MOAB: Mesh Oriented datABase  (version 5.3.1)
MsqGeomPrim.cpp
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00001 /* *****************************************************************
00002     MESQUITE -- The Mesh Quality Improvement Toolkit
00003 
00004     Copyright 2007 Sandia National Laboratories.  Developed at the
00005     University of Wisconsin--Madison under SNL contract number
00006     624796.  The U.S. Government and the University of Wisconsin
00007     retain certain rights to this software.
00008 
00009     This library is free software; you can redistribute it and/or
00010     modify it under the terms of the GNU Lesser General Public
00011     License as published by the Free Software Foundation; either
00012     version 2.1 of the License, or (at your option) any later version.
00013 
00014     This library is distributed in the hope that it will be useful,
00015     but WITHOUT ANY WARRANTY; without even the implied warranty of
00016     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
00017     Lesser General Public License for more details.
00018 
00019     You should have received a copy of the GNU Lesser General Public License
00020     (lgpl.txt) along with this library; if not, write to the Free Software
00021     Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
00022 
00023     (2007) kraftche@cae.wisc.edu
00024 
00025   ***************************************************************** */
00026 
00027 /** \file MsqGeomPrim.cpp
00028  *  \brief
00029  *  \author Jason Kraftcheck
00030  */
00031 
00032 #include "Mesquite.hpp"
00033 #include "MsqGeomPrim.hpp"
00034 
00035 namespace MBMesquite
00036 {
00037 
00038 bool MsqLine::intersect( const MsqLine& other, double& param, double epsilon ) const
00039 {
00040     if( !closest( other, param ) ) return false;
00041     Vector3D p1 = point( param );
00042     Vector3D p2 = other.point( other.closest( p1 ) );
00043     return ( p1 - p2 ).length_squared() < epsilon * epsilon;
00044 }
00045 
00046 bool MsqLine::closest( const MsqLine& other, double& param ) const
00047 {
00048     const Vector3D N = other.direction() * ( direction() * other.direction() );
00049     const double D   = -( N % other.point() );
00050     const double dot = N % direction();
00051     if( dot < DBL_EPSILON ) return false;  // parallel
00052     param = -( N % point() + D ) / dot;
00053     return true;
00054 }
00055 
00056 bool MsqCircle::three_point( const Vector3D& p1, const Vector3D& p2, const Vector3D& p3, MsqCircle& result )
00057 {
00058     Vector3D norm = ( p1 - p2 ) * ( p3 - p2 );
00059     if( norm.length_squared() < DBL_EPSILON ) return false;
00060 
00061     MsqLine line1( 0.5 * ( p1 + p2 ), norm * ( p1 - p2 ) );
00062     MsqLine line2( 0.5 * ( p2 + p3 ), norm * ( p3 - p2 ) );
00063     double t_xsect;
00064     if( !line1.closest( line2, t_xsect ) ) return false;
00065 
00066     Vector3D center = line1.point( t_xsect );
00067     double radius   = ( ( center - p1 ).length() + ( center - p2 ).length() + ( center - p3 ).length() ) / 3.0;
00068     result          = MsqCircle( center, norm, radius );
00069     return true;
00070 }
00071 
00072 bool MsqCircle::two_point( const Vector3D& center, const Vector3D& p1, const Vector3D& p2, MsqCircle& result )
00073 {
00074     Vector3D norm = ( p1 - center ) * ( p2 - center );
00075     if( norm.length_squared() < DBL_EPSILON ) return false;
00076 
00077     double radius = 0.5 * ( ( center - p1 ).length() + ( center - p2 ).length() );
00078     result        = MsqCircle( center, norm, radius );
00079     return true;
00080 }
00081 
00082 Vector3D MsqCircle::radial_vector() const
00083 {
00084     int min_idx = 0;
00085     if( normal()[1] < normal()[min_idx] ) min_idx = 1;
00086     if( normal()[2] < normal()[min_idx] ) min_idx = 2;
00087     Vector3D vect( 0, 0, 0 );
00088     vect[min_idx] = 1;
00089     vect          = normal() * vect;
00090     vect *= radius() / vect.length();
00091     return vect;
00092 }
00093 
00094 Vector3D MsqCircle::closest( const Vector3D& point ) const
00095 {
00096     const Vector3D from_center = point - center();
00097     const Vector3D norm_proj   = normal() * ( normal() % from_center );  // unit normal!
00098     const Vector3D in_plane    = from_center - norm_proj;
00099     const double length        = in_plane.length();
00100     if( length < DBL_EPSILON )
00101         return center() + radial_vector();
00102     else
00103         return center() + in_plane * radius() / length;
00104 }
00105 
00106 bool MsqCircle::closest( const Vector3D& point, Vector3D& result_pt, Vector3D& result_tngt ) const
00107 {
00108     const Vector3D from_center = point - center();
00109     Vector3D in_plane          = from_center - ( from_center % normal() );
00110     if( in_plane.length_squared() < DBL_EPSILON ) return false;
00111 
00112     result_pt   = center() + in_plane * radius() / in_plane.length();
00113     result_tngt = in_plane * normal();
00114     return true;
00115 }
00116 
00117 MsqPlane::MsqPlane( const Vector3D& p_normal, double coeff )
00118 {
00119     const double len = p_normal.length();
00120     mNormal          = p_normal / len;
00121     mCoeff           = coeff / len;
00122 }
00123 
00124 MsqPlane::MsqPlane( const Vector3D& p_normal, const Vector3D& p_point )
00125     : mNormal( p_normal / p_normal.length() ), mCoeff( -( mNormal % p_point ) )
00126 {
00127 }
00128 
00129 MsqPlane::MsqPlane( double a, double b, double c, double d ) : mNormal( a, b, c ), mCoeff( d )
00130 {
00131     const double len = mNormal.length();
00132     mNormal /= len;
00133     mCoeff /= len;
00134 }
00135 
00136 bool MsqPlane::intersect( const MsqPlane& plane, MsqLine& result ) const
00137 {
00138     const double dot = normal() % plane.normal();
00139     const double det = dot * dot - 1.0;
00140     if( fabs( det ) < DBL_EPSILON )  // parallel
00141         return false;
00142 
00143     const double s1 = ( coefficient() - dot * plane.coefficient() ) / det;
00144     const double s2 = ( plane.coefficient() - dot * coefficient() ) / det;
00145     result          = MsqLine( s1 * normal() + s2 * plane.normal(), normal() * plane.normal() );
00146     return true;
00147 }
00148 
00149 bool MsqPlane::intersect( const MsqLine& line, double& result ) const
00150 {
00151     const double dot = line.direction() % normal();
00152     if( fabs( dot ) < DBL_EPSILON ) return false;
00153 
00154     result = -( normal() % line.point() + coefficient() ) / dot;
00155     return true;
00156 }
00157 
00158 Vector3D MsqSphere::closest( const Vector3D& point ) const
00159 {
00160     Vector3D diff = point - center();
00161     double len    = diff.length();
00162     if( len < DBL_EPSILON )
00163     {
00164         // pick any point
00165         diff = Vector3D( 1, 0, 0 );
00166         len  = 1;
00167     }
00168 
00169     return center() + diff * radius() / len;
00170 }
00171 
00172 bool MsqSphere::closest( const Vector3D& point, Vector3D& point_on_sphere, Vector3D& normal_at_point ) const
00173 {
00174     normal_at_point = point - center();
00175     double len      = normal_at_point.length();
00176     if( len < DBL_EPSILON ) return false;
00177 
00178     normal_at_point /= len;
00179     point_on_sphere = center() + radius() * normal_at_point;
00180     return true;
00181 }
00182 
00183 bool MsqSphere::intersect( const MsqPlane& plane, MsqCircle& result ) const
00184 {
00185     const Vector3D plane_pt  = plane.closest( center() );
00186     const Vector3D plane_dir = plane_pt - center();
00187     const double dir_sqr     = plane_dir.length_squared();
00188     if( dir_sqr < DBL_EPSILON )
00189     {  // plane passes through center of sphere
00190         result = MsqCircle( center(), plane.normal(), radius() );
00191         return true;
00192     }
00193 
00194     double rad_sqr = radius() * radius() - plane_dir.length_squared();
00195     if( rad_sqr < 0 )  // no intersection
00196         return false;
00197 
00198     result = MsqCircle( plane_pt, plane_dir, sqrt( rad_sqr ) );
00199     return true;
00200 }
00201 
00202 bool MsqSphere::intersect( const MsqSphere& sphere, MsqCircle& result ) const
00203 {
00204     const Vector3D d  = sphere.center() - center();
00205     const double dist = d.length();
00206     if( dist > ( radius() + sphere.radius() ) ) return false;
00207 
00208     const double r1_sqr = radius() * radius();
00209     const double r2_sqr = sphere.radius() * sphere.radius();
00210     const double f      = ( d % d + r1_sqr - r2_sqr ) / 2;
00211     // const double d1 = f / dist;
00212 
00213     const double rad = sqrt( r1_sqr - f * f / ( d % d ) );
00214     Vector3D c       = center() + d * f / ( d % d );
00215     result           = MsqCircle( c, d, rad );
00216     return true;
00217 }
00218 
00219 }  // namespace MBMesquite
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