/*
* missing in CGAL?
*/
squared_distance_t squaredDistancePointTriangle3D(
const Point_3& p,
const Triangle_3& abc
)
{
#if CGAL_VERSION_NR >= 1041001000 // >= 4.10
return CGAL::squared_distance(p, abc);
#else
Point_3 a = abc.vertex( 0 );
Point_3 b = abc.vertex( 1 );
Point_3 c = abc.vertex( 2 );
/*
* project P on ABC plane as projP.
*/
Point_3 projP = Plane_3( a, b, c ).projection( p );
squared_distance_t dMin ;
if ( abc.has_on( projP ) ) {
// Is projP is in the triangle, return distance from P to its projection
// on the plane
dMin = CGAL::squared_distance( p, projP ) ;
}
else {
// Else, the distance is the minimum from P to triangle sides
dMin = CGAL::squared_distance( p, Segment_3( a,b ) ) ;
dMin = std::min( dMin, CGAL::squared_distance( p, Segment_3( b,c ) ) );
dMin = std::min( dMin, CGAL::squared_distance( p, Segment_3( c,a ) ) );
}
return dMin ;
#endif
}
squared_distance_t squaredDistanceSegmentTriangle3D(
const Segment_3& sAB,
const Triangle_3& tABC
)
{
typedef Kernel::FT squared_distance_t ;
/*
* If [sAsB] intersects the triangle (tA,tB,tC), distance is 0.0
*/
if ( boost::none != CGAL::intersection( sAB, tABC ) ) {
return 0.0 ;
}
/*
* else, distance is the min of the following values :
* - distance from sA to the Triangle
* - distance from sB to the Triangle
* - distance from sAB to the side of the Triangles
*/
squared_distance_t dMin = squaredDistancePointTriangle3D( sAB.vertex( 0 ), tABC );
dMin = std::min( dMin, squaredDistancePointTriangle3D( sAB.vertex( 1 ), tABC ) );
for ( int i = 0; i < 3; i++ ) {
dMin = std::min( dMin, CGAL::squared_distance( sAB,
Segment_3( tABC.vertex( i ), tABC.vertex( i+1 ) ) )
) ;
}
return dMin ;
}
void Viewer::drawFacet(const Triangle_3& t, const QColor& /*clr*/)
{
// disable lighting
::glDisable( GL_LIGHTING );
// disable depth buffer writing
::glDepthMask( GL_FALSE );
qglColor( m_colorFacet );
::glBegin(GL_TRIANGLES);
Point_3 p0 = t.vertex(0);
Point_3 p1 = t.vertex(1);
Point_3 p2 = t.vertex(2);
::glVertex3f( p0.x(), p0.y(), p0.z() );
::glVertex3f( p1.x(), p1.y(), p1.z() );
::glVertex3f( p2.x(), p2.y(), p2.z() );
::glEnd();
// resume depth buffer writing
::glDepthMask( GL_TRUE );
// resume lighting
::glEnable( GL_LIGHTING );
}
/*
* missing in CGAL?
*/
squared_distance_t squaredDistanceTriangleTriangle3D(
const Triangle_3& triangleA,
const Triangle_3& triangleB
)
{
if ( boost::none != CGAL::intersection( triangleA, triangleB ) ) {
return squared_distance_t( 0 );
}
/*
* min of distance from A segments to B triangle and B segments to A triangle
*/
squared_distance_t dMin = squaredDistanceSegmentTriangle3D(
Segment_3( triangleA.vertex( 0 ), triangleA.vertex( 1 ) ),
triangleB
);
dMin = std::min( dMin, squaredDistanceSegmentTriangle3D(
Segment_3( triangleA.vertex( 1 ), triangleA.vertex( 2 ) ),
triangleB
) );
dMin = std::min( dMin, squaredDistanceSegmentTriangle3D(
Segment_3( triangleA.vertex( 2 ), triangleA.vertex( 0 ) ),
triangleB
) );
dMin = std::min( dMin, squaredDistanceSegmentTriangle3D(
Segment_3( triangleB.vertex( 0 ), triangleB.vertex( 1 ) ),
triangleA
) );
dMin = std::min( dMin, squaredDistanceSegmentTriangle3D(
Segment_3( triangleB.vertex( 1 ), triangleB.vertex( 2 ) ),
triangleA
) );
dMin = std::min( dMin, squaredDistanceSegmentTriangle3D(
Segment_3( triangleB.vertex( 2 ), triangleB.vertex( 0 ) ),
triangleA
) );
return dMin ;
}