geometrytools.cpp

   1 //
   2 // ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
   3 // +                                                                      +
   4 // + This file is part of enGrid.                                         +
   5 // +                                                                      +
   6 // + Copyright 2008,2009 Oliver Gloth                                     +
   7 // +                                                                      +
   8 // + enGrid is free software: you can redistribute it and/or modify       +
   9 // + it under the terms of the GNU General Public License as published by +
  10 // + the Free Software Foundation, either version 3 of the License, or    +
  11 // + (at your option) any later version.                                  +
  12 // +                                                                      +
  13 // + enGrid is distributed in the hope that it will be useful,            +
  14 // + but WITHOUT ANY WARRANTY; without even the implied warranty of       +
  15 // + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the        +
  16 // + GNU General Public License for more details.                         +
  17 // +                                                                      +
  18 // + You should have received a copy of the GNU General Public License    +
  19 // + along with enGrid. If not, see <http://www.gnu.org/licenses/>.       +
  20 // +                                                                      +
  21 // ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
  22 //
  23 #include "geometrytools.h"
  24 #include "containertricks.h"
  25
  26 #include <vtkCellType.h>
  27
  28 namespace GeometryTools {
  29
  30 void rotate(vec3_t g1, vec3_t g2,vec3_t g3, vec3_t &b, double theta)
  31 {
  32   //cout << b << endl;
  33   mat3_t g_t;
  34   g_t[0] = g1;
  35   g_t[1] = g2;
  36   g_t[2] = g3;
  37   mat3_t g = g_t.transp();
  38   //cout << g << endl;
  39   vec3_t bb = g_t*b;
  40   //cout << bb << endl;
  41   mat3_t rot = mat3_t::identity();
  42   rot[0][0] = cos(theta);
  43   rot[0][1] = -sin(theta);
  44   rot[1][0] = sin(theta);
  45   rot[1][1] = cos(theta);
  46   //cout << rot << endl;
  47   vec3_t bbb = rot*bb;
  48   //cout << bbb << endl;
  49   b = g*bbb;
  50   //cout << b << endl;
  51 };
  52
  53 vec3_t rotate(vec3_t v, vec3_t axis, double theta)
  54 {
  55   axis.normalise();
  56
  57   // transposed base of rotate system
  58   mat3_t g_t;
  59
  60   // compute projection of v in axis direction
  61   vec3_t v_axis = (axis*v)*axis;
  62
  63   // compute first orthogonal vector (first base vector)
  64   g_t[0] = v-v_axis;
  65   g_t[0].normalise();
  66
  67   // second base vector is the normalised axis
  68   g_t[1] = axis;
  69
  70   // compute second orthogonal vector (third base vector)
  71   g_t[2] = g_t[0].cross(g_t[1]);
  72
  73   // base of rotate system
  74   mat3_t g = g_t.transp();
  75
  76   // matrix for rotation around g_t[1];
  77   mat3_t rot = mat3_t::identity();
  78   rot[0][0] = cos(theta);
  79   rot[0][2] = sin(theta);
  80   rot[2][0] = -sin(theta);
  81   rot[2][2] = cos(theta);
  82
  83   // transfer v to rotate system
  84   vec3_t v_r = g_t*v;
  85
  86   // rotate the vector and transfer it back
  87   v_r = rot*v_r;
  88   v = g*v_r;
  89
  90   return v;
  91 };
  92
  93 vec3_t orthogonalVector(vec3_t v)
  94 {
  95   v.normalise();
  96   vec3_t u = v;
  97   int i_min = 0;
  98   int i_max = 0;
  99   for (int i = 1; i < 3; ++i) {
 100     if (v[i] > v[i_max]) i_max = i;
 101     if (v[i] < v[i_min]) i_min = i;
 102   };
 103   double h = u[i_min];
 104   u[i_min] = u[i_max];
 105   u[i_max] = h;
 106   u -= (u*v)*v;
 107   u.normalise();
 108   return u;
 109 };
 110
 111
 112 double intersection(vec3_t x_straight, vec3_t v_straight, vec3_t x_plane, vec3_t u_plane, vec3_t v_plane)
 113 {
 114   vec3_t n = u_plane.cross(v_plane);
 115   return intersection(x_straight,v_straight,x_plane,n);
 116 };
 117
 118 double intersection(vec3_t x_straight, vec3_t v_straight, vec3_t x_plane, vec3_t n_plane)
 119 {
 120   double k = (x_plane*n_plane - x_straight*n_plane)/(v_straight*n_plane);
 121   return k;
 122 };
 123
 124 bool intersection (double &k1, double &k2, vec2_t r1, vec2_t u1, vec2_t r2, vec2_t u2)
 125 {
 126   double ave_length = .5*(sqrt(u1[0]*u1[0]+u1[1]*u1[1]) + sqrt(u2[0]*u2[0]+u2[1]*u2[1]));
 127   double DET = (u1[0]*u2[1]-u1[1]*u2[0]);
 128   if (fabs(DET) > 1e-6*ave_length) {
 129     k1 = -(u2[0]*r2[1]-u2[0]*r1[1]-r2[0]*u2[1]+r1[0]*u2[1])/DET;
 130     k2 = -(-u1[1]*r2[0]+u1[0]*r2[1]-u1[0]*r1[1]+u1[1]*r1[0])/DET;
 131     return true;
 132   } else {
 133     return false;
 134   };
 135 };
 136
 137 void sliceTriangle(const vector<vec3_t> &Tin, vec3_t x, vec3_t n, vector<vector<vec3_t> > &Tout)
 138 {
 139   vec3_t a = Tin[0];
 140   vec3_t b = Tin[1];
 141   vec3_t c = Tin[2];
 142   double kab = intersection(a,b-a,x,n);
 143   double kbc = intersection(b,c-b,x,n);
 144   double kca = intersection(c,a-c,x,n);
 145   bool ab_cut = ((kab >= 0) && (kab <= 1));
 146   bool bc_cut = ((kbc >= 0) && (kbc <= 1));
 147   bool ca_cut = ((kca >= 0) && (kca <= 1));
 148   if (ab_cut && bc_cut && ca_cut) {
 149     //cerr << "invalid triangle (SliceTriangle) A" << endl;
 150     //exit(EXIT_FAILURE);
 151     if      ((kab <= kbc) && (kab <= kca)) ab_cut = false;
 152     else if ((kbc <= kab) && (kbc <= kca)) bc_cut = false;
 153     else                                   ca_cut = false;
 154   };
 155   if (ab_cut && bc_cut) {
 156     vec3_t ab = a + kab*(b-a);
 157     vec3_t bc = b + kbc*(c-b);
 158     Tout.resize(3,vector<vec3_t>(3));
 159     clinit(Tout[0]) = a,ab,bc;
 160     clinit(Tout[1]) = ab,b,bc;
 161     clinit(Tout[2]) = bc,c,a;
 162   } else if (bc_cut && ca_cut) {
 163     vec3_t bc = b + kbc*(c-b);
 164     vec3_t ca = c + kca*(a-c);
 165     Tout.resize(3,vector<vec3_t>(3));
 166     clinit(Tout[0]) = a,bc,ca;
 167     clinit(Tout[1]) = a,b,bc;
 168     clinit(Tout[2]) = bc,c,ca;
 169   } else if (ca_cut && ab_cut) {
 170     vec3_t ca = c + kca*(a-c);
 171     vec3_t ab = a + kab*(b-a);
 172     Tout.resize(3,vector<vec3_t>(3));
 173     clinit(Tout[0]) = a,ab,ca;
 174     clinit(Tout[1]) = ab,b,ca;
 175     clinit(Tout[2]) = b,c,ca;
 176   } else {
 177     Tout.resize(1,vector<vec3_t>(3));
 178     clinit(Tout[0]) = a,b,c;
 179   };
 180 };
 181
 182
 183 double tetraVol(vec3_t x0, vec3_t x1, vec3_t x2, vec3_t x3, bool neg)
 184 {
 185   vec3_t v1 = x1-x0;
 186   vec3_t v2 = x2-x0;
 187   vec3_t v3 = x3-x0;
 188   double V = v1*(v2.cross(v3));
 189   V /= 6.0;
 190   if (!neg && (V < 0)) {
 191     vec3_t v4 = x2-x1;
 192     vec3_t v5 = x3-x1;
 193     vec3_t v6 = x3-x2;
 194     double Lmin = 1e99;
 195     double Lmax = 0;
 196     Lmin = min(Lmin,v1.abs());
 197     Lmin = min(Lmin,v2.abs());
 198     Lmin = min(Lmin,v3.abs());
 199     Lmin = min(Lmin,v4.abs());
 200     Lmin = min(Lmin,v5.abs());
 201     Lmin = min(Lmin,v6.abs());
 202     Lmax = max(Lmax,v1.abs());
 203     Lmax = max(Lmax,v2.abs());
 204     Lmax = max(Lmax,v3.abs());
 205     Lmax = max(Lmax,v4.abs());
 206     Lmax = max(Lmax,v5.abs());
 207     Lmax = max(Lmax,v6.abs());
 208     if (Lmin/Lmax < 1e-6) {
 209       V = 0;
 210       V = -1e99;
 211     } else {
 212       V = -1e99;
 213     };
 214     //V *= 1e6;
 215   };
 216   return V; //fabs(V);
 217 };
 218
 219 double pyraVol(vec3_t x0, vec3_t x1, vec3_t x2, vec3_t x3, vec3_t x4, bool neg)
 220 {
 221   double V1 = tetraVol(x0, x1, x3, x4, neg) + tetraVol(x1, x2, x3, x4, neg);
 222   double V2 = tetraVol(x0, x1, x2, x4, neg) + tetraVol(x2, x3, x0, x4, neg);
 223   return min(V1,V2);
 224   /*
 225   double V = 0;
 226   vec3_t m0 = .25*(x0+x1+x2+x3);
 227   V += tetraVol(x0, x1, m0, x4, neg);
 228   V += tetraVol(x1, x2, m0, x4, neg);
 229   V += tetraVol(x2, x3, m0, x4, neg);
 230   V += tetraVol(x3, x0, m0, x4, neg);
 231   return V;
 232   */
 233 };
 234
 235 double prismVol(vec3_t x0, vec3_t x1, vec3_t x2, vec3_t x3, vec3_t x4, vec3_t x5, bool neg)
 236 {
 237   double V = 0;
 238   vec3_t p  = 1.0/6.0*(x0+x1+x2+x3+x4+x5);
 239   V += tetraVol(x0, x2, x1, p, neg);
 240   V += tetraVol(x3, x4, x5, p, neg);
 241   V += pyraVol (x0, x1, x4, x3, p, neg);
 242   V += pyraVol (x1, x2, x5, x4, p, neg);
 243   V += pyraVol (x0, x3, x5, x2, p, neg);
 244   return V;
 245 };
 246
 247 double hexaVol(vec3_t x0, vec3_t x1, vec3_t x2, vec3_t x3, vec3_t x4, vec3_t x5, vec3_t x6, vec3_t x7, bool neg)
 248 {
 249   double V = 0;
 250   vec3_t p = 1.0/8.0*(x0+x1+x2+x3+x4+x5+x6+x7);
 251   V += pyraVol(x0, x1, x3, x2, p, neg);
 252   V += pyraVol(x0, x4, x5, x1, p, neg);
 253   V += pyraVol(x4, x6, x7, x5, p, neg);
 254   V += pyraVol(x2, x3, x7, x6, p, neg);
 255   V += pyraVol(x1, x5, x7, x3, p, neg);
 256   V += pyraVol(x0, x2, x6, x4, p, neg);
 257   return V;
 258 };
 259
 260 double triArea(vec3_t x0, vec3_t x1, vec3_t x2)
 261 {
 262   vec3_t a = x1-x0;
 263   vec3_t b = x2-x0;
 264   double A = 0.5*((a.cross(b)).abs());
 265   return A;
 266 };
 267
 268 double quadArea(vec3_t x0, vec3_t x1, vec3_t x2, vec3_t x3)
 269 {
 270   double A = 0;
 271   vec3_t p = .25*(x0+x1+x2+x3);
 272   A += triArea(x0,x1,p);
 273   A += triArea(x1,x2,p);
 274   A += triArea(x2,x3,p);
 275   A += triArea(x3,x0,p);
 276   return A;
 277 };
 278
 279 vec3_t triNormal(vec3_t x0, vec3_t x1, vec3_t x2)
 280 {
 281   vec3_t a = x1-x0;
 282   vec3_t b = x2-x0;
 283   vec3_t n = 0.5*(a.cross(b));
 284   return n;
 285 };
 286
 287 vec3_t quadNormal(vec3_t x0, vec3_t x1, vec3_t x2, vec3_t x3)
 288 {
 289   vec3_t n;
 290   clinit(n) = 0,0,0;
 291   vec3_t p = .25*(x0+x1+x2+x3);
 292   n += triNormal(x0,x1,p);
 293   n += triNormal(x1,x2,p);
 294   n += triNormal(x2,x3,p);
 295   n += triNormal(x3,x0,p);
 296   return n;
 297 };
 298
 299 vec3_t triNormal(vtkUnstructuredGrid *grid, vtkIdType p1, vtkIdType p2, vtkIdType p3)
 300 {
 301   vec3_t x1, x2, x3;
 302   grid->GetPoint(p1,x1.data());
 303   grid->GetPoint(p2,x2.data());
 304   grid->GetPoint(p3,x3.data());
 305   return triNormal(x1,x2,x3);
 306 };
 307
 308 vec3_t quadNormal(vtkUnstructuredGrid *grid, vtkIdType p1, vtkIdType p2, vtkIdType p3, vtkIdType p4)
 309 {
 310   vec3_t x1, x2, x3, x4;
 311   grid->GetPoint(p1,x1.data());
 312   grid->GetPoint(p2,x2.data());
 313   grid->GetPoint(p3,x3.data());
 314   grid->GetPoint(p4,x4.data());
 315   return quadNormal(x1,x2,x3,x4);
 316 };
 317
 318 vec3_t cellNormal(vtkUnstructuredGrid *grid, vtkIdType i)
 319 {
 320   vtkIdType *pts;
 321   vtkIdType npts;
 322   vec3_t n;
 323   clinit(n) = 0,0,0;
 324   grid->GetCellPoints(i,npts,pts);
 325   if      (npts == 3) return triNormal(grid,pts[0],pts[1],pts[2]);
 326   else if (npts == 4) return quadNormal(grid,pts[0],pts[1],pts[2],pts[3]);
 327   return n;
 328 };
 329
 330 double cellVA(vtkUnstructuredGrid *grid, vtkIdType cellId, bool neg)
 331 {
 332   vtkIdType *pts;
 333   vtkIdType  Npts;
 334   vec3_t     p[8];
 335   grid->GetCellPoints(cellId, Npts, pts);
 336   for (int i_pts = 0; i_pts < Npts; ++i_pts) {
 337     grid->GetPoints()->GetPoint(pts[i_pts], p[i_pts].data());
 338   };
 339   vtkIdType cellType = grid->GetCellType(cellId);
 340   if      (cellType == VTK_TRIANGLE)   return triArea (p[0], p[1], p[2]);
 341   else if (cellType == VTK_QUAD)       return quadArea(p[0], p[1], p[2], p[3]);
 342   else if (cellType == VTK_TETRA)      return tetraVol(p[0], p[1], p[2], p[3], neg);
 343   else if (cellType == VTK_PYRAMID)    return pyraVol (p[0], p[1], p[2], p[3], p[4], neg);
 344   else if (cellType == VTK_WEDGE)      return prismVol(p[0], p[1], p[2], p[3], p[4], p[5], neg);
 345   else if (cellType == VTK_HEXAHEDRON) return hexaVol (p[0], p[1], p[2], p[3], p[4], p[5], p[6], p[7], neg);
 346   return 0.0;
 347 };
 348
 349 } // namespace
 350
 351
 352
 353