c++ - 将特征 Affine3d 转换为 Affine2d

Question

我有一个3D仿射变换，我希望从中丢弃任何 z 轴信息。有没有一种方便的方法可以从 a 转换Affine3d为 and Affine2d？

Answer 1

尝试以下操作：

Affine2d S2d = Translation2d(S3d.translation().topRows<2>()) *
               S3d.linear().topLeftCorner<2,2>();

演示：

#include <Eigen/Dense>
#include <iostream>
#include <string>

int main()
{
    using namespace Eigen;
    using namespace std;

    Vector3d p3d(1.,2.,3.);
    cout << p3d << endl << endl;
    Affine3d S3d = Translation3d(2.,2.,2.)*Scaling(3.,2.,5.);
    Vector3d scalled = S3d*p3d;
    cout << S3d.matrix() << endl << endl;
    cout << scalled << endl << endl;

    cout << string(16,'_') << endl;

    Vector2d p2d = p3d.topRows<2>();
    cout << p2d << endl << endl;
    Affine2d S2d = Translation2d(S3d.translation().topRows<2>()) *
                   S3d.linear().topLeftCorner<2,2>();
    Vector2d scalled2d = S2d*p2d;
    cout << S2d.matrix() << endl << endl;
    cout << scalled2d << endl << endl;
}

输出：

1
2
3

3 0 0 2
0 2 0 2
0 0 5 2
0 0 0 1

5
6
17

________________
1
2

3 0 2
0 2 2
0 0 1

5
6