matplotlib Axes3D 中的 mayavi 3d 对象
mayavi 3d object in matplotlib Axes3D
有时我发现自己对 matplotlib 的 mplot3d 中缺少某些渲染功能感到沮丧。在大多数情况下，我确实发现我可以在 mayavi 中得到我想要的东西，但 matplotlib 3d 轴仍然是更可取的，如果只是为了美观，比如 LaTeX 化标签和与我的其他图形的视觉一致性。
我的问题是关于明显的 hack：是否可以在没有轴的 mayavi 中绘制一些 3d 对象（表面或 3d 散点图或其他），导出该图像，然后将其放置在正确的 matplotlib Axes3D 中大小、方向、坐标投影等？任何人都可以想出完成此任务所需的大纲，或者甚至可以提供一个框架解决方案吗？
前段时间我摆弄了一下，发现我可以轻松导出透明背景的 mayavi 图形并将其放在空的 matplotlib Axes3D（带有刻度、标签等）中，但我没有让 mayavi 和 matplotlib 的相机配置相匹配。简单地在两种环境中将方位角、仰角和距离这三个常用参数设置为相等并不能解决问题；大概需要的是对渲染整个场景的透视（或其他）转换的一些考虑，而我在那个领域相当无能为力。
这似乎很有用：
http://docs.enthought.com/mayavi/mayavi/auto/example_mlab_3D_to_2D.html
我使用 PGFPlots 手册的 mlab_3D_to_2D.py example 和“支持外部三维图形”部分为 Mayavi -> PGFPlots 制作了一个概念验证解决方案。
程序：
- 运行用Mayavi修改
mlab_3D_to_2D.py生成img.png。四个随机点被打印到控制台，将它们复制到剪贴板。请注意图形大小和分辨率是硬编码到脚本中的，这些应该针对不同的图像大小进行编辑或自动提取。
- 将点粘贴到
mlab_pgf.tex。
- 运行
mlab_pgf.tex. 上的 LaTeX
结果：
已修改 mlab_3D_to_2D.py：
# Modified mlab_3D_to_2D.py from https://docs.enthought.com/mayavi/mayavi/auto/example_mlab_3D_to_2D.html
# Original copyright notice:
# Author: S. Chris Colbert <sccolbert@gmail.com>
# Copyright (c) 2009, S. Chris Colbert
# License: BSD Style
from __future__ import print_function
# this import is here because we need to ensure that matplotlib uses the
# wx backend and having regular code outside the main block is PyTaboo.
# It needs to be imported first, so that matplotlib can impose the
# version of Wx it requires.
import matplotlib
# matplotlib.use('WXAgg')
import pylab as pl
import numpy as np
from mayavi import mlab
from mayavi.core.ui.mayavi_scene import MayaviScene
def get_world_to_view_matrix(mlab_scene):
"""returns the 4x4 matrix that is a concatenation of the modelview transform and
perspective transform. Takes as input an mlab scene object."""
if not isinstance(mlab_scene, MayaviScene):
raise TypeError('argument must be an instance of MayaviScene')
# The VTK method needs the aspect ratio and near and far clipping planes
# in order to return the proper transform. So we query the current scene
# object to get the parameters we need.
scene_size = tuple(mlab_scene.get_size())
clip_range = mlab_scene.camera.clipping_range
aspect_ratio = float(scene_size[0])/float(scene_size[1])
# this actually just gets a vtk matrix object, we can't really do anything with it yet
vtk_comb_trans_mat = mlab_scene.camera.get_composite_projection_transform_matrix(
aspect_ratio, clip_range[0], clip_range[1])
# get the vtk mat as a numpy array
np_comb_trans_mat = vtk_comb_trans_mat.to_array()
return np_comb_trans_mat
def get_view_to_display_matrix(mlab_scene):
""" this function returns a 4x4 matrix that will convert normalized
view coordinates to display coordinates. It's assumed that the view should
take up the entire window and that the origin of the window is in the
upper left corner"""
if not (isinstance(mlab_scene, MayaviScene)):
raise TypeError('argument must be an instance of MayaviScene')
# this gets the client size of the window
x, y = tuple(mlab_scene.get_size())
# normalized view coordinates have the origin in the middle of the space
# so we need to scale by width and height of the display window and shift
# by half width and half height. The matrix accomplishes that.
view_to_disp_mat = np.array([[x/2.0, 0., 0., x/2.0],
[ 0., -y/2.0, 0., y/2.0],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 1.]])
return view_to_disp_mat
def apply_transform_to_points(points, trans_mat):
"""a function that applies a 4x4 transformation matrix to an of
homogeneous points. The array of points should have shape Nx4"""
if not trans_mat.shape == (4, 4):
raise ValueError('transform matrix must be 4x4')
if not points.shape[1] == 4:
raise ValueError('point array must have shape Nx4')
return np.dot(trans_mat, points.T).T
def test_surf():
"""Test surf on regularly spaced co-ordinates like MayaVi."""
def f(x, y):
sin, cos = np.sin, np.cos
return sin(x + y) + sin(2 * x - y) + cos(3 * x + 4 * y)
x, y = np.mgrid[-7.:7.05:0.1, -5.:5.05:0.05]
z = f(x, y)
s = mlab.surf(x, y, z)
#cs = contour_surf(x, y, f, contour_z=0)
return x, y, z, s
if __name__ == '__main__':
f = mlab.figure()
f.scene.parallel_projection = True
N = 4
# x, y, z, m = test_mesh()
x, y, z, s = test_surf()
mlab.move(forward=2.0)
# now were going to create a single N x 4 array of our points
# adding a fourth column of ones expresses the world points in
# homogenous coordinates
W = np.ones(x.flatten().shape)
hmgns_world_coords = np.column_stack((x.flatten(), y.flatten(), z.flatten(), W))
# applying the first transform will give us 'unnormalized' view
# coordinates we also have to get the transform matrix for the
# current scene view
comb_trans_mat = get_world_to_view_matrix(f.scene)
view_coords = \
apply_transform_to_points(hmgns_world_coords, comb_trans_mat)
# to get normalized view coordinates, we divide through by the fourth
# element
norm_view_coords = view_coords / (view_coords[:, 3].reshape(-1, 1))
# the last step is to transform from normalized view coordinates to
# display coordinates.
view_to_disp_mat = get_view_to_display_matrix(f.scene)
disp_coords = apply_transform_to_points(norm_view_coords, view_to_disp_mat)
# at this point disp_coords is an Nx4 array of homogenous coordinates
# where X and Y are the pixel coordinates of the X and Y 3D world
# coordinates, so lets take a screenshot of mlab view and open it
# with matplotlib so we can check the accuracy
img = mlab.screenshot(figure=f, mode='rgba', antialiased=True)
pl.imsave("img.png", img)
pl.imshow(img)
# mlab.close(f)
idx = np.random.choice(range(disp_coords[:, 0:2].shape[0]), N, replace=False)
for i in idx:
# print('Point %d: (x, y) ' % i, disp_coords[:, 0:2][i], hmgns_world_coords[:, 0:3][i])
a = hmgns_world_coords[:, 0:3][i]
a = str(list(a)).replace('[', '(').replace(']', ')').replace(' ',',')
# See note below about 298.
b = np.array([0, 298]) - disp_coords[:, 0:2][i]
b = b * np.array([-1, 1])
# Important! These values are not constant.
# The image is 400 x 298 pixels, or 288 x 214.6 pt.
b[0] = b[0] / 400 * 288
b[1] = b[1] / 298 * 214.6
b = str(list(b)).replace('[', '(').replace(']', ')').replace(' ',',')
print(a, "=>", b)
pl.plot([disp_coords[:, 0][i]], [disp_coords[:, 1][i]], 'ro')
pl.show()
# you should check that the printed coordinates correspond to the
# proper points on the screen
mlab.show()
#EOF
mlab_pgf.py:
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
grid=both,minor tick num=1,
xlabel=$x$,ylabel=$y$,zlabel=$z$,
xmin=-7,
xmax=7,
ymin=-5,
ymax=5,
zmin=-3,
zmax=3,
]
\addplot3 graphics [
points={% important, paste points generated by `mlab_3D_to_2D.py`
(5.100000000000001, -3.8, 2.9491697063900895) => (69.82857610254948, 129.60245304203693)
(-6.2, -3.0999999999999996, 0.6658335107904079) => (169.834990346303, 158.6375879061911)
(-1.7999999999999998, 0.4500000000000002, -1.0839565197346115) => (162.75120267070378, 103.53696636434113)
(-5.3, -4.9, 0.6627774166307937) => (147.33354714145847, 162.93938533017257)
},
] {img.png};
\end{axis}
\end{tikzpicture}
\end{document}
有时我发现自己对 matplotlib 的 mplot3d 中缺少某些渲染功能感到沮丧。在大多数情况下，我确实发现我可以在 mayavi 中得到我想要的东西，但 matplotlib 3d 轴仍然是更可取的，如果只是为了美观，比如 LaTeX 化标签和与我的其他图形的视觉一致性。
我的问题是关于明显的 hack：是否可以在没有轴的 mayavi 中绘制一些 3d 对象（表面或 3d 散点图或其他），导出该图像，然后将其放置在正确的 matplotlib Axes3D 中大小、方向、坐标投影等？任何人都可以想出完成此任务所需的大纲，或者甚至可以提供一个框架解决方案吗？
前段时间我摆弄了一下，发现我可以轻松导出透明背景的 mayavi 图形并将其放在空的 matplotlib Axes3D（带有刻度、标签等）中，但我没有让 mayavi 和 matplotlib 的相机配置相匹配。简单地在两种环境中将方位角、仰角和距离这三个常用参数设置为相等并不能解决问题；大概需要的是对渲染整个场景的透视（或其他）转换的一些考虑，而我在那个领域相当无能为力。
这似乎很有用： http://docs.enthought.com/mayavi/mayavi/auto/example_mlab_3D_to_2D.html
我使用 PGFPlots 手册的 mlab_3D_to_2D.py example 和“支持外部三维图形”部分为 Mayavi -> PGFPlots 制作了一个概念验证解决方案。
程序：
- 运行用Mayavi修改
mlab_3D_to_2D.py生成img.png。四个随机点被打印到控制台，将它们复制到剪贴板。请注意图形大小和分辨率是硬编码到脚本中的，这些应该针对不同的图像大小进行编辑或自动提取。 - 将点粘贴到
mlab_pgf.tex。 - 运行
mlab_pgf.tex. 上的 LaTeX
结果：
已修改 mlab_3D_to_2D.py：
# Modified mlab_3D_to_2D.py from https://docs.enthought.com/mayavi/mayavi/auto/example_mlab_3D_to_2D.html
# Original copyright notice:
# Author: S. Chris Colbert <sccolbert@gmail.com>
# Copyright (c) 2009, S. Chris Colbert
# License: BSD Style
from __future__ import print_function
# this import is here because we need to ensure that matplotlib uses the
# wx backend and having regular code outside the main block is PyTaboo.
# It needs to be imported first, so that matplotlib can impose the
# version of Wx it requires.
import matplotlib
# matplotlib.use('WXAgg')
import pylab as pl
import numpy as np
from mayavi import mlab
from mayavi.core.ui.mayavi_scene import MayaviScene
def get_world_to_view_matrix(mlab_scene):
"""returns the 4x4 matrix that is a concatenation of the modelview transform and
perspective transform. Takes as input an mlab scene object."""
if not isinstance(mlab_scene, MayaviScene):
raise TypeError('argument must be an instance of MayaviScene')
# The VTK method needs the aspect ratio and near and far clipping planes
# in order to return the proper transform. So we query the current scene
# object to get the parameters we need.
scene_size = tuple(mlab_scene.get_size())
clip_range = mlab_scene.camera.clipping_range
aspect_ratio = float(scene_size[0])/float(scene_size[1])
# this actually just gets a vtk matrix object, we can't really do anything with it yet
vtk_comb_trans_mat = mlab_scene.camera.get_composite_projection_transform_matrix(
aspect_ratio, clip_range[0], clip_range[1])
# get the vtk mat as a numpy array
np_comb_trans_mat = vtk_comb_trans_mat.to_array()
return np_comb_trans_mat
def get_view_to_display_matrix(mlab_scene):
""" this function returns a 4x4 matrix that will convert normalized
view coordinates to display coordinates. It's assumed that the view should
take up the entire window and that the origin of the window is in the
upper left corner"""
if not (isinstance(mlab_scene, MayaviScene)):
raise TypeError('argument must be an instance of MayaviScene')
# this gets the client size of the window
x, y = tuple(mlab_scene.get_size())
# normalized view coordinates have the origin in the middle of the space
# so we need to scale by width and height of the display window and shift
# by half width and half height. The matrix accomplishes that.
view_to_disp_mat = np.array([[x/2.0, 0., 0., x/2.0],
[ 0., -y/2.0, 0., y/2.0],
[ 0., 0., 1., 0.],
[ 0., 0., 0., 1.]])
return view_to_disp_mat
def apply_transform_to_points(points, trans_mat):
"""a function that applies a 4x4 transformation matrix to an of
homogeneous points. The array of points should have shape Nx4"""
if not trans_mat.shape == (4, 4):
raise ValueError('transform matrix must be 4x4')
if not points.shape[1] == 4:
raise ValueError('point array must have shape Nx4')
return np.dot(trans_mat, points.T).T
def test_surf():
"""Test surf on regularly spaced co-ordinates like MayaVi."""
def f(x, y):
sin, cos = np.sin, np.cos
return sin(x + y) + sin(2 * x - y) + cos(3 * x + 4 * y)
x, y = np.mgrid[-7.:7.05:0.1, -5.:5.05:0.05]
z = f(x, y)
s = mlab.surf(x, y, z)
#cs = contour_surf(x, y, f, contour_z=0)
return x, y, z, s
if __name__ == '__main__':
f = mlab.figure()
f.scene.parallel_projection = True
N = 4
# x, y, z, m = test_mesh()
x, y, z, s = test_surf()
mlab.move(forward=2.0)
# now were going to create a single N x 4 array of our points
# adding a fourth column of ones expresses the world points in
# homogenous coordinates
W = np.ones(x.flatten().shape)
hmgns_world_coords = np.column_stack((x.flatten(), y.flatten(), z.flatten(), W))
# applying the first transform will give us 'unnormalized' view
# coordinates we also have to get the transform matrix for the
# current scene view
comb_trans_mat = get_world_to_view_matrix(f.scene)
view_coords = \
apply_transform_to_points(hmgns_world_coords, comb_trans_mat)
# to get normalized view coordinates, we divide through by the fourth
# element
norm_view_coords = view_coords / (view_coords[:, 3].reshape(-1, 1))
# the last step is to transform from normalized view coordinates to
# display coordinates.
view_to_disp_mat = get_view_to_display_matrix(f.scene)
disp_coords = apply_transform_to_points(norm_view_coords, view_to_disp_mat)
# at this point disp_coords is an Nx4 array of homogenous coordinates
# where X and Y are the pixel coordinates of the X and Y 3D world
# coordinates, so lets take a screenshot of mlab view and open it
# with matplotlib so we can check the accuracy
img = mlab.screenshot(figure=f, mode='rgba', antialiased=True)
pl.imsave("img.png", img)
pl.imshow(img)
# mlab.close(f)
idx = np.random.choice(range(disp_coords[:, 0:2].shape[0]), N, replace=False)
for i in idx:
# print('Point %d: (x, y) ' % i, disp_coords[:, 0:2][i], hmgns_world_coords[:, 0:3][i])
a = hmgns_world_coords[:, 0:3][i]
a = str(list(a)).replace('[', '(').replace(']', ')').replace(' ',',')
# See note below about 298.
b = np.array([0, 298]) - disp_coords[:, 0:2][i]
b = b * np.array([-1, 1])
# Important! These values are not constant.
# The image is 400 x 298 pixels, or 288 x 214.6 pt.
b[0] = b[0] / 400 * 288
b[1] = b[1] / 298 * 214.6
b = str(list(b)).replace('[', '(').replace(']', ')').replace(' ',',')
print(a, "=>", b)
pl.plot([disp_coords[:, 0][i]], [disp_coords[:, 1][i]], 'ro')
pl.show()
# you should check that the printed coordinates correspond to the
# proper points on the screen
mlab.show()
#EOF
mlab_pgf.py:
\documentclass{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
grid=both,minor tick num=1,
xlabel=$x$,ylabel=$y$,zlabel=$z$,
xmin=-7,
xmax=7,
ymin=-5,
ymax=5,
zmin=-3,
zmax=3,
]
\addplot3 graphics [
points={% important, paste points generated by `mlab_3D_to_2D.py`
(5.100000000000001, -3.8, 2.9491697063900895) => (69.82857610254948, 129.60245304203693)
(-6.2, -3.0999999999999996, 0.6658335107904079) => (169.834990346303, 158.6375879061911)
(-1.7999999999999998, 0.4500000000000002, -1.0839565197346115) => (162.75120267070378, 103.53696636434113)
(-5.3, -4.9, 0.6627774166307937) => (147.33354714145847, 162.93938533017257)
},
] {img.png};
\end{axis}
\end{tikzpicture}
\end{document}