python - matplotlib Axes3D 中的 mayavi 3d 对象

Question

我有时会因为 matplotlib 的 mplot3d 中缺少某些渲染功能而感到沮丧。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，但是 matplotlib 3d 轴仍然更可取，如果只是为了美观，比如 LaTeX 化的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情况下在 Mayavi 中绘制一些 3d 对象(表面或 3d 散点图或其他)，导出该图像，然后将其放置在具有正确大小、方向、坐标的 matplotlib Axes3D 中投影等？任何人都可以想出实现这一目标需要什么的大纲，或者甚至提供一个框架解决方案？

前段时间我摆弄了这个，发现我在导出透明背景 mayavi 图形并将其放置在空的 matplotlib Axes3D(带有刻度、标签等)方面没有问题，但我并没有得到什么mayavi 和 matplotlib 的相机配置相匹配。简单地将方位角、仰角和距离这三个常用参数在两种环境中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)变换进行一些考虑，而我在该领域相当无能为力。

看起来这可能有用:
http://docs.enthought.com/mayavi/mayavi/auto/example_mlab_3D_to_2D.html

Answer 1

我使用 mlab_3D_to_2D.py example 和 PGFPlots 手册的“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:

使用 Mayavi 运行修改后的 mlab_3D_to_2D.py 以生成 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被硬编码到脚本中，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 中。

在 mlab_pgf.tex 上运行 LaTeX。

结果:

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}