Line data    Source code

       1             : // The libMesh Finite Element Library.
       2             : // Copyright (C) 2002-2025 Benjamin S. Kirk, John W. Peterson, Roy H. Stogner
       3             : 
       4             : // This library is free software; you can redistribute it and/or
       5             : // modify it under the terms of the GNU Lesser General Public
       6             : // License as published by the Free Software Foundation; either
       7             : // version 2.1 of the License, or (at your option) any later version.
       8             : 
       9             : // This library is distributed in the hope that it will be useful,
      10             : // but WITHOUT ANY WARRANTY; without even the implied warranty of
      11             : // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
      12             : // Lesser General Public License for more details.
      13             : 
      14             : // You should have received a copy of the GNU Lesser General Public
      15             : // License along with this library; if not, write to the Free Software
      16             : // Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
      17             : 
      18             : // Local includes
      19             : #include "libmesh/face.h"
      20             : #include "libmesh/int_range.h"
      21             : #include "libmesh/point.h"
      22             : 
      23             : // C++ includes
      24             : 
      25             : 
      26             : namespace libMesh
      27             : {
      28             : 
      29     5688675 : Point Face::quasicircumcenter () const
      30             : {
      31     5796539 :   const Point p0 = this->point(0);
      32             : 
      33             :   // We have to use vertex-polygon area rather than real area if we
      34             :   // want this to be consistent for faces with curved edges
      35     1973336 :   Real total_area = 0;
      36     1973336 :   Point weighted_cc_sum;
      37             : 
      38    11378934 :   for (auto v : make_range(2u, this->n_vertices()))
      39             :     {
      40     5798255 :       const Point p1 = this->point(v-1);
      41     5690259 :       const Point p2 = this->point(v);
      42             : 
      43     1973468 :       const Point a = p1-p0;
      44     1973468 :       const Point b = p2-p0;
      45     5582263 :       const Point axb = a.cross(b);
      46     1973468 :       const Real norm2_axb = axb.norm_sq();
      47     5690259 :       const Real area = sqrt(norm2_axb)/2;
      48             : 
      49     5582263 :       const Point cc_minus_p0 = ((a.norm_sq() * b - b.norm_sq() * a).cross(axb)) / 2 / norm2_axb;
      50             : 
      51     1973468 :       weighted_cc_sum += area*cc_minus_p0;
      52     5690259 :       total_area += area;
      53             :     }
      54             : 
      55     1973336 :   weighted_cc_sum /= total_area;
      56     1973336 :   weighted_cc_sum += p0;
      57             : 
      58     7662011 :   return weighted_cc_sum;
      59             : }
      60             : 
      61             : } // namespace libMesh