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#include <mystdlib.h>
#include <myadt.hpp>
#include <gprim.hpp>
#include <linalg.hpp>
namespace netgen
{
Transformation3d :: Transformation3d ()
{
for (int i = 0; i < 3; i++)
{
offset[i] = 0;
for (int j = 0; j < 3; j++)
lin[i][j] = 0;
}
}
Transformation3d :: Transformation3d (const Vec3d & translate)
{
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
lin[i][j] = 0;
for (int i = 0; i < 3; i++)
{
offset[i] = translate.X(i+1);
lin[i][i] = 1;
}
}
Transformation3d ::
Transformation3d (const Point3d & 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"
Transformation3d tc(c);
Transformation3d tcinv;
tc.CalcInverse (tcinv);
Transformation3d 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;
}
Transformation3d :: Transformation3d (const Point3d ** pp)
{
for (int i = 1; i <= 3; i++)
{
offset[i-1] = (*pp[0]).X(i);
for (int j = 1; j <= 3; j++)
lin[i-1][j-1] = (*pp[j]).X(i) - (*pp[0]).X(i);
}
}
Transformation3d :: Transformation3d (const Point3d pp[])
{
for (int i = 1; i <= 3; i++)
{
offset[i-1] = pp[0].X(i);
for (int j = 1; j <= 3; j++)
lin[i-1][j-1] = pp[j].X(i) - pp[0].X(i);
}
}
void Transformation3d :: CalcInverse (Transformation3d & inv) const
{
static DenseMatrix a(3), inva(3);
static Vector b(3), sol(3);
for (int i = 0; i < 3; i++)
{
b(i) = offset[i];
for (int j = 0; j < 3; j++)
a(i, j) = lin[i][j];
}
::netgen::CalcInverse (a, inva);
inva.Mult (b, sol);
for (int i = 0; i < 3; i++)
{
inv.offset[i] = -sol(i);
for (int j = 0; j < 3; j++)
inv.lin[i][j] = inva(i, j);
}
}
void Transformation3d::
Combine (const Transformation3d & ta, const Transformation3d & tb)
{
// o = o_a+ m_a o_b
// m = m_a m_b
for (int i = 0; i <= 2; i++)
{
offset[i] = ta.offset[i];
for (int j = 0; j <= 2; j++)
offset[i] += ta.lin[i][j] * tb.offset[j];
}
for (int i = 0; i <= 2; i++)
for (int j = 0; j <= 2; j++)
{
lin[i][j] = 0;
for (int k = 0; k <= 2; k++)
lin[i][j] += ta.lin[i][k] * tb.lin[k][j];
}
}
void Transformation3d :: 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++)
{
offset[i] = 0;
for (j = 0; j <= 2; j++)
lin[i][j] = 0;
}
lin[dir][dir] = 1;
lin[pos1][pos1] = co;
lin[pos2][pos2] = co;
lin[pos1][pos2] = si;
lin[pos2][pos1] = -si;
}
ostream & operator<< (ostream & ost, Transformation3d & trans)
{
ost << "offset = ";
for (int i = 0; i <= 2; i++)
ost << trans.offset[i] << " ";
ost << endl << "linear = " << endl;
for (int i = 0; i <= 2; i++)
{
for (int j = 0; j <= 2; j++)
ost << trans.lin[i][j] << " ";
ost << endl;
}
return ost;
}
template <>
Transformation<3> :: Transformation (const Point<3> & c, const Vec<3> & axes, double angle)
{
Vec<3> vc(c);
Transformation<3> tc(vc);
Transformation<3> tcinv(-vc);
Transformation<3> r, ht, ht2;
// r.SetAxisRotation (3, alpha);
Vec<3> naxes = axes;
naxes.Normalize();
Vec<3> n1 = naxes.GetNormal();
Vec<3> n2 = Cross(naxes, n1);
r.v = Vec<3>(0,0,0);
double co = cos(angle);
double si = sin(angle);
for (int i = 0; i < 3; i++)
for (int j = 0; j < 3; j++)
r.m(i,j) = naxes(i)*naxes(j) + co*(n1(i)*n1(j)+n2(i)*n2(j)) + si*( (n2(i)*n1(j)-n2(j)*n1(i)) );
ht.Combine (tc, r);
Combine (ht, tcinv);
}
template <int D>
Transformation<D> :: Transformation (const Point<D> * pp)
{
v = Vec<D> (pp[0]);
for (int i = 0; i < D; i++)
for (int j = 0; j < D; j++)
m(j,i) = pp[i+1](j)-pp[0](j);
}
template class Transformation<3>;
}
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