I want to solve the question below: A point Pw is in the world coordinate system. A C0 coordinate system and the Pw in the Co coordinate is Pc0. Now, I transform the C0 coordinate system to C1 coordinate system, ask: How I transform the Pw subject to Pc0 = Pc1. The image shows how I calculate the transform T.
And the code to confirm the result is below, unfortunately, the Pc0 != Pc1. I don't know what's wrong with the computation. Can you provide some advice? Thanks a lot.
int main() {
//Pw
Eigen::Vector3d Pw ( 1,0,0 );
//Tc0w
Eigen::AngleAxisd rotation_vector_c0w ( M_PI/2, Eigen::Vector3d ( 1,0,0 ) );
Eigen::Matrix3d Rc0w = rotation_vector_c0w.toRotationMatrix();
Eigen::Vector3d tc0w (1,2,3);
Eigen::Isometry3d Tc0w=Eigen::Isometry3d::Identity();
Tc0w.rotate ( rotation_vector_c0w );
Tc0w.pretranslate ( tc0w );
std::cout << "Transform matrix Tc0w= \n" << Tc0w.matrix() <<std::endl;
//Pc0
Eigen::Vector3d Pc0 = Tc0w*Pw;
std::cout<<"Pc0:"<<std::endl<<Pc0<<std::endl;
//Tc1c0
Eigen::AngleAxisd rotation_vector_c1c0 ( M_PI/4, Eigen::Vector3d ( 1,1,0 ) );
Eigen::Vector3d tc1c0 (1,2,3);
Eigen::Isometry3d Tc1c0=Eigen::Isometry3d::Identity();
Tc1c0.rotate ( rotation_vector_c1c0 );
Tc1c0.pretranslate ( tc1c0 );
std::cout << "Transform matrix Tc1c0= \n" << Tc1c0.matrix() <<std::endl;
std::cout << "Transform matrix Tc0c1= \n" << Tc1c0.inverse().matrix() <<std::endl;
//compute T
Eigen::Isometry3d T = Tc0w.inverse()* Tc1c0.inverse()*Tc0w;
std::cout << "Transform matrix T= \n" << T.matrix() <<std::endl;
//confirm Pc1
Eigen::Vector3d Pc1 = Tc1c0*Tc0w*T*Pw;
std::cout<<"Pc1 = "<<std::endl<<Pc1<<std::endl;
std::cout << "Hello, World!" << std::endl;
return 0;
}
AngleAxis requires a normalized rotation axis. Try this:
Eigen::AngleAxisd rotation_vector_c1c0 ( M_PI/4, Eigen::Vector3d ( 1,1,0 ).normalized() );
Corresponding link to documentation: http://eigen.tuxfamily.org/dox/classEigen_1_1AngleAxis.html#ab58bae23f0af86d66d8aa1dc5c1dbe39