嗯，我自己用了wikipedia article、SO post和一些蠻力解決了這個問題。對不起，代碼墻，但你必須畫出所有的繪圖輪廓和標簽等等。在import numpy as np

import matplotlib.pyplot as plt

from mpl_toolkits.mplot3d import axes3d, Axes3D

from itertools import combinations

import pandas as pd

def plot_ax(): #plot tetrahedral outline

verts=[[0,0,0],

[1,0,0],

[0.5,np.sqrt(3)/2,0],

[0.5,0.28867513, 0.81649658]]

lines=combinations(verts,2)

for x in lines:

line=np.transpose(np.array(x))

ax.plot3D(line[0],line[1],line[2],c='0')

def label_points(): #create labels of each vertices of the simplex

a=(np.array([1,0,0,0])) # Barycentric coordinates of vertices (A or c1)

b=(np.array([0,1,0,0])) # Barycentric coordinates of vertices (B or c2)

c=(np.array([0,0,1,0])) # Barycentric coordinates of vertices (C or c3)

d=(np.array([0,0,0,1])) # Barycentric coordinates of vertices (D or c3)

labels=['a','b','c','d']

cartesian_points=get_cartesian_array_from_barycentric([a,b,c,d])

for point,label in zip(cartesian_points,labels):

if 'a' in label:

ax.text(point[0],point[1]-0.075,point[2], label, size=16)

elif 'b' in label:

ax.text(point[0]+0.02,point[1]-0.02,point[2], label, size=16)

else:

ax.text(point[0],point[1],point[2], label, size=16)

def get_cartesian_array_from_barycentric(b): #tranform from "barycentric" composition space to cartesian coordinates

verts=[[0,0,0],

[1,0,0],

[0.5,np.sqrt(3)/2,0],

[0.5,0.28867513, 0.81649658]]

#create transformation array vis https://en.wikipedia.org/wiki/Barycentric_coordinate_system

t = np.transpose(np.array(verts))

t_array=np.array([t.dot(x) for x in b]) #apply transform to all points

return t_array

def plot_3d_tern(df,c='1'): #use function "get_cartesian_array_from_barycentric" to plot the scatter points

#args are b=dataframe to plot and c=scatter point color

bary_arr=df.values

cartesian_points=get_cartesian_array_from_barycentric(bary_arr)

ax.scatter(cartesian_points[:,0],cartesian_points[:,1],cartesian_points[:,2],c=c)

#Create Dataset 1

np.random.seed(123)

c1=np.random.normal(8,2.5,20)

c2=np.random.normal(8,2.5,20)

c3=np.random.normal(8,2.5,20)

c4=[100-x for x in c1+c2+c3] #make sur ecomponents sum to 100

#df unecessary but that is the format of my real data

df1=pd.DataFrame(data=[c1,c2,c3,c4],index=['c1','c2','c3','c4']).T

df1=df1/100

#Create Dataset 2

np.random.seed(1234)

c1=np.random.normal(16,2.5,20)

c2=np.random.normal(16,2.5,20)

c3=np.random.normal(16,2.5,20)

c4=[100-x for x in c1+c2+c3]

df2=pd.DataFrame(data=[c1,c2,c3,c4],index=['c1','c2','c3','c4']).T

df2=df2/100

#Create Dataset 3

np.random.seed(12345)

c1=np.random.normal(25,2.5,20)

c2=np.random.normal(25,2.5,20)

c3=np.random.normal(25,2.5,20)

c4=[100-x for x in c1+c2+c3]

df3=pd.DataFrame(data=[c1,c2,c3,c4],index=['c1','c2','c3','c4']).T

df3=df3/100

fig = plt.figure()

ax = Axes3D(fig) #Create a 3D plot in most recent version of matplot

plot_ax() #call function to draw tetrahedral outline

label_points() #label the vertices

plot_3d_tern(df1,'b') #call function to plot df1

plot_3d_tern(df2,'r') #...plot df2

plot_3d_tern(df3,'g') #...

總結

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