mirror of
https://github.com/NGSolve/netgen.git
synced 2024-11-12 00:59:16 +05:00
158 lines
3.3 KiB
C++
158 lines
3.3 KiB
C++
#ifndef FILE_GEOMFUNCS
|
|
#define FILE_GEOMFUNCS
|
|
|
|
/* *************************************************************************/
|
|
/* File: geomfuncs.hpp */
|
|
/* Author: Joachim Schoeberl */
|
|
/* Date: 20. Jul. 02 */
|
|
/* *************************************************************************/
|
|
|
|
|
|
template <int D>
|
|
inline double Abs (const Vec<D> & v)
|
|
{
|
|
double sum = 0;
|
|
for (int i = 0; i < D; i++)
|
|
sum += v(i) * v(i);
|
|
return sqrt (sum);
|
|
}
|
|
|
|
|
|
template <int D>
|
|
inline double Abs2 (const Vec<D> & v)
|
|
{
|
|
double sum = 0;
|
|
for (int i = 0; i < D; i++)
|
|
sum += v(i) * v(i);
|
|
return sum;
|
|
}
|
|
|
|
|
|
|
|
template <int D>
|
|
inline double Dist (const Point<D> & a, const Point<D> & b)
|
|
{
|
|
return Abs (a-b);
|
|
}
|
|
|
|
template <int D>
|
|
inline double Dist2 (const Point<D> & a, const Point<D> & b)
|
|
{
|
|
return Abs2 (a-b);
|
|
}
|
|
|
|
|
|
template <int D>
|
|
inline Point<D> Center (const Point<D> & a, const Point<D> & b)
|
|
{
|
|
Point<D> res;
|
|
for (int i = 0; i < D; i++)
|
|
res(i) = 0.5 * (a(i) + b(i));
|
|
return res;
|
|
}
|
|
|
|
template <int D>
|
|
inline Point<D> Center (const Point<D> & a, const Point<D> & b, const Point<D> & c)
|
|
{
|
|
Point<D> res;
|
|
for (int i = 0; i < D; i++)
|
|
res(i) = (1.0/3.0) * (a(i) + b(i) + c(i));
|
|
return res;
|
|
}
|
|
|
|
template <int D>
|
|
inline Point<D> Center (const Point<D> & a, const Point<D> & b, const Point<D> & c, const Point<D> & d)
|
|
{
|
|
Point<D> res;
|
|
for (int i = 0; i < D; i++)
|
|
res(i) = (1.0/4.0) * (a(i) + b(i) + c(i) + d(i));
|
|
return res;
|
|
}
|
|
|
|
|
|
|
|
inline Vec<3> Cross (const Vec<3> & v1, const Vec<3> & v2)
|
|
{
|
|
return Vec<3>
|
|
( v1(1) * v2(2) - v1(2) * v2(1),
|
|
v1(2) * v2(0) - v1(0) * v2(2),
|
|
v1(0) * v2(1) - v1(1) * v2(0) );
|
|
}
|
|
|
|
|
|
inline double Determinant (const Vec<3> & col1,
|
|
const Vec<3> & col2,
|
|
const Vec<3> & col3)
|
|
{
|
|
return
|
|
col1(0) * ( col2(1) * col3(2) - col2(2) * col3(1)) +
|
|
col1(1) * ( col2(2) * col3(0) - col2(0) * col3(2)) +
|
|
col1(2) * ( col2(0) * col3(1) - col2(1) * col3(0));
|
|
}
|
|
|
|
|
|
|
|
template <>
|
|
inline Vec<2> Vec<2> :: GetNormal () const
|
|
{
|
|
return Vec<2> (-x[1], x[0]);
|
|
}
|
|
|
|
template <>
|
|
inline Vec<3> Vec<3> :: GetNormal () const
|
|
{
|
|
if (fabs (x[0]) > fabs (x[2]))
|
|
return Vec<3> (-x[1], x[0], 0);
|
|
else
|
|
return Vec<3> (0, x[2], -x[1]);
|
|
}
|
|
|
|
|
|
|
|
// template <int H, int W>
|
|
inline void CalcInverse (const Mat<2,2> & m, Mat<2,2> & inv)
|
|
{
|
|
double det = m(0,0) * m(1,1) - m(0,1) * m(1,0);
|
|
if (det == 0)
|
|
{
|
|
inv = 0;
|
|
return;
|
|
}
|
|
|
|
double idet = 1.0 / det;
|
|
inv(0,0) = idet * m(1,1);
|
|
inv(0,1) = -idet * m(0,1);
|
|
inv(1,0) = -idet * m(1,0);
|
|
inv(1,1) = idet * m(0,0);
|
|
}
|
|
|
|
void CalcInverse (const Mat<3,3> & m, Mat<3,3> & inv);
|
|
|
|
inline void CalcInverse (const Mat<2,3> & m, Mat<3,2> & inv)
|
|
{
|
|
Mat<2,2> a = m * Trans (m);
|
|
Mat<2,2> ainv;
|
|
CalcInverse (a, ainv);
|
|
inv = Trans (m) * ainv;
|
|
}
|
|
|
|
void CalcInverse (const Mat<3,2> & m, Mat<2,3> & inv);
|
|
|
|
inline void CalcInverse (const Mat<3,2> & m, Mat<2,3> & inv)
|
|
{
|
|
Mat<2,2> a = Trans (m) * m;
|
|
Mat<2,2> ainv;
|
|
CalcInverse (a, ainv);
|
|
inv = ainv * Trans (m);
|
|
}
|
|
|
|
|
|
double Det (const Mat<2,2> & m);
|
|
double Det (const Mat<3,3> & m);
|
|
|
|
// eigenvalues of a symmetric matrix
|
|
void EigenValues (const Mat<3,3> & m, Vec<3> & ev);
|
|
void EigenValues (const Mat<2,2> & m, Vec<3> & ev);
|
|
|
|
#endif
|