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219 | /* *****************************************************************
MESQUITE -- The Mesh Quality Improvement Toolkit
Copyright 2007 Sandia National Laboratories. Developed at the
University of Wisconsin--Madison under SNL contract number
624796. The U.S. Government and the University of Wisconsin
retain certain rights to this software.
This library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
This library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
(lgpl.txt) along with this library; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
(2007) [email protected]
***************************************************************** */
/** \file MsqGeomPrim.cpp
* \brief
* \author Jason Kraftcheck
*/
#include "Mesquite.hpp"
#include "MsqGeomPrim.hpp"
namespace MBMesquite
{
bool MsqLine::intersect( const MsqLine& other, double& param, double epsilon ) const
{
if( !closest( other, param ) ) return false;
Vector3D p1 = point( param );
Vector3D p2 = other.point( other.closest( p1 ) );
return ( p1 - p2 ).length_squared() < epsilon * epsilon;
}
bool MsqLine::closest( const MsqLine& other, double& param ) const
{
const Vector3D N = other.direction() * ( direction() * other.direction() );
const double D = -( N % other.point() );
const double dot = N % direction();
if( dot < DBL_EPSILON ) return false; // parallel
param = -( N % point() + D ) / dot;
return true;
}
bool MsqCircle::three_point( const Vector3D& p1, const Vector3D& p2, const Vector3D& p3, MsqCircle& result )
{
Vector3D norm = ( p1 - p2 ) * ( p3 - p2 );
if( norm.length_squared() < DBL_EPSILON ) return false;
MsqLine line1( 0.5 * ( p1 + p2 ), norm * ( p1 - p2 ) );
MsqLine line2( 0.5 * ( p2 + p3 ), norm * ( p3 - p2 ) );
double t_xsect;
if( !line1.closest( line2, t_xsect ) ) return false;
Vector3D center = line1.point( t_xsect );
double radius = ( ( center - p1 ).length() + ( center - p2 ).length() + ( center - p3 ).length() ) / 3.0;
result = MsqCircle( center, norm, radius );
return true;
}
bool MsqCircle::two_point( const Vector3D& center, const Vector3D& p1, const Vector3D& p2, MsqCircle& result )
{
Vector3D norm = ( p1 - center ) * ( p2 - center );
if( norm.length_squared() < DBL_EPSILON ) return false;
double radius = 0.5 * ( ( center - p1 ).length() + ( center - p2 ).length() );
result = MsqCircle( center, norm, radius );
return true;
}
Vector3D MsqCircle::radial_vector() const
{
int min_idx = 0;
if( normal()[1] < normal()[min_idx] ) min_idx = 1;
if( normal()[2] < normal()[min_idx] ) min_idx = 2;
Vector3D vect( 0, 0, 0 );
vect[min_idx] = 1;
vect = normal() * vect;
vect *= radius() / vect.length();
return vect;
}
Vector3D MsqCircle::closest( const Vector3D& point ) const
{
const Vector3D from_center = point - center();
const Vector3D norm_proj = normal() * ( normal() % from_center ); // unit normal!
const Vector3D in_plane = from_center - norm_proj;
const double length = in_plane.length();<--- Shadow variable
if( length < DBL_EPSILON )
return center() + radial_vector();
else
return center() + in_plane * radius() / length;
}
bool MsqCircle::closest( const Vector3D& point, Vector3D& result_pt, Vector3D& result_tngt ) const
{
const Vector3D from_center = point - center();
Vector3D in_plane = from_center - ( from_center % normal() );
if( in_plane.length_squared() < DBL_EPSILON ) return false;
result_pt = center() + in_plane * radius() / in_plane.length();
result_tngt = in_plane * normal();
return true;
}
MsqPlane::MsqPlane( const Vector3D& p_normal, double coeff )
{
const double len = p_normal.length();
mNormal = p_normal / len;
mCoeff = coeff / len;
}
MsqPlane::MsqPlane( const Vector3D& p_normal, const Vector3D& p_point )
: mNormal( p_normal / p_normal.length() ), mCoeff( -( mNormal % p_point ) )
{
}
MsqPlane::MsqPlane( double a, double b, double c, double d ) : mNormal( a, b, c ), mCoeff( d )
{
const double len = mNormal.length();
mNormal /= len;
mCoeff /= len;
}
bool MsqPlane::intersect( const MsqPlane& plane, MsqLine& result ) const
{
const double dot = normal() % plane.normal();
const double det = dot * dot - 1.0;
if( fabs( det ) < DBL_EPSILON ) // parallel
return false;
const double s1 = ( coefficient() - dot * plane.coefficient() ) / det;
const double s2 = ( plane.coefficient() - dot * coefficient() ) / det;
result = MsqLine( s1 * normal() + s2 * plane.normal(), normal() * plane.normal() );
return true;
}
bool MsqPlane::intersect( const MsqLine& line, double& result ) const
{
const double dot = line.direction() % normal();
if( fabs( dot ) < DBL_EPSILON ) return false;
result = -( normal() % line.point() + coefficient() ) / dot;
return true;
}
Vector3D MsqSphere::closest( const Vector3D& point ) const
{
Vector3D diff = point - center();
double len = diff.length();
if( len < DBL_EPSILON )
{
// pick any point
diff = Vector3D( 1, 0, 0 );
len = 1;
}
return center() + diff * radius() / len;
}
bool MsqSphere::closest( const Vector3D& point, Vector3D& point_on_sphere, Vector3D& normal_at_point ) const
{
normal_at_point = point - center();
double len = normal_at_point.length();
if( len < DBL_EPSILON ) return false;
normal_at_point /= len;
point_on_sphere = center() + radius() * normal_at_point;
return true;
}
bool MsqSphere::intersect( const MsqPlane& plane, MsqCircle& result ) const
{
const Vector3D plane_pt = plane.closest( center() );
const Vector3D plane_dir = plane_pt - center();
const double dir_sqr = plane_dir.length_squared();
if( dir_sqr < DBL_EPSILON )
{ // plane passes through center of sphere
result = MsqCircle( center(), plane.normal(), radius() );
return true;
}
double rad_sqr = radius() * radius() - plane_dir.length_squared();
if( rad_sqr < 0 ) // no intersection
return false;
result = MsqCircle( plane_pt, plane_dir, sqrt( rad_sqr ) );
return true;
}
bool MsqSphere::intersect( const MsqSphere& sphere, MsqCircle& result ) const
{
const Vector3D d = sphere.center() - center();
const double dist = d.length();
if( dist > ( radius() + sphere.radius() ) ) return false;
const double r1_sqr = radius() * radius();
const double r2_sqr = sphere.radius() * sphere.radius();
const double f = ( d % d + r1_sqr - r2_sqr ) / 2;
// const double d1 = f / dist;
const double rad = sqrt( r1_sqr - f * f / ( d % d ) );
Vector3D c = center() + d * f / ( d % d );
result = MsqCircle( c, d, rad );
return true;
}
} // namespace MBMesquite
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