如何使用变换通过 Eigen 中的 Matrix3d 旋转矩阵旋转点 MatrixXd

Question

我有以下 MatrixXd V，代表二维形状的点：

==========================================
Bounding box vertices (AV) (Rows: 8 Cols: 3)
==========================================
[[ 2.367639937564554,  3.100420929531666,                  0]
 [ 2.367639937564554,  3.100420929531666,                  0]
 [ 2.367639937564554, -3.097445263635904,                  0]
 [ 2.367639937564554, -3.097445263635904,                  0]
 [-2.362324650030633,  3.100420929531666,                  0]
 [-2.362324650030633,  3.100420929531666,                  0]
 [-2.362324650030633, -3.097445263635904,                  0]
 [-2.362324650030633, -3.097445263635904,                  0]]

我想通过这个 Matrix3d 旋转矩阵旋转形状：

==========================================
RM: (RM)  (Rows: 3 Cols: 3)
==========================================
[[   0.997496638487424, -0.07071390391068358,                    0]
 [ 0.07071390391068358,    0.997496638487424,                    0]
 [                   0,                    0,                    1]]
==========================================

我想不出正确的方法...我已经检查过转换：

Affine3d tf = RM;
tf.rotate(V);

当然这行不通，因为 Eigen 报告没有从 'Eigen::Matrix3d' 到 'Eigen::Affine3d' 的可行转换。

简而言之，如何告诉 Eigen 使用这个旋转矩阵 (RM) 作为变换并将其应用于目标矩阵 (V)？

因为我已经有了旋转矩阵，所以我没有理由使用四元数...

谢谢

Answer 1

Of course this doesn't work, as Eigen reports no viable conversion from 'Eigen::Matrix3d' to 'Eigen::Affine3d'.

Affine3d 来自 Transform class 而不是 Matrix class。试试这个：

Affine3d tf = Affine3d(RM);

现在关于旋转，我想出了这个小演示：

#include <iostream>
#include <eigen3/Eigen/Dense>
using Eigen::Matrix3d;
using Eigen::MatrixXd;
using Eigen::Affine3d;

int main(){

//obviously not a rotation matrix, but needed some numbers only
Matrix3d rot = Matrix3d::Random();
std::cout << "We have the rotation matrix:" << std::endl;
std::cout << rot << std::endl;

Affine3d aff_rot = Affine3d(rot);
std::cout << "Affine version:" << std::endl;
std::cout << aff_rot.matrix() << std::endl;

MatrixXd points = MatrixXd::Random(8,3);
std::cout << "Some random points:" << std::endl;
std::cout << points << std::endl;

std::cout << std::endl << std::endl;
MatrixXd m = aff_rot * points.transpose().colwise().homogeneous();
MatrixXd result = m.transpose();

std::cout << "Result:" << std::endl;
std::cout << result << std::endl;

return 0;
}

此处旋转应用于左侧，但您可以调整代码以将其应用于右侧。

Answer 2

为什么不直接将坐标矩阵乘以旋转矩阵？

#include <iostream>
#include <Eigen/Core>
#include <Eigen/Geometry>

int main(){

Eigen::MatrixXd AV(8,3);
AV << 
  2.367639937564554,  3.100420929531666,   0, 
  2.367639937564554,  3.100420929531666,   0, 
  2.367639937564554, -3.097445263635904,   0, 
  2.367639937564554, -3.097445263635904,   0, 
 -2.362324650030633,  3.100420929531666,   0, 
 -2.362324650030633,  3.100420929531666,   0, 
 -2.362324650030633, -3.097445263635904,   0, 
 -2.362324650030633, -3.097445263635904,   0; 

Eigen::Matrix3d RM(3,3);
RM <<  0.997496638487424,  -0.07071390391068358,  0,
       0.07071390391068358, 0.997496638487424,    0,
       0,                   0,                    1;


Eigen::AngleAxisd aa(RM);
std::cout << "Axis: " << aa.axis().transpose() << " angle:" << aa.angle() << std::endl;

Eigen::MatrixXd result = AV * RM;
std::cout << "Result:" << std::endl  << result << std::endl;

return 0;
}

产生：

Axis: 0 0 1 angle:0.070773
Result:
 2.58096  2.92523        0
 2.58096  2.92523        0
 2.14268 -3.25712        0
 2.14268 -3.25712        0
-2.13717  3.25971        0
-2.13717  3.25971        0
-2.57544 -2.92264        0
-2.57544 -2.92264        0

如何使用变换通过 Eigen 中的 Matrix3d 旋转矩阵旋转点 MatrixXd

How to rotate a point MatrixXd by a Matrix3d rotation matrix in Eigen using transformations

c++

matrix

eigen