如何在matplotlib中遮挡表面图后面的线? [英] How to obscure a line behind a surface plot in matplotlib?

问题描述

我想使用Matplotlib通过球面上的色图绘制数据.另外，我想添加一个3D线图.到目前为止，我的代码是:

I want to plot data using Matplotlib via a colormap on the surface of a sphere. Additionally, I would like to add a 3D line plot. The code I have so far is this:

import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np


NPoints_Phi         = 30
NPoints_Theta       = 30

radius              = 1
pi                  = np.pi
cos                 = np.cos
sin                 = np.sin

phi_array           = ((np.linspace(0, 1, NPoints_Phi))**1) * 2*pi
theta_array         = (np.linspace(0, 1, NPoints_Theta) **1) * pi


phi, theta          = np.meshgrid(phi_array, theta_array) 


x_coord             = radius*sin(theta)*cos(phi)
y_coord             = radius*sin(theta)*sin(phi)
z_coord             = radius*cos(theta)


#Make colormap the fourth dimension
color_dimension     = x_coord 
minn, maxx          = color_dimension.min(), color_dimension.max()
norm                = matplotlib.colors.Normalize(minn, maxx)
m                   = plt.cm.ScalarMappable(norm=norm, cmap='jet')
m.set_array([])
fcolors             = m.to_rgba(color_dimension)



theta2              = np.linspace(-np.pi,  0, 1000)
phi2                = np.linspace( 0 ,  5 * 2*np.pi , 1000)


x_coord_2           = radius * np.sin(theta2) * np.cos(phi2)
y_coord_2           = radius * np.sin(theta2) * np.sin(phi2)
z_coord_2           = radius * np.cos(theta2)

# plot
fig                 = plt.figure()

ax                  = fig.gca(projection='3d')
ax.plot(x_coord_2, y_coord_2, z_coord_2,'k|-', linewidth=1 )
ax.plot_surface(x_coord,y_coord,z_coord, rstride=1, cstride=1, facecolors=fcolors, vmin=minn, vmax=maxx, shade=False)
fig.show()

此代码生成的图像如下所示:这几乎是我想要的.但是，黑线在背景中时应被表面图遮挡，而在前景中时应可见.换句话说，黑线不应照耀"通过球体.

This code produces an image that looks like this: which is ALMOST what I want. However, the black line should be obscured by the surface plot when it is in the background and visible when it is in the foreground. In other words, the black line should not "shine through" the sphere.

这可以在Matplotlib中完成而无需使用Mayavi吗?

Can this be done in Matplotlib and without the use of Mayavi?

推荐答案

问题是matplotlib不是光线追踪器，并且它并不是真正设计成具有3D功能的绘图库.因此，它可以与2D空间中的图层系统配合使用，并且对象可以位于更前面或后面的图层中.可以使用zorder关键字参数将其设置为大多数绘图功能.但是，在matplotlib中没有意识到某个对象是3D空间中另一个对象的前面还是后面.因此，您可以使整条线可见(在球体的前面)，也可以使其隐藏(在球体的后面).

The problem is that matplotlib is no ray tracer and it's not really designed to be a 3D capable plotting library. As such it works with a system of layers in 2D space, and objects can be in a layer more in front or more to the back. This can be set with the zorder keyword argument to most plotting functions. However there is no awareness in matplotlib about whether an object is in front or behind another object in 3D space. Therefore you can either have the complete line visible (in front of the sphere) or hidden (behind it).

解决方案是计算您自己应该可见的点.我在这里谈论点是因为一条线将通过"球体连接可见点，这是不需要的.因此，我仅限于绘制点-但是，如果您有足够的点，它们看起来就像一条线:-).或者，可以通过在不连接的点之间使用附加的nan坐标来隐藏线.我将自己限制在此处，不要使解决方案变得比需要的复杂.

The solution would be to calculate the points that should be visible by yourself. I'm talking about points here because a line would be connecting visible points "through" the sphere, which is unwanted. I therefore restrict myself to plotting points - but if you have enough of them, they look like a line :-). Alternatively lines can be hidden by using an additional nan coordinate in between points that are not to be connected; I'm restricting myself to points here not to make the solution more complicated than it needs to be.

对于一个完美的球体，计算哪些点应该可见并不难，其想法如下:

The calculation of which points should be visible is not too hard for a perfect sphere, and the idea is the following:

1. 获取3D图的视角
2. 由此，在沿视图方向的数据坐标中计算到视平面的法线向量.
3. 计算此法向矢量(在下面的代码中称为X)与线点之间的标量积，以便将该标量积用作是否显示点的条件.如果标量乘积小于0，则从观察者的角度来看，相应的点位于观察平面的另一侧，因此不应显示.
4. 根据条件过滤点.

1. Obtain the viewing angle of the 3D plot
2. From that, calculate the normal vector to the plane of vision in data coordinates in direction of the view.
3. Calculate the scalar product between this normal vector (called X in the code below) and the line points in order to use this scalar product as a condition on whether to show the points or not. If the scalar product is smaller than 0 then the respective point is on the other side of the viewing plane as seen from the observer and should therefore not be shown.
4. Filter the points by the condition.

然后另一项可选任务是，当用户旋转视图时，针对情况调整显示的点.这是通过将motion_notify_event连接到根据新设置的视角使用上面的步骤更新数据的功能来实现的.

One further optional task is then to adapt the points shown for the case when the user rotates the view. This is accomplished by connecting the motion_notify_event to a function that updates the data using the procedure from above, based on the newly set viewing angle.

有关如何实现此功能的信息，请参见下面的代码.

See the code below on how to implement this.

import matplotlib
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np


NPoints_Phi         = 30
NPoints_Theta       = 30

phi_array           = ((np.linspace(0, 1, NPoints_Phi))**1) * 2*np.pi
theta_array         = (np.linspace(0, 1, NPoints_Theta) **1) * np.pi

radius=1
phi, theta          = np.meshgrid(phi_array, theta_array) 

x_coord             = radius*np.sin(theta)*np.cos(phi)
y_coord             = radius*np.sin(theta)*np.sin(phi)
z_coord             = radius*np.cos(theta)

#Make colormap the fourth dimension
color_dimension     = x_coord 
minn, maxx          = color_dimension.min(), color_dimension.max()
norm                = matplotlib.colors.Normalize(minn, maxx)
m                   = plt.cm.ScalarMappable(norm=norm, cmap='jet')
m.set_array([])
fcolors             = m.to_rgba(color_dimension)

theta2              = np.linspace(-np.pi,  0, 1000)
phi2                = np.linspace( 0, 5 * 2*np.pi , 1000)

x_coord_2           = radius * np.sin(theta2) * np.cos(phi2)
y_coord_2           = radius * np.sin(theta2) * np.sin(phi2)
z_coord_2           = radius * np.cos(theta2)

# plot
fig = plt.figure()

ax = fig.gca(projection='3d')
# plot empty plot, with points (without a line)
points, = ax.plot([],[],[],'k.', markersize=5, alpha=0.9)
#set initial viewing angles
azimuth, elev = 75, 21
ax.view_init(elev, azimuth )

def plot_visible(azimuth, elev):
    #transform viewing angle to normal vector in data coordinates
    a = azimuth*np.pi/180. -np.pi
    e = elev*np.pi/180. - np.pi/2.
    X = [ np.sin(e) * np.cos(a),np.sin(e) * np.sin(a),np.cos(e)]  
    # concatenate coordinates
    Z = np.c_[x_coord_2, y_coord_2, z_coord_2]
    # calculate dot product 
    # the points where this is positive are to be shown
    cond = (np.dot(Z,X) >= 0)
    # filter points by the above condition
    x_c = x_coord_2[cond]
    y_c = y_coord_2[cond]
    z_c = z_coord_2[cond]
    # set the new data points
    points.set_data(x_c, y_c)
    points.set_3d_properties(z_c, zdir="z")
    fig.canvas.draw_idle()

plot_visible(azimuth, elev)
ax.plot_surface(x_coord,y_coord,z_coord, rstride=1, cstride=1, 
            facecolors=fcolors, vmin=minn, vmax=maxx, shade=False)

# in order to always show the correct points on the sphere, 
# the points to be shown must be recalculated one the viewing angle changes
# when the user rotates the plot
def rotate(event):
    if event.inaxes == ax:
        plot_visible(ax.azim, ax.elev)

c1 = fig.canvas.mpl_connect('motion_notify_event', rotate)

plt.show()

最后，可能需要对markersize，alpha和点数进行一些操作，才能从中获得最视觉上的吸引力.

At the end one may have to play a bit with the markersize, alpha and the number of points in order to get the most visually appealing result out of this.

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