我使用 Mayavi -> PGFPlots 制作了一个概念验证解决方案mlab_3D_to_2D.py example https://docs.enthought.com/mayavi/mayavi/auto/example_mlab_3D_to_2D.html以及 PGFPlots 手册的“对外部三维图形的支持”部分。
程序：
- 运行修改后的
mlab_3D_to_2D.py使用 Mayavi 生成img.png。四个随机点打印到控制台，将它们复制到剪贴板。请注意，图形尺寸和分辨率被硬编码到脚本中，应针对不同的图像尺寸对其进行编辑或自动提取。
- 将点粘贴到
mlab_pgf.tex.
- 运行 LaTeX
mlab_pgf.tex.
Result:
修改的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 <[email protected] /cdn-cgi/l/email-protection>
# 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}
