Eigen combine rotation and translation into one matrix

Question

I have a rotation matrix rot (Eigen::Matrix3d) and a translation vector transl (Eigen::Vector3d) and I want them both together in a 4x4 transformation matrix. I just for the life of me can't figure out how to do this in Eigen. I think Affine can be used somehow but I don't understand how it works.

Essentially I want a combination of How translation a matrix(4x4) in Eigen? and Multiplying Transform and Matrix types in Eigen

My code (that doesn't compile as I don't understand how Affine works) looks like this:

Eigen::Affine3d r(rot);
Eigen::Affine3d t(transl);
Eigen::Matrix4d m = t.matrix();
m *= r.matrix();

Solution 1

Another method is to do the following:

Eigen::Matrix3d R;
// Find your Rotation Matrix
Eigen::Vector3d T;
// Find your translation Vector
Eigen::Matrix4d Trans; // Your Transformation Matrix
Trans.setIdentity();   // Set to Identity to make bottom row of Matrix 0,0,0,1
Trans.block<3,3>(0,0) = R;
Trans.block<3,1>(0,3) = T;

This method literally copies the Rotation matrix into the first 3 rows and columns and the translation vector to the 4th column. Then sets the bottom right matrix entry to 1. You final matrix will look like:

R R R T
R R R T
R R R T
0 0 0 1

where R are the corresponding values from the rotation matrix and T the values from the Translation vector.

Solution 2

You didn't post the compilation errors, nor what are rot and transl. Below is a working sample showing, how you can create a 4x4 transformation matrix.

#include <Eigen/Geometry>

Eigen::Affine3d create_rotation_matrix(double ax, double ay, double az) {
  Eigen::Affine3d rx =
      Eigen::Affine3d(Eigen::AngleAxisd(ax, Eigen::Vector3d(1, 0, 0)));
  Eigen::Affine3d ry =
      Eigen::Affine3d(Eigen::AngleAxisd(ay, Eigen::Vector3d(0, 1, 0)));
  Eigen::Affine3d rz =
      Eigen::Affine3d(Eigen::AngleAxisd(az, Eigen::Vector3d(0, 0, 1)));
  return rz * ry * rx;
}

int main() {
  Eigen::Affine3d r = create_rotation_matrix(1.0, 1.0, 1.0);
  Eigen::Affine3d t(Eigen::Translation3d(Eigen::Vector3d(1,1,2)));

  Eigen::Matrix4d m = (t * r).matrix(); // Option 1

  Eigen::Matrix4d m = t.matrix(); // Option 2
  m *= r.matrix();
  return 0;
}

Solution 3

Another way is to use the Eigen::Transform.

Let's take a example such as to implemente this affine transform ,

#include <Eigen/Dense>
#include <Eigen/Geometry>
using namespace Eigen;

Matrix4f create_affine_matrix(float a, float b, float c, Vector3f trans)
{
    Transform<float, 3, Eigen::Affine> t;
    t = Translation<float, 3>(trans);
    t.rotate(AngleAxis<float>(a, Vector3f::UnitX()));
    t.rotate(AngleAxis<float>(b, Vector3f::UnitY()));
    t.rotate(AngleAxis<float>(c, Vector3f::UnitZ()));
    return t.matrix();
}

You can also implemented as the following

Matrix4f create_affine_matrix(float a, float b, float c, Vector3f trans)
{
    Transform<float, 3, Eigen::Affine> t;
    t = AngleAxis<float>(c, Vector3f::UnitZ());
    t.prerotate(AngleAxis<float>(b, Vector3f::UnitY()));
    t.prerotate(AngleAxis<float>(a, Vector3f::UnitX()));
    t.pretranslate(trans);
    return t.matrix();
}

The difference between the first implementation and the second is like the difference between Fix Angle and Euler Angle, you can refer to this video.