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#ifndef FILE_TRANSFORM3D
#define FILE_TRANSFORM3D
/* *************************************************************************/
/* File: transform3d.hh */
/* Author: Joachim Schoeberl */
/* Date: 22. Mar. 98 */
/* *************************************************************************/
/*
Affine - Linear mapping in 3D space
*/
#include "geom3d.hpp"
#include "geomfuncs.hpp"
namespace netgen
{
class Transformation3d;
ostream & operator<< (ostream & ost, Transformation3d & trans);
class Transformation3d
{
double lin[3][3];
double offset[3];
public:
///
Transformation3d ();
/// Unit tet is mapped to tet described by pp
Transformation3d (const Point3d ** pp);
/// Unit tet is mapped to tet described by pp
Transformation3d (const Point3d pp[]);
/// translation
Transformation3d (const Vec3d & translate);
/// rotation with ...
Transformation3d (const Point3d & c, double alpha, double beta, double gamma);
///
void CalcInverse (Transformation3d & inv) const;
/// this = ta x tb
void Combine (const Transformation3d & ta, const Transformation3d & tb);
/// dir = 1..3 (== x..z)
void SetAxisRotation (int dir, double alpha);
///
void Transform (const Point3d & from, Point3d & to) const
{
for (int i = 1; i <= 3; i++)
{
to.X(i) = offset[i-1] + lin[i-1][0] * from.X(1) +
lin[i-1][1] * from.X(2) + lin[i-1][2] * from.X(3);
}
}
///
void Transform (Point3d & p) const
{
Point3d hp;
Transform (p, hp);
p = hp;
}
/// transform vector, apply only linear part, not offset
void Transform (const Vec3d & from, Vec3d & to) const
{
for (int i = 1; i <= 3; i++)
{
to.X(i) = lin[i-1][0] * from.X(1) +
lin[i-1][1] * from.X(2) + lin[i-1][2] * from.X(3);
}
}
friend ostream & operator<< (ostream & ost, Transformation3d & trans);
};
template <int D>
class Transformation
{
Mat<D> m;
Vec<D> v;
public:
///
Transformation () { m = 0; v = 0; }
/// Unit tet is mapped to tet described by pp
Transformation (const Point<D> * pp);
/// translation
Transformation (const Vec<D> & translate)
{
v = translate;
m = 0;
for (int i = 0; i < D; i++)
m(i,i) = 1;
}
Transformation (const Point<D> & c, const Vec<3> & axes, double angle);
// rotation with ...
Transformation (const Point<D> & c, double alpha, double beta, double gamma)
{
// total = T_c x Rot_0 x T_c^{-1}
// Use Euler angles, see many books from tech mech, e.g.
// Shabana "multibody systems"
Vec<D> vc(c);
Transformation<D> tc(vc);
Transformation<D> tcinv(-vc);
// tc.CalcInverse (tcinv);
Transformation<D> r1, r2, r3, ht, ht2;
r1.SetAxisRotation (3, alpha);
r2.SetAxisRotation (1, beta);
r3.SetAxisRotation (3, gamma);
ht.Combine (tc, r3);
ht2.Combine (ht, r2);
ht.Combine (ht2, r1);
Combine (ht, tcinv);
// cout << "Rotation - Transformation:" << (*this) << endl;
// (*testout) << "Rotation - Transformation:" << (*this) << endl;
}
Mat<D> & GetMatrix() { return m; }
Vec<D> & GetVector() { return v; }
void DoArchive(Archive& ar)
{
ar & m & v;
}
///
Transformation CalcInverse () const
{
Transformation inv;
// inv.m = Inv(m);
::netgen::CalcInverse (m, inv.m);
inv.v = inv.m * (-v);
return inv;
}
/// this = ta x tb
void Combine (const Transformation & ta, const Transformation & tb)
{
v = ta.v + ta.m * tb.v;
m = ta.m * tb.m;
}
/// dir = 1..3 (== x..z)
void SetAxisRotation (int dir, double alpha)
{
double co = cos(alpha);
double si = sin(alpha);
dir--;
int pos1 = (dir+1) % 3;
int pos2 = (dir+2) % 3;
int i, j;
for (i = 0; i <= 2; i++)
{
v(i) = 0;
for (j = 0; j <= 2; j++)
m(i,j) = 0;
}
m(dir,dir) = 1;
m(pos1, pos1) = co;
m(pos2, pos2) = co;
m(pos1, pos2) = si;
m(pos2, pos1) = -si;
}
///
void Transform (const Point<D> & from, Point<D> & to) const
{
to = Point<D> (v + m * Vec<D>(from));
}
void Transform (Point<D> & p) const
{
p = Point<D> (v + m * Vec<D>(p));
}
/// transform vector, apply only linear part, not offset
void Transform (const Vec<D> & from, Vec<D> & to) const
{
to = m * from;
}
Point<D> operator() (Point<D> from) const { Point<D> to; Transform(from, to); return to; }
Vec<D> operator() (Vec<D> from) const { Vec<D> to; Transform(from, to); return to; }
};
template <int D>
ostream & operator<< (ostream & ost, Transformation<D> & trans);
}
#endif
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