Author
shaniadolphin
求解目的
本文将展示位姿估计的一种应用，即通过单目相机对环境进行测量。简单来说，本文的工作就是利用下面的两幅图，在已知P1、P2、P3、P4四点世界坐标的情况下，计算出其它点的世界坐标。
如图所示，一个标准的标定板，标定板每个格子的尺寸是30mm，通过标定四周的4个点P1、P2、P3、P4，旁边有茶罐，有待求点为P5、P6。
这种应用可以利用一个已经尺寸物体，通过两张不同视角的照片求未知物体的尺寸。比如上图中的通过已知的标定板求茶罐的尺寸。而在现实应用中可以用这种方式来求车的尺寸，建筑的高度，货物的体积等等。
求解原理
如下图，根据P1、P2、P3、P4四点的空间坐标，通过openCV的PNP函数，可以计算出两次拍照的相机位姿，从而进一步计算出相机的坐标
与
。那么将
与
，
与
连成直线，获得两条直线方程
和
，组成方程组求解得到它们的交点，即为待求目标点的坐标。
1. 求出
点的相机坐标系坐标
关于P点如何从二维映射到三维，参考上图，
的坐标通过解
已经求出，待求点P在图像中的像素坐标为
。
求出
在相机坐标系中的坐标
(也就是上图中的
点)。具体的转换公式如下，式中
为相机镜头的焦距
，在本次实验中使用的是中一光学的35mm手动镜头。
为点的像素坐标，其余为相机内参数。
输入拍到的图片的点，包括待求点的像素坐标，示例如下：
P11 = np.array([0, 0, 0])
P12 = np.array([0, 300, 0])
P13 = np.array([210, 0, 0])
P14 = np.array([210, 300, 0])
p11 = np.array([1765, 725])
p12 = np.array([3068, 1254])
p13 = np.array([1249, 1430])
p14 = np.array([2648, 2072])
p4psolver1.Points3D[0] = np.array([P11,P12,P13,P14])
p4psolver1.Points2D[0] = np.array([p11,p12,p13,p14])
#p4psolver1.point2find = np.array([4149, 671])
#p4psolver1.point2find = np.array([675, 835])
p4psolver1.point2find = np.array([691, 336])
读取标定文件中的相机内参，代码如下，在代码里预设了相机的传感器大小，笔者所用的D7000单反是DX画幅的，根据可查到的资料，传感器的规格为23.6mm*15.6mm。
笔者用在本机的镜头是中一的35mm手动定焦镜头。
def getudistmap(self, filename):
with open(filename, 'r',newline='') as csvfile:
spamreader = csv.reader(csvfile, delimiter=',', quotechar='"')
rows = [row for row in spamreader]
self.cameraMatrix = np.zeros((3, 3))
#Dt = np.zeros((4, 1))
size_w = 23.6
size_h = 15.6
imageWidth = int(rows[0][1])
imageHeight = int(rows[0][2])
self.cameraMatrix[0][0] = rows[1][1]
self.cameraMatrix[1][1] = rows[1][2]
self.cameraMatrix[0][2] = rows[1][3]
self.cameraMatrix[1][2] = rows[1][4]
self.cameraMatrix[2][2] = 1
print(len(rows[2]))
if len(rows[2]) == 5:
print('fisheye')
self.distCoefs = np.zeros((4, 1))
self.distCoefs[0][0] = rows[2][1]
self.distCoefs[1][0] = rows[2][2]
self.distCoefs[2][0] = rows[2][3]
self.distCoefs[3][0] = rows[2][4]
scaled_K = self.cameraMatrix * 0.8 # The values of K is to scale with image dimension.
scaled_K[2][2] = 1.0
#newcameramtx = cv2.fisheye.estimateNewCameraMatrixForUndistortRectify(self.cameraMatrix, self.distCoefs, (imageWidth, imageHeight), np.eye(3), balance=0)
#map1, map2 = cv2.fisheye.initUndistortRectifyMap(self.cameraMatrix, self.distCoefs, np.eye(3), newcameramtx, (imageWidth, imageHeight), cv2.CV_32FC1)
else:
print('normal')
self.distCoefs = np.zeros((1, 5))
self.distCoefs[0][0] = rows[2][1]
self.distCoefs[0][1] = rows[2][2]
self.distCoefs[0][2] = rows[2][3]
self.distCoefs[0][3] = rows[2][4]
self.distCoefs[0][4] = rows[2][5]
#newcameramtx, roi = cv2.getOptimalNewCameraMatrix(self.cameraMatrix, self.distCoefs, (imageWidth, imageHeight), 1, (imageWidth, imageHeight))
#map1, map2 = cv2.initUndistortRectifyMap(self.cameraMatrix, self.distCoefs, None, newcameramtx, (imageWidth, imageHeight), cv2.CV_32FC1)
print('dim = %d*%d'%(imageWidth, imageHeight))
print('Kt = \n', self.cameraMatrix)
#print('newcameramtx = \n', newcameramtx)
print('Dt = \n', self.distCoefs)
self.f = [self.cameraMatrix[0][0]*(size_w/imageWidth), self.cameraMatrix[1][1]*(size_h/imageHeight)]
#self.f = [350, 350]
print('f = \n', self.f)
#print(map1,'\n',map2.T)
return
然后就可以将像素坐标转换到世界坐标了：
def WordFrame2ImageFrame(self, WorldPoints):
pro_points, jacobian = cv2.projectPoints(WorldPoints, self.rvecs, self.tvecs, self.cameraMatrix, self.distCoefs)
return pro_points
def ImageFrame2CameraFrame(self, pixPoints):
fx = self.cameraMatrix[0][0]
u0 = self.cameraMatrix[0][2]
fy = self.cameraMatrix[1][1]
v0 = self.cameraMatrix[1][2]
zc = (self.f[0]+self.f[1])/2
xc = (pixPoints[0] - u0) * self.f[0] / fx #f=fx*传感器尺寸/分辨率
yc = (pixPoints[1] - v0) * self.f[1] / fy
point = np.array([xc,yc,zc])
return point
2.求出P点在世界坐标系中的方向向量
通过以上运算得到了
，但这个点坐标是在相机坐标系中的，需要进一步求解
点在世界坐标系中对应的坐标
。
为了将
转为
，即求出原点
在相机坐标系下的坐标，需要使用到解
求位姿时得到的三个欧拉角
。相机坐标系
按照
轴、
轴、
轴的顺序旋转以上角度后将与世界坐标系
完全平行，在这三次旋转中
也会与坐标系一起旋转的，其在世界系
中的位置会发生改变。为了保证
系旋转后
点依然保持在世界坐标系W原本的位置，需要对
进行三次反向旋转，旋转后得到点
在相机坐标系
中新的坐标值记为
，
的值等于世界坐标系中向量
的值。最终，
点的世界坐标
=
的值+
的世界坐标值，具体操作如下：
第一次旋转：
原始相机坐标系
绕
轴旋转了
变为
系，
，将
点绕
轴旋转
，得到
，其为
系中
的坐标。
def CodeRotateByZ(self, x, y, thetaz):#将空间点绕Z轴旋转
x1=x #将变量拷贝一次，保证&x == &outx这种情况下也能计算正确
y1=y
rz = thetaz*3.141592653589793/180
outx = math.cos(rz)*x1 - math.sin(rz)*y1
outy = math.sin(rz)*x1 + math.cos(rz)*y1
return outx,outy
第二次旋转：
绕
轴旋转了
变为
系，
，将
点绕
轴旋转
，得到
，其为
系中
的坐标。
def CodeRotateByY(self, x, z, thetay):
x1=x
z1=z
ry = thetay * 3.141592653589793 / 180
outx = math.cos(ry) * x1 + math.sin(ry) * z1
outz = math.cos(ry) * z1 - math.sin(ry) * x1
return outx,outz
第三次旋转：
绕
轴旋转了
变为
系，
，将
点绕
轴旋转
，得到
，其为
系中
的坐标。
def CodeRotateByX(self, y, z, thetax):
y1=y
z1=z
rx = (thetax * 3.141592653589793) / 180
outy = math.cos(rx) * y1 - math.sin(rx) * z1
outz = math.cos(rx) * z1 + math.sin(rx) * y1
return outy,outz
此时，世界坐标系中，相机的位置坐标为
。结合上面的旋转函数，完整的求解代码如下所示：
def solver(self):
retval, self.rvec, self.tvec = cv2.solvePnP(self.Points3D, self.Points2D, self.cameraMatrix, self.distCoefs)
#print('self.rvec:',self.rvec)
#print('self.tvec:',self.tvec)
thetax,thetay,thetaz = self.rotationVectorToEulerAngles(self.rvec, 0)
x = self.tvec[0][0]
y = self.tvec[1][0]
z = self.tvec[2][0]
self.Position_OwInCx = x
self.Position_OwInCy = y
self.Position_OwInCz = z
self.Position_theta = [thetax, thetay, thetaz]
#print('Position_theta:',self.Position_theta)
x, y = self.CodeRotateByZ(x, y, -1 * thetaz)
x, z = self.CodeRotateByY(x, z, -1 * thetay)
y, z = self.CodeRotateByX(y, z, -1 * thetax)
self.Theta_W2C = (-1*thetax, -1*thetay,-1*thetaz)
self.Position_OcInWx = x*(-1)
self.Position_OcInWy = y*(-1)
self.Position_OcInWz = z*(-1)
self.Position_OcInW = np.array([self.Position_OcInWx, self.Position_OcInWy, self.Position_OcInWz])
print('Position_OcInW:', self.Position_OcInW)
通过世界坐标系的相机坐标a1，P点坐标a2，构成第一条直线A。
def SetLineA(self, A1x, A1y, A1z, A2x, A2y, A2z):
self.a1 = np.array([A1x, A1y, A1z])
self.a2 = np.array([A2x, A2y, A2z])
3. 最后，根据两幅图得到的两条直线，计算出P点的世界坐标
对另外一幅图也进行如上操作，获得两条直线A、B，因此求出两条直线A与B的交点即可求出目标点的世界坐标。然而在现实中，由于误差的存在，A与B基本不会相交，因此在计算时需要求他们之间的最近点。
class GetDistanceOf2linesIn3D():
def __init__(self):
print('GetDistanceOf2linesIn3D class')
def dot(self, ax, ay, az, bx, by, bz):
result = ax*bx + ay*by + az*bz
return result
def cross(self, ax, ay, az, bx, by, bz):
x = ay*bz - az*by
y = az*bx - ax*bz
z = ax*by - ay*bx
return x,y,z
def crossarray(self, a, b):
x = a[1]*b[2] - a[2]*b[1]
y = a[2]*b[0] - a[0]*b[2]
z = a[0]*b[1] - a[1]*b[0]
return np.array([x,y,z])
def norm(self, ax, ay, az):
return math.sqrt(self.dot(ax, ay, az, ax, ay, az))
def norm2(self, one):
return math.sqrt(np.dot(one, one))
def SetLineA(self, A1x, A1y, A1z, A2x, A2y, A2z):
self.a1 = np.array([A1x, A1y, A1z])
self.a2 = np.array([A2x, A2y, A2z])
def SetLineB(self, B1x, B1y, B1z, B2x, B2y, B2z):
self.b1 = np.array([B1x, B1y, B1z])
self.b2 = np.array([B2x, B2y, B2z])
def GetDistance(self):
d1 = self.a2 - self.a1
d2 = self.b2 - self.b1
e = self.b1 - self.a1
cross_e_d2 = self.crossarray(e,d2)
cross_e_d1 = self.crossarray(e,d1)
cross_d1_d2 = self.crossarray(d1,d2)
dd = self.norm2(cross_d1_d2)
t1 = np.dot(cross_e_d2, cross_d1_d2)
t2 = np.dot(cross_e_d1, cross_d1_d2)
t1 = t1/(dd*dd)
t2 = t2/(dd*dd)
self.PonA = self.a1 + (self.a2 - self.a1) * t1
self.PonB = self.b1 + (self.b2 - self.b1) * t2
self.distance = self.norm2(self.PonB - self.PonA)
print('distance=', self.distance)
return self.distance
总结与验证
通过以上的讲解，说明了大致的原理和过程。完整的求解代码及结果如下，其中代码中打开的“calibration.csv”是一个标定生成的文件，存取了笔者D7000标定后得到的内参，如表格清单所示。
表格清单：
dim
3696
2448
cameraMatrix
5546.18009098042
5572.883
1821.049
1347.461
distCoefs
-0.12735
0.200792
-0.00209
0.000943
-0.79439
代码清单：
#!/usr/bin/env python3
# coding:utf-8
import cv2
import numpy as np
import time
from PIL import Image,ImageTk
import threading
import os
import re
import subprocess
import random
import math
import csv
import argparse
class PNPSolver():
def __init__(self):
self.COLOR_WHITE = (255,255,255)
self.COLOR_BLUE = (255,0,0)
self.COLOR_LBLUE = (255, 200, 100)
self.COLOR_GREEN = (0,240,0)
self.COLOR_RED = (0,0,255)
self.COLOR_DRED = (0,0,139)
self.COLOR_YELLOW = (29,227,245)
self.COLOR_PURPLE = (224,27,217)
self.COLOR_GRAY = (127,127,127)
self.Points3D = np.zeros((1, 4, 3), np.float32) #存放4组世界坐标位置
self.Points2D = np.zeros((1, 4, 2), np.float32) #存放4组像素坐标位置
self.point2find = np.zeros((1, 2), np.float32)
self.cameraMatrix = None
self.distCoefs = None
self.f = 0
def rotationVectorToEulerAngles(self, rvecs, anglestype):
R = np.zeros((3, 3), dtype=np.float64)
cv2.Rodrigues(rvecs, R)
sy = math.sqrt(R[2,1] * R[2,1] + R[2,2] * R[2,2])
singular = sy < 1e-6
if not singular:
x = math.atan2(R[2,1] , R[2,2])
y = math.atan2(-R[2,0], sy)
z = math.atan2(R[1,0], R[0,0])
else :
x = math.atan2(-R[1,2], R[1,1])
y = math.atan2(-R[2,0], sy)
z = 0
if anglestype == 0:
x = x*180.0/3.141592653589793
y = y*180.0/3.141592653589793
z = z*180.0/3.141592653589793
elif anglestype == 1:
x = x
y = y
z = z
print(x)
return x,y,z
def CodeRotateByZ(self, x, y, thetaz):#将空间点绕Z轴旋转
x1=x #将变量拷贝一次，保证&x == &outx这种情况下也能计算正确
y1=y
rz = thetaz*3.141592653589793/180
outx = math.cos(rz)*x1 - math.sin(rz)*y1
outy = math.sin(rz)*x1 + math.cos(rz)*y1
return outx,outy
def CodeRotateByY(self, x, z, thetay):
x1=x
z1=z
ry = thetay * 3.141592653589793 / 180
outx = math.cos(ry) * x1 + math.sin(ry) * z1
outz = math.cos(ry) * z1 - math.sin(ry) * x1
return outx,outz
def CodeRotateByX(self, y, z, thetax):
y1=y
z1=z
rx = (thetax * 3.141592653589793) / 180
outy = math.cos(rx) * y1 - math.sin(rx) * z1
outz = math.cos(rx) * z1 + math.sin(rx) * y1
return outy,outz
def solver(self):
retval, self.rvec, self.tvec = cv2.solvePnP(self.Points3D, self.Points2D, self.cameraMatrix, self.distCoefs)
thetax,thetay,thetaz = self.rotationVectorToEulerAngles(self.rvec, 0)
x = self.tvec[0][0]
y = self.tvec[1][0]
z = self.tvec[2][0]
self.Position_OwInCx = x
self.Position_OwInCy = y
self.Position_OwInCz = z
self.Position_theta = [thetax, thetay, thetaz]
#print('Position_theta:',self.Position_theta)
x, y = self.CodeRotateByZ(x, y, -1 * thetaz)
x, z = self.CodeRotateByY(x, z, -1 * thetay)
y, z = self.CodeRotateByX(y, z, -1 * thetax)
self.Theta_W2C = ([-1*thetax, -1*thetay,-1*thetaz])
self.Position_OcInWx = x*(-1)
self.Position_OcInWy = y*(-1)
self.Position_OcInWz = z*(-1)
self.Position_OcInW = np.array([self.Position_OcInWx, self.Position_OcInWy, self.Position_OcInWz])
print('Position_OcInW:', self.Position_OcInW)
def WordFrame2ImageFrame(self, WorldPoints):
pro_points, jacobian = cv2.projectPoints(WorldPoints, self.rvecs, self.tvecs, self.cameraMatrix, self.distCoefs)
return pro_points
def ImageFrame2CameraFrame(self, pixPoints):
fx = self.cameraMatrix[0][0]
u0 = self.cameraMatrix[0][2]
fy = self.cameraMatrix[1][1]
v0 = self.cameraMatrix[1][2]
zc = (self.f[0]+self.f[1])/2
xc = (pixPoints[0] - u0) * self.f[0] / fx #f=fx*传感器尺寸/分辨率
yc = (pixPoints[1] - v0) * self.f[1] / fy
point = np.array([xc,yc,zc])
return point
def getudistmap(self, filename):
with open(filename, 'r',newline='') as csvfile:
spamreader = csv.reader(csvfile, delimiter=',', quotechar='"')
rows = [row for row in spamreader]
self.cameraMatrix = np.zeros((3, 3))
#Dt = np.zeros((4, 1))
size_w = 23.6
size_h = 15.6
imageWidth = int(rows[0][1])
imageHeight = int(rows[0][2])
self.cameraMatrix[0][0] = rows[1][1]
self.cameraMatrix[1][1] = rows[1][2]
self.cameraMatrix[0][2] = rows[1][3]
self.cameraMatrix[1][2] = rows[1][4]
self.cameraMatrix[2][2] = 1
print(len(rows[2]))
if len(rows[2]) == 5:
print('fisheye')
self.distCoefs = np.zeros((4, 1))
self.distCoefs[0][0] = rows[2][1]
self.distCoefs[1][0] = rows[2][2]
self.distCoefs[2][0] = rows[2][3]
self.distCoefs[3][0] = rows[2][4]
scaled_K = self.cameraMatrix * 0.8 # The values of K is to scale with image dimension.
scaled_K[2][2] = 1.0
else:
print('normal')
self.distCoefs = np.zeros((1, 5))
self.distCoefs[0][0] = rows[2][1]
self.distCoefs[0][1] = rows[2][2]
self.distCoefs[0][2] = rows[2][3]
self.distCoefs[0][3] = rows[2][4]
self.distCoefs[0][4] = rows[2][5]
print('dim = %d*%d'%(imageWidth, imageHeight))
print('Kt = \n', self.cameraMatrix)
print('Dt = \n', self.distCoefs)
self.f = [self.cameraMatrix[0][0]*(size_w/imageWidth), self.cameraMatrix[1][1]*(size_h/imageHeight)]
print('f = \n', self.f)
return
class GetDistanceOf2linesIn3D():
def __init__(self):
print('GetDistanceOf2linesIn3D class')
def dot(self, ax, ay, az, bx, by, bz):
result = ax*bx + ay*by + az*bz
return result
def cross(self, ax, ay, az, bx, by, bz):
x = ay*bz - az*by
y = az*bx - ax*bz
z = ax*by - ay*bx
return x,y,z
def crossarray(self, a, b):
x = a[1]*b[2] - a[2]*b[1]
y = a[2]*b[0] - a[0]*b[2]
z = a[0]*b[1] - a[1]*b[0]
return np.array([x,y,z])
def norm(self, ax, ay, az):
return math.sqrt(self.dot(ax, ay, az, ax, ay, az))
def norm2(self, one):
return math.sqrt(np.dot(one, one))
def SetLineA(self, A1x, A1y, A1z, A2x, A2y, A2z):
self.a1 = np.array([A1x, A1y, A1z])
self.a2 = np.array([A2x, A2y, A2z])
def SetLineB(self, B1x, B1y, B1z, B2x, B2y, B2z):
self.b1 = np.array([B1x, B1y, B1z])
self.b2 = np.array([B2x, B2y, B2z])
def GetDistance(self):
d1 = self.a2 - self.a1
d2 = self.b2 - self.b1
e = self.b1 - self.a1
cross_e_d2 = self.crossarray(e,d2)
cross_e_d1 = self.crossarray(e,d1)
cross_d1_d2 = self.crossarray(d1,d2)
dd = self.norm2(cross_d1_d2)
t1 = np.dot(cross_e_d2, cross_d1_d2)
t2 = np.dot(cross_e_d1, cross_d1_d2)
t1 = t1/(dd*dd)
t2 = t2/(dd*dd)
self.PonA = self.a1 + (self.a2 - self.a1) * t1
self.PonB = self.b1 + (self.b2 - self.b1) * t2
self.distance = self.norm2(self.PonB - self.PonA)
print('distance=', self.distance)
return self.distance
if __name__ == "__main__":
print("***************************************")
print("test example")
print("***************************************")
parser = argparse.ArgumentParser(description='test')
parser.add_argument('-file', type=str, default = 'calibration.csv')
args = parser.parse_args()
calibrationfile = args.file
p4psolver1 = PNPSolver()
'''
P11 = np.array([0, 0, 0])
P12 = np.array([0, 200, 0])
P13 = np.array([150, 0, 0])
P14 = np.array([150, 200, 0])
p11 = np.array([2985, 1688])
p12 = np.array([5081, 1690])
p13 = np.array([2997, 2797])
p14 = np.array([5544, 2757])
'''
P11 = np.array([0, 0, 0])
P12 = np.array([0, 300, 0])
P13 = np.array([210, 0, 0])
P14 = np.array([210, 300, 0])
p11 = np.array([1765, 725])
p12 = np.array([3068, 1254])
p13 = np.array([1249, 1430])
p14 = np.array([2648, 2072])
p4psolver1.Points3D[0] = np.array([P11,P12,P13,P14])
p4psolver1.Points2D[0] = np.array([p11,p12,p13,p14])
#p4psolver1.point2find = np.array([4149, 671])
#p4psolver1.point2find = np.array([675, 835])
p4psolver1.point2find = np.array([691, 336])
p4psolver1.getudistmap(calibrationfile)
p4psolver1.solver()
p4psolver2 = PNPSolver()
'''
P21 = np.array([0, 0, 0])
P22 = np.array([0, 200, 0])
P23 = np.array([150, 0, 0])
P24 = np.array([150, 200, 0])
p21 = np.array([3062, 3073])
p22 = np.array([3809, 3089])
p23 = np.array([3035, 3208])
p24 = np.array([3838, 3217])
'''
P21 = np.array([0, 0, 0])
P22 = np.array([0, 300, 0])
P23 = np.array([210, 0, 0])
P24 = np.array([210, 300, 0])
p21 = np.array([1307, 790])
p22 = np.array([2555, 797])
p23 = np.array([1226, 1459])
p24 = np.array([2620, 1470])
p4psolver2.Points3D[0] = np.array([P21,P22,P23,P24])
p4psolver2.Points2D[0] = np.array([p21,p22,p23,p24])
#p4psolver2.point2find = np.array([3439, 2691])
#p4psolver2.point2find = np.array([712, 1016])
p4psolver2.point2find = np.array([453, 655])
p4psolver2.getudistmap(calibrationfile)
p4psolver2.solver()
point2find1_CF = p4psolver1.ImageFrame2CameraFrame(p4psolver1.point2find)
#Oc1P_x1 = point2find1_CF[0]
#Oc1P_y1 = point2find1_CF[1]
#Oc1P_z1 = point2find1_CF[2]
Oc1P_1 = np.array(point2find1_CF)
print(Oc1P_1)
Oc1P_1[0], Oc1P_1[1] = p4psolver1.CodeRotateByZ(Oc1P_1[0], Oc1P_1[1], p4psolver1.Theta_W2C[2])
Oc1P_1[0], Oc1P_1[2] = p4psolver1.CodeRotateByY(Oc1P_1[0], Oc1P_1[2], p4psolver1.Theta_W2C[1])
Oc1P_1[1], Oc1P_1[2] = p4psolver1.CodeRotateByX(Oc1P_1[1], Oc1P_1[2], p4psolver1.Theta_W2C[0])
a1 = np.array([p4psolver1.Position_OcInWx, p4psolver1.Position_OcInWy, p4psolver1.Position_OcInWz])
a2 = a1 + Oc1P_1
#a2 = (p4psolver1.Position_OcInWx + Oc1P_1[0], p4psolver1.Position_OcInWy + Oc1P_y1, p4psolver1.Position_OcInWz + Oc1P_z1)
point2find2_CF = p4psolver2.ImageFrame2CameraFrame(p4psolver2.point2find)
#Oc2P_x2 = point2find2_CF[0]
#Oc2P_y2 = point2find2_CF[1]
#Oc2P_z2 = point2find2_CF[2]
Oc2P_2 = np.array(point2find2_CF)
print(Oc2P_2)
Oc2P_2[0], Oc2P_2[1] = p4psolver2.CodeRotateByZ(Oc2P_2[0], Oc2P_2[1], p4psolver2.Theta_W2C[2])
Oc2P_2[0], Oc2P_2[2] = p4psolver2.CodeRotateByY(Oc2P_2[0], Oc2P_2[2], p4psolver2.Theta_W2C[1])
Oc2P_2[1], Oc2P_2[2] = p4psolver2.CodeRotateByX(Oc2P_2[1], Oc2P_2[2], p4psolver2.Theta_W2C[0])
b1 = ([p4psolver2.Position_OcInWx, p4psolver2.Position_OcInWy, p4psolver2.Position_OcInWz])
b2 = b1 + Oc2P_2
#b2 = (p4psolver2.Position_OcInWx + Oc2P_x2, p4psolver2.Position_OcInWy + Oc2P_y2, p4psolver2.Position_OcInWz + Oc2P_z2)
g = GetDistanceOf2linesIn3D()
g.SetLineA(a1[0], a1[1], a1[2], a2[0], a2[1], a2[2])
g.SetLineB(b1[0], b1[1], b1[2], b2[0], b2[1], b2[2])
distance = g.GetDistance()
pt = (g.PonA + g.PonB)/2
print(pt)
A = np.array([241.64926392,-78.7377477,166.08307887])
B = np.array([141.010851,-146.64449841,167.28164652])
print(math.sqrt(np.dot(A-B,A-B)))
A点的世界坐标点是：
distance= 0.13766177937900279
[241.64926392 -78.7377477 166.08307887]
B点的世界坐标点是：
distance= 0.7392672771306183
[ 141.010851 -146.64449841 167.28164652]
计算AB点的距离：
A = np.array([241.64926392,-78.7377477,166.08307887])
B = np.array([141.010851,-146.64449841,167.28164652])
print(math.sqrt(np.dot(A-B,A-B)))
结果为：
121.41191667813395
从数据可以看出茶罐的高度约为171mm(玻璃标定板的高度为4mm)，对角的长度约为121mm。
也可以在生成世界坐标数据的时候，在Z轴数据中填入标定板的高度，如下所示：
P11 = np.array([0, 0, 4])
P12 = np.array([0, 300, 4])
P13 = np.array([210, 0, 4])
P14 = np.array([210, 300, 4])
P21 = np.array([0, 0, 4])
P22 = np.array([0, 300, 4])
P23 = np.array([210, 0, 4])
P24 = np.array([210, 300, 4])
即可直接得到对应的结果：
[ 141.010851 -146.64449841 171.28164652]
121.41191667813395
参考文档
#
链接地址
文档名称
1
https://www.cnblogs.com/singlex/p/pose_estimation_3.html
2
https://www.cnblogs.com/singlex/p/6037020.html
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