Python实现obb包围盒及包围框

最近在做一个关于牙齿正畸的实验，用到了碰撞检测，自然想到用obb包围盒来简化碰撞检测的过程，python目前貌似没有现成的包可以用，一怒之下自己写了一个，虽然是用在牙齿模型上，但是只要给出三维空间中任一模型的坐标集，均可以套用这个方法实现obb包围盒(部分代码有删减)。

import numpy as np
from numpy.linalg import solve
def tooth_obb_box(dot):
    
    covariance_matrix = np.cov(np.transpose(dot))
    a,b=np.linalg.eig(covariance_matrix)


    project=np.zeros((3,len(dot),3))
    for i in range(3):
        for j in range(len(dot)):
            project[i,j]=

    #将投影
    re_project=np.zeros((3,len(dot),3))

    for i in range(3):
        for j in range(len(dot)):

    P=np.zeros((3,2,3))
    for i in range(3):

    center=np.zeros((3,3))
    for i in range(3):

    pro=np.transpose(b)
    K=np.sum(np.multiply(center,pro),axis=1)

    parameter_a=pro#系数矩阵
    parameter_b=K.T   #常数项列矩阵

    ps=np.flipud(pro)
    bs=np.zeros((6,1))
    k=0
    for i in range(3):
        for j in range(2):

            k=k+1
    point_a=ps#系数矩阵
    point_b=np.zeros((8,3))


    res=1
    ans=np.zeros((8,3))
    vec=np.zeros((8,3))
    les=np.zeros((8,1))
    for i in range(8):
        les[i]=np.sqrt(sum(np.multiply(vec[i],vec[i])))

    cos=np.zeros((8,1))
    for i in range(8):
    return b,x,ans,vec,les,cos

效果如下:

obb包围盒的python实现

完整的牙齿包围盒.png

包围框的实现：

import numpy as np
from sympy import *
import matplotlib.pyplot as plt
dot=np.array([[3.7, 1.7], [4.1, 3.8], [4.7, 2.9], [5.2, 2.8], [6.0, 4.0], [6.3, 3.6], [9.7, 6.3], [10.0, 4.9]])
# dot=np.random.rand(30,2)
covariance_matrix = np.cov(np.transpose(dot))
print(covariance_matrix)
a,b=np.linalg.eig(covariance_matrix)

#特征向量的斜率分别为k1,k2
k1=b[1,0]/b[0,0]
k2=b[1,1]/b[0,1]
#每个点在两个特征向量上的投影分别表示为project1和project2
project1=np.zeros((len(dot),2))
project2=np.zeros((len(dot),2))
for i in range(len(dot)):
    project1[i,0]=(k1*(dot[i,1])+dot[i,0])/(k1*k1+1)
    project1[i,1]=k1*project1[i,0]

    project2[i,0]=(k2*(dot[i,1]-9)+dot[i,0])/(k2*k2+1)
    project2[i,1]=k2*project2[i,0]+9

#求解投影点的均值
mean_p1=[(max(project1[:,0])+min(project1[:,0]))/2,(max(project1[:,1])+min(project1[:,1]))/2]
mean_p2=[(max(project2[:,0])+min(project2[:,0]))/2,(max(project2[:,1])+min(project2[:,1]))/2]

#求中心点坐标
center1=
center2=

#四个外围轮廓，分别有四条直线组成
#line1与line2
x_12=
y_12=
#line2与line3
x_23=
y_23=
#line1与line4
x_14=
y_14=
#line3与line4
x_34=
y_34=


plt.plot(dot[:,0],dot[:,1],'o')

plt.plot(center1,center2,'r*')

plt.plot([x_12,x_23,x_34,x_14,x_12],[y_12,y_23,y_34,y_14,y_12],'r')

plt.xlim(0,20)
plt.ylim(0,10)
plt.show()

效果图：

obb包围框的python实现