plot_trisurface 使用自定义颜色数组

Question

我基本上想在其支持上“显示”三维 Dirichlet 分布的 pdf。下面的函数 simplex 计算该支撑上的规则点，这些点存储在数组 sim 中。数组 pdf 保存 sim.

中每一行的标量密度

我首先想到的是使用三角剖分。但是，plot_trisurface 的 color 参数仅支持所有三角形使用一种颜色。设置 cmap 根据 z 坐标值对三角形着色（见图 1）。 plot_trisurface 也忽略了 facecolors kwarg。然而，我想要的是根据 pdf.

为表面着色

作为我发现的解决方法，我可以将表面插值为 3d 散点图。这通常会提供所需的可视化效果，但我清楚地看到它是一个散点图；特别是在边界上。（见图2）

有没有办法将 pdf 投影绘制到单纯形上？

import itertools
import matplotlib.pyplot as plt
import numpy as np
from scipy import stats


def simplex(n_vals):
    base = np.linspace(0, 1, n_vals, endpoint=False)
    coords = np.asarray(list(itertools.product(base, repeat=3)))
    return coords[np.isclose(coords.sum(axis=-1), 1.0)]


sim = simplex(20)
pdf = stats.dirichlet([1.1, 1.5, 1.3]).pdf(sim.T)

fig1 = plt.figure()
ax1 = fig1.add_subplot(1, 2, 1, projection='3d', azim=20)
ax2 = fig1.add_subplot(1, 2, 2, projection='3d', azim=20)
ax1.plot_trisurf(x, y, z, color='k')
ax2.plot_trisurf(x, y, z, cmap='Spectral')

fig2 = plt.figure()
ax21 = fig2.add_subplot(projection='3d', azim=20)
ax21.scatter3D(*sim.T, s=50, alpha=.5, c=pdf, cmap='Spectral')

Answer 1

这是一种通过使用正确的颜色为三角剖分对象中的每个三角形着色的方法。这是你要找的吗？唯一的问题是每个补丁都有统一的颜色，这使得补丁有点可见。

# Setup is the same

import itertools
import matplotlib.pyplot as plt
from pylab import get_cmap
from matplotlib.tri import Triangulation, LinearTriInterpolator
import numpy as np
from scipy import stats
from mpl_toolkits.mplot3d.art3d import Poly3DCollection

def simplex(n_vals):
    base = np.linspace(0, 1, n_vals, endpoint=False)
    coords = np.asarray(list(itertools.product(base, repeat=3)))
    return coords[np.isclose(coords.sum(axis=-1), 1.0)]

sim = simplex(20)
pdf = stats.dirichlet([1.1, 1.5, 1.3]).pdf(sim.T)

# For shorter notation we define x, y and z:

x = sim[:, 0]
y = sim[:, 1]
z = sim[:, 2]

# Creating a triangulation object and using it to extract the actual triangles. 
# Note if it is necessary that no patch will be vertical (i.e. along the z direction)

tri = Triangulation(x, y)

triangle_vertices = np.array([np.array([[x[T[0]], y[T[0]], z[T[0]]],
                                        [x[T[1]], y[T[1]], z[T[1]]], 
                                        [x[T[2]], y[T[2]], z[T[2]]]]) for T in tri.triangles])

# Finding coordinate for the midpoints of each triangle. 
# This will be used to extract the color

midpoints = np.average(triangle_vertices, axis = 1)
midx = midpoints[:, 0]
midy = midpoints[:, 1]

# Interpolating the pdf and using it with the selected cmap to produce the color RGB vector for each face. 
# Some roundoff and normalization are needed

face_color_function = LinearTriInterpolator(tri, pdf)
face_color_index = face_color_function(midx, midy)
face_color_index[face_color_index < 0] = 0
face_color_index /= np.max(pdf)

cmap = get_cmap('Spectral')

# Creating the patches and plotting

collection = Poly3DCollection(triangle_vertices, facecolors=cmap(face_color_index), edgecolors=None)

fig = plt.figure()
ax = fig.gca(projection='3d')
ax.add_collection(collection)
plt.show()

显然提高分辨率会使情节更流畅。

Answer 2

这个图，配一个colorbar，

由以下脚本生成 — 定义在脚本末尾的函数 map_colors 可能会让一般 reader.

感兴趣

import numpy as np
import matplotlib.pyplot as plt
from scipy import stats
from itertools import product as Π

# the distribution that we want to study
dirichlet = stats.dirichlet([1.1, 1.5, 1.3])

# generate the "mesh"
N = 30 # no. of triangles along an edge
s = np.linspace(0, 1, N+1)
x, y, z = np.array([(x,y,1-x-y) for x,y in Π(s,s) if x+y<1+1E-6]).T

# plot as usual
fig = plt.figure() 
ax = fig.add_subplot(1, 1, 1, projection='3d', azim=20) 
p3dc = ax.plot_trisurf(x, y, z)

########## change the face colors ####################
mappable = map_colors(p3dc, dirichlet.pdf, 'Spectral')
# ####################################################

# possibly add a colormap
plt.colorbar(mappable, shrink=0.67, aspect=16.7)

# we are done
plt.show()

def map_colors(p3dc, func, cmap='viridis'):
    """
Color a tri-mesh according to a function evaluated in each barycentre.

    p3dc: a Poly3DCollection, as returned e.g. by ax.plot_trisurf
    func: a single-valued function of 3 arrays: x, y, z
    cmap: a colormap NAME, as a string

    Returns a ScalarMappable that can be used to instantiate a colorbar.
    """
    
    from matplotlib.cm import ScalarMappable, get_cmap
    from matplotlib.colors import Normalize
    from numpy import array

    # reconstruct the triangles from internal data
    x, y, z, _ = p3dc._vec
    slices = p3dc._segslices
    triangles = array([array((x[s],y[s],z[s])).T for s in slices])

    # compute the barycentres for each triangle
    xb, yb, zb = triangles.mean(axis=1).T
    
    # compute the function in the barycentres
    values = func(xb, yb, zb)

    # usual stuff
    norm = Normalize()
    colors = get_cmap(cmap)(norm(values))

    # set the face colors of the Poly3DCollection
    p3dc.set_fc(colors)

    # if the caller wants a colorbar, they need this
    return ScalarMappable(cmap=cmap, norm=norm)

plot_trisurface 使用自定义颜色数组

plot_trisurface with custom color array

python

matplotlib

triangulation