WFMath  1.0.2
ball_funcs.h
00001 // ball_funcs.h (n-dimensional ball implementation)
00002 //
00003 //  The WorldForge Project
00004 //  Copyright (C) 2000, 2001  The WorldForge Project
00005 //
00006 //  This program is free software; you can redistribute it and/or modify
00007 //  it under the terms of the GNU General Public License as published by
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00009 //  (at your option) any later version.
00010 //
00011 //  This program is distributed in the hope that it will be useful,
00012 //  but WITHOUT ANY WARRANTY; without even the implied warranty of
00013 //  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
00014 //  GNU General Public License for more details.
00015 //
00016 //  You should have received a copy of the GNU General Public License
00017 //  along with this program; if not, write to the Free Software
00018 //  Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
00019 //
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00021 //  the Worldforge Web Site at http://www.worldforge.org.
00022 //
00023 
00024 // Author: Ron Steinke
00025 
00026 #ifndef WFMATH_BALL_FUNCS_H
00027 #define WFMATH_BALL_FUNCS_H
00028 
00029 #include <wfmath/ball.h>
00030 
00031 #include <wfmath/axisbox.h>
00032 #include <wfmath/miniball.h>
00033 
00034 #include <cassert>
00035 
00036 namespace WFMath {
00037 
00038 template<int dim>
00039 AxisBox<dim> Ball<dim>::boundingBox() const
00040 {
00041   Point<dim> p_low, p_high;
00042 
00043   for(int i = 0; i < dim; ++i) {
00044     p_low[i] = m_center[i] - m_radius;
00045     p_high[i] = m_center[i] + m_radius;
00046   }
00047 
00048   bool valid = m_center.isValid();
00049 
00050   p_low.setValid(valid);
00051   p_high.setValid(valid);
00052 
00053   return AxisBox<dim>(p_low, p_high, true);
00054 }
00055 
00056 template<int dim, template<class, class> class container>
00057 Ball<dim> BoundingSphere(const container<Point<dim>, std::allocator<Point<dim> > >& c)
00058 {
00059   _miniball::Miniball<dim> m;
00060   _miniball::Wrapped_array<dim> w;
00061 
00062   typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator i, end = c.end();
00063   bool valid = true;
00064 
00065   for(i = c.begin(); i != end; ++i) {
00066     valid = valid && i->isValid();
00067     for(int j = 0; j < dim; ++j)
00068       w[j] = (*i)[j];
00069     m.check_in(w);
00070   }
00071 
00072   m.build();
00073 
00074 #ifndef NDEBUG
00075   double dummy;
00076 #endif
00077   assert("Check that bounding sphere is good to library accuracy" &&
00078          m.accuracy(dummy) < numeric_constants<CoordType>::epsilon());
00079 
00080   w = m.center();
00081   Point<dim> center;
00082 
00083   for(int j = 0; j < dim; ++j)
00084     center[j] = w[j];
00085 
00086   center.setValid(valid);
00087 
00088   return Ball<dim>(center, std::sqrt(m.squared_radius()));
00089 }
00090 
00091 template<int dim, template<class, class> class container>
00092 Ball<dim> BoundingSphereSloppy(const container<Point<dim>, std::allocator<Point<dim> > >& c)
00093 {
00094   // This is based on the algorithm given by Jack Ritter
00095   // in Volume 2, Number 4 of Ray Tracing News
00096   // <http://www.acm.org/tog/resources/RTNews/html/rtnews7b.html>
00097 
00098   typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator i = c.begin(),
00099                                                 end = c.end();
00100   if (i == end) {
00101     return Ball<dim>();
00102   }
00103 
00104   CoordType min[dim], max[dim];
00105   typename container<Point<dim>, std::allocator<Point<dim> > >::const_iterator min_p[dim], max_p[dim];
00106   bool valid = i->isValid();
00107 
00108   for(int j = 0; j < dim; ++j) {
00109     min[j] = max[j] = (*i)[j];
00110     min_p[j] = max_p[j] = i;
00111   }
00112 
00113   while(++i != end) {
00114     valid = valid && i->isValid();
00115     for(int j = 0; j < dim; ++j) {
00116       if(min[j] > (*i)[j]) {
00117         min[j] = (*i)[j];
00118         min_p[j] = i;
00119       }
00120       if(max[j] < (*i)[j]) {
00121         max[j] = (*i)[j];
00122         max_p[j] = i;
00123       }
00124     }
00125   }
00126 
00127   CoordType span = -1;
00128   int direction = -1;
00129 
00130   for(int j = 0; j < dim; ++j) {
00131     CoordType new_span = max[j] - min[j];
00132     if(new_span > span) {
00133       span = new_span;
00134       direction = j;
00135     }
00136   }
00137 
00138   assert("Have a direction of maximum size" && direction != -1);
00139 
00140   Point<dim> center = Midpoint(*(min_p[direction]), *(max_p[direction]));
00141   CoordType dist = SloppyDistance(*(min_p[direction]), center);
00142 
00143   for(i = c.begin(); i != end; ++i) {
00144     if(i == min_p[direction] || i == max_p[direction])
00145       continue; // We already have these
00146 
00147     CoordType new_dist = SloppyDistance(*i, center);
00148 
00149     if(new_dist > dist) {
00150       CoordType delta_dist = (new_dist - dist) / 2;
00151       // Even though new_dist may be too large, delta_dist / new_dist
00152       // always gives enough of a shift to include the new point.
00153       center += (*i - center) * delta_dist / new_dist;
00154       dist += delta_dist;
00155       assert("Shifted ball contains new point" &&
00156              SquaredDistance(*i, center) <= dist * dist);
00157     }
00158   }
00159 
00160   center.setValid(valid);
00161 
00162   return Ball<dim>(center, dist);
00163 }
00164 
00165 // These two are here, instead of defined in the class, to
00166 // avoid include order problems
00167 
00168 template<int dim>
00169 inline Ball<dim> Point<dim>::boundingSphere() const
00170 {
00171   return Ball<dim>(*this, 0);
00172 }
00173 
00174 template<int dim>
00175 inline Ball<dim> Point<dim>::boundingSphereSloppy() const
00176 {
00177   return Ball<dim>(*this, 0);
00178 }
00179 
00180 } // namespace WFMath
00181 
00182 #endif  // WFMATH_BALL_FUNCS_H