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

Question

I have the following MatrixXd V, representing points of a 2d shape:

==========================================
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]]

and I want to rotate the shape by this Matrix3d rotation matrix:

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

I'm not able to figure the correct way to do this... I've checked with transformations:

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

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

In short, how do I tell Eigen to use this rotation matrix (RM) as a transformation and apply it to the target matrix (V)?

As I already have the rotation matrix, I have no reason to use quaternions...

Thank you

Answer 1

Why don't just multiply the coordinates matrix by the rotation matrix?

#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;
}

Which produces:

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

Answer 2

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

Affine3d is from the Transform class and not the Matrix class. Try this:

Affine3d tf = Affine3d(RM);

Now regarding the rotation, I came up with this small demo:

#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;
}

Here the rotation is applied on left side, but you can adapt the code to apply it on the right side.