr, zr, 10, zdir="x", cmap=cmap, offset=xMin)
ax.contour(xr, fr, zr, 10, zdir="y", cmap=cmap, offset=yMax)
if scatter:
ax.scatter(pts[:, 0], pts[:, 1], pts[:, 2], alpha=0.1)
ax.set_xlabel("x")
ax.set_ylabel("y")
ax.set_zlabel("z")
fig.colorbar(collec, shrink=0.5, aspect=5)
plt.show()
def mkData():
"""
Create a random point cloud near a random plane, and define a function on
the plane for colors and contours.
"""
offset = 1 # generate points near a unit square, xy-plane
pts = 2 * np.random.rand(numPts, 3) - 1
pts[:, 2] = offset * (2 * np.random.rand(numPts) - 1)
x = 2 * np.ravel(pts[:, 0])
y = 2 * np.ravel(pts[:, 1])
f = x * np.exp(-x**2 - y**2) # just some function for colors, contours
width = 100 # scale unit square to a larger rectangle
height = 20
pts[:, 0] *= width
pts[:, 1] *= height
(e1, e2, e3) =[2 * np.pi * np.random.rand() for _ in range(3)]
(c1, s1) = (math.cos(e1), math.sin(e1)) # rotate scaled rectangle
(c2, s2) = (math.cos(e2), math.sin(e2))
(c3, s3) = (math.cos(e3), math.sin(e3))
Ta2b = np.array(( # do not have scipy.spatial.transform
[ c1 *c2, s2, -s1 * c2],
[s1 * s3 - c1 * s2 * c3, c2 * c3, c1 *s3 + s1 * s2 * c3],
[s1 * c3 + c1 * s2 * s3, -c2 * s3, c1 *c3 - s1 * s2 * s3]))
pts = (Ta2b @ pts.T).T
dist = 500 # translate away from the origin
Ra2bNb = dist * (2 * np.random.rand(3, 1) - 1)
pts += Ra2bNb.T
return (pts, f)
def mkTris(pts):
"Triangulate the point cloud."
u = np.ravel(pts[:, 0])
v = np.ravel(pts[:, 1])
try:
return mpl.tri.Triangulation(u, v)
except (ValueError, RuntimeError) as ex:
sys.exit(f"Unable to compute triangulation: {ex}.")
def resample(ax, tris, pts, f):
"Resample the triangulation onto a regular grid for contours."
(xMin, xMax) = ax.get_xlim()
(yMin, yMax) = ax.get_ylim()
(zMin, zMax) = ax.get_zlim()
x = np.linspace(xMin, xMax, numGrid)
y = np.linspace(yMin, yMax, numGrid)
(xm, ym)=np.meshgrid(x, y)
fInterp = mpl.tri.CubicTriInterpolator(tris, f)
fm = fInterp(xm, ym)
zInterp = mpl.tri.CubicTriInterpolator(tris, pts[:,2])
zm = zInterp(xm, ym)
return (xm, ym, zm, fm, xMin, xMax, yMin, yMax, zMin, zMax)
if __name__ == "__main__":
main()