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172 lines
3.7 KiB
C++
172 lines
3.7 KiB
C++
#ifndef FILE_GEOMFUNCS
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#define FILE_GEOMFUNCS
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/* *************************************************************************/
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/* File: geomfuncs.hpp */
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/* Author: Joachim Schoeberl */
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/* Date: 20. Jul. 02 */
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/* *************************************************************************/
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namespace netgen
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{
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template <int D>
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inline double Abs (const Vec<D> & v)
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{
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double sum = 0;
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for (int i = 0; i < D; i++)
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sum += v(i) * v(i);
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return sqrt (sum);
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}
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template <int D>
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inline double Abs2 (const Vec<D> & v)
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{
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double sum = 0;
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for (int i = 0; i < D; i++)
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sum += v(i) * v(i);
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return sum;
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}
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template <int D>
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inline double Dist (const Point<D> & a, const Point<D> & b)
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{
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return Abs (a-b);
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}
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template <int D>
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inline double Dist2 (const Point<D> & a, const Point<D> & b)
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{
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return Abs2 (a-b);
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}
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template <int D>
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inline Point<D> Center (const Point<D> & a, const Point<D> & b)
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{
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Point<D> res;
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for (int i = 0; i < D; i++)
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res(i) = 0.5 * (a(i) + b(i));
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return res;
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}
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template <int D>
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inline Point<D> Center (const Point<D> & a, const Point<D> & b, const Point<D> & c)
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{
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Point<D> res;
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for (int i = 0; i < D; i++)
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res(i) = (1.0/3.0) * (a(i) + b(i) + c(i));
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return res;
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}
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template <int D>
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inline Point<D> Center (const Point<D> & a, const Point<D> & b, const Point<D> & c, const Point<D> & d)
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{
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Point<D> res;
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for (int i = 0; i < D; i++)
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res(i) = (1.0/4.0) * (a(i) + b(i) + c(i) + d(i));
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return res;
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}
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/*
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new wrong code problem with MSVC2010:
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using Cross ( & , & ) computes wrong cross-product, problem arises in
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Surface::DefineTangentialPlane, e.g. with example boxcyl.geo
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*/
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// inline Vec<3> Cross (const Vec<3> & v1, const Vec<3> & v2)
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template <typename T>
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inline Vec<3,T> Cross (Vec<3,T> v1, Vec<3,T> v2)
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{
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return Vec<3,T>
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( v1(1) * v2(2) - v1(2) * v2(1),
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v1(2) * v2(0) - v1(0) * v2(2),
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v1(0) * v2(1) - v1(1) * v2(0) );
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}
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inline double Determinant (const Vec<3> & col1,
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const Vec<3> & col2,
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const Vec<3> & col3)
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{
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return
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col1(0) * ( col2(1) * col3(2) - col2(2) * col3(1)) +
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col1(1) * ( col2(2) * col3(0) - col2(0) * col3(2)) +
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col1(2) * ( col2(0) * col3(1) - col2(1) * col3(0));
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}
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template <>
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inline Vec<2> Vec<2> :: GetNormal () const
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{
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return Vec<2> (-x[1], x[0]);
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}
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template <>
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inline Vec<3> Vec<3> :: GetNormal () const
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{
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if (fabs (x[0]) > fabs (x[2]))
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return Vec<3> (-x[1], x[0], 0);
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else
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return Vec<3> (0, x[2], -x[1]);
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}
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// template <int H, int W>
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inline void CalcInverse (const Mat<2,2> & m, Mat<2,2> & inv)
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{
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double det = m(0,0) * m(1,1) - m(0,1) * m(1,0);
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if (det == 0)
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{
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inv = 0;
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return;
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}
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double idet = 1.0 / det;
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inv(0,0) = idet * m(1,1);
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inv(0,1) = -idet * m(0,1);
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inv(1,0) = -idet * m(1,0);
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inv(1,1) = idet * m(0,0);
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}
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void CalcInverse (const Mat<3,3> & m, Mat<3,3> & inv);
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inline void CalcInverse (const Mat<2,3> & m, Mat<3,2> & inv)
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{
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Mat<2,2> a = m * Trans (m);
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Mat<2,2> ainv;
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CalcInverse (a, ainv);
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inv = Trans (m) * ainv;
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}
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void CalcInverse (const Mat<3,2> & m, Mat<2,3> & inv);
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inline void CalcInverse (const Mat<3,2> & m, Mat<2,3> & inv)
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{
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Mat<2,2> a = Trans (m) * m;
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Mat<2,2> ainv;
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CalcInverse (a, ainv);
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inv = ainv * Trans (m);
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}
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double Det (const Mat<2,2> & m);
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double Det (const Mat<3,3> & m);
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// eigenvalues of a symmetric matrix
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void EigenValues (const Mat<3,3> & m, Vec<3> & ev);
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void EigenValues (const Mat<2,2> & m, Vec<3> & ev);
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}
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#endif
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