159 lines
4.2 KiB
C++
159 lines
4.2 KiB
C++
#include <iostream>
|
|
using namespace std;
|
|
#include <vcg/math/quaternion.h>
|
|
#include <vcg/math/matrix33.h>
|
|
|
|
|
|
using namespace vcg;
|
|
|
|
|
|
|
|
ostream &operator<<(ostream &o, Point3f &q) {
|
|
o.precision(6) ;
|
|
o.setf( ios::fixed, ios::floatfield ) ;
|
|
o << "[" << q[0] << " " << q[1] << " " << q[2] << "]";
|
|
return o;
|
|
}
|
|
|
|
ostream &operator<<(ostream &o, Quaternionf &q) {
|
|
o.precision(6) ;
|
|
o.setf( ios::fixed, ios::floatfield ) ;
|
|
o << "[" << q[0] << " " << q[1] << " " << q[2] << " " << q[3] << "]";
|
|
return o;
|
|
}
|
|
|
|
ostream &operator<<(ostream &o, Matrix33f &m) {
|
|
o.precision(6) ;
|
|
o.setf( ios::fixed, ios::floatfield ) ;
|
|
for(int i = 0; i < 3; i++) {
|
|
o << "[";
|
|
for(int j = 0; j < 3; j++) {
|
|
o << m[i][j] << " ";
|
|
}
|
|
o << "] ";
|
|
}
|
|
return o;
|
|
}
|
|
ostream &operator<<(ostream &o, Matrix44f &m) {
|
|
o.precision(6) ;
|
|
o.setf( ios::fixed, ios::floatfield ) ;
|
|
for(int i = 0; i < 4; i++) {
|
|
o << "[";
|
|
for(int j = 0; j < 4; j++) {
|
|
o << m[i][j] << " ";
|
|
}
|
|
o << "] ";
|
|
}
|
|
return o;
|
|
}
|
|
|
|
bool verify(Quaternionf &q){
|
|
cout << "Quaternion: " << q << endl;
|
|
Matrix33f m;
|
|
q.ToMatrix(m);
|
|
cout << "To Matrix: " << m << endl;
|
|
cout << "Row norms: " << m.GetRow(0).Norm() << " "
|
|
<< m.GetRow(1).Norm() << " "
|
|
<< m.GetRow(2).Norm() << endl;
|
|
Point3f p(3, 4, 5);
|
|
Point3f qp = q.Rotate(p);
|
|
Point3f mp = m*p;
|
|
cout << "Rotating p: " << p << endl;
|
|
cout << "q*p = " << qp << " m*p: " << mp << endl;
|
|
q.FromMatrix(m);
|
|
cout << "Back to: " << q << endl << endl;
|
|
return true;
|
|
}
|
|
|
|
bool verify(Matrix33f &m) {
|
|
cout << "Matrix: " << m << endl;
|
|
cout << "Det: " << m.Determinant() << endl;
|
|
cout << "Row norms: " << m.GetRow(0).Norm() << " "
|
|
<< m.GetRow(1).Norm() << " "
|
|
<< m.GetRow(2).Norm() << endl;
|
|
cout << "Column norms: " << m.GetColumn(0).Norm() << " "
|
|
<< m.GetColumn(1).Norm() << " "
|
|
<< m.GetColumn(2).Norm() << endl;
|
|
Matrix33f im = m;
|
|
im.Transpose();
|
|
im = im*m;
|
|
cout << "Check ortonormality: " << im << endl;
|
|
Quaternionf q;
|
|
q.FromMatrix(m);
|
|
cout << "To Quaternion: " << q << endl;
|
|
|
|
float alpha = 2*acos(q[0]);
|
|
Point3f axis(q[1], q[2], q[3]);
|
|
cout << "Norm: " << axis.SquaredNorm() + q[0]*q[0] << endl;
|
|
axis.Normalize();
|
|
cout << "angle: " << 2*acos(q[0]) << " Axis: " << axis << endl;
|
|
|
|
Point3f p(3, 4, 5);
|
|
Point3f qp = q.Rotate(p);
|
|
Point3f mp = m*p;
|
|
cout << "Rotating p: " << p << endl;
|
|
cout << "q*p = " << qp << " m*p: " << mp << endl;
|
|
q.ToMatrix(m);
|
|
cout << "Back to: " << m << endl<< endl;
|
|
}
|
|
|
|
int main() {
|
|
|
|
Quaternionf q(1, 0, 0, 0); /*identity*/
|
|
// cout << "Verify identity: " << endl;
|
|
verify(q);
|
|
|
|
q.FromAxis(M_PI/2, Point3f(0, 0, 1));
|
|
// cout << "Verify 90 degrees\n";
|
|
verify(q);
|
|
|
|
q.FromAxis(M_PI/4, Point3f(0, 1, 1));
|
|
// cout << "Verify 45 degrees\n";
|
|
verify(q);
|
|
|
|
Matrix33f m;
|
|
m[0][0] = 0.70145; m[0][1] = 0.372035; m[0][2] = 0.607913;
|
|
m[1][0] = -0.628023; m[1][1] = 0.725922; m[1][2] = 0.2804;
|
|
m[2][0] = -0.336978; m[2][1] = -0.57847; m[2][2] = 0.742845;
|
|
|
|
cout << "verify matrix: " << endl;
|
|
verify(m);
|
|
verify(m);
|
|
|
|
q.FromAxis(0.7, Point3f(-0.20, -0.42, -0.83));
|
|
cout << "verify from axis: " << endl;
|
|
verify(q);
|
|
|
|
// Quaternionf q(0.648947, -0.114828, -0.104375, -0.385262);
|
|
Quaternionf iq= Inverse(q);
|
|
//Matrix33f m;
|
|
|
|
cout << "matrix: " << m << endl;
|
|
|
|
Point3f p(3, 4, 5);
|
|
//test this matrix:
|
|
cout << "norms: " << m.GetRow(0).Norm() << " " << m.GetRow(1).Norm() << " " << m.GetRow(2).Norm() << endl;
|
|
q.FromMatrix(m);
|
|
q.ToMatrix(m);
|
|
cout << "quaternion: " << q[0] << " " << q[1] << " " << q[2] << " " << q[3] <<endl;
|
|
cout << "matrix: " << endl;
|
|
for(int i = 0; i < 3; i++) {
|
|
for(int j = 0; j < 3; j++) {
|
|
cout << m[i][j] << " ";
|
|
}
|
|
cout << endl;
|
|
}
|
|
cout << endl;
|
|
|
|
cout << "Point: " << p[0] << " " << p[1] << " " << p[2] << endl;
|
|
|
|
Point3f r = q.Rotate(p);
|
|
cout << "Rotated by q: " << r[0] << " " << r[1] << " " << r[2] << endl;
|
|
r = m*p;
|
|
cout << "Rotated by m: " << r[0] << " " << r[1] << " " << r[2] << endl;
|
|
|
|
q.FromMatrix(m);
|
|
cout << "quaternion: " << q[0] << " " << q[1] << " " << q[2] << " " << q[3] <<endl;
|
|
return 0;
|
|
}
|