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 ;
}
/*
* 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
}
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 );
}
double Q(const Triangle_3& t)
{
const double S = sqrt(t.squared_area());
const double p = (1/2.0) * (dist(t[0],t[1]) + dist(t[1],t[2]) + dist(t[2],t[0]));
const double rho = S/p;
const double h = max(dist(t[0],t[1]), max(dist(t[1],t[2]), dist(t[2],t[0])));
return (6/sqrt(3)) * rho/h;
}
/*
* 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 ;
}
// -------------------------------------------------------------
// dg_voronoi_point
// -------------------------------------------------------------
// This function computes a voronoi point when some degeneracies
// have been discovered about the four points of a tetrahedron.
//
// In this function we assume that the degeneracies occured
// because of the coplanarity. We approximate the circumcenter
// of the tetrahedron by the circumcenter of one of the triangular
// facets.
// -------------------------------------------------------------
Point
dg_voronoi_point(const Point &a,
const Point &b,
const Point &c,
const Point &d,
bool &is_correct_computation)
{
// First, we check if our assumption is correct.
// This is more of a debugging purpose than of
// actual computation.
Tetrahedron t = Tetrahedron(a,b,c,d);
if( ! t.is_degenerate() )
{
// cerr << "error in the assumption of coplanarity." << endl;
/*
// debug
cout << "{OFF " << endl;
cout << "4 4 0" << endl;
cout << a << "\n" << b << "\n" << c << "\n" << d << endl;
cout << "3\t0 1 2" << endl;
cout << "3\t0 2 3" << endl;
cout << "3\t0 3 1" << endl;
cout << "3\t1 2 3" << endl;
cout << "}" << endl;
// end debug
*/
}
// Approximate the circumcenter of the tetrahedron with that of
// one of its triangular facets. The facet should not be collinear.
// The following boolean variable will keep track if we have found
// a valid circumcenter (of a triangle) to replace that of a
// tetrahedron.
Point cc = CGAL::ORIGIN;
is_correct_computation = false;
Point p[4] = {a,b,c,d};
for(int i = 0; i < 4; i ++)
{
// first check if the facet is degenerate or not.
Triangle_3 t = Triangle_3(p[(i+1)%4], p[(i+2)%4], p[(i+3)%4]);
if( t.is_degenerate() ) continue;
// since we found a non-degenerate triangle we can now compute
// its circumcenter and we will be done.
cc = nondg_cc_tr_3(p[(i+1)%4], p[(i+2)%4], p[(i+3)%4], is_correct_computation);
if( is_correct_computation )
break;
}
if( is_correct_computation )
{
if(cc == CGAL::ORIGIN) cerr << "<dg_vp : returning cc as ORIGIN>" << endl;
return cc;
}
cerr << "four points are colinear. " << endl;
// for the time being, I just average the four points. What should be
// the circumcenter of a tetrahedron whose four points are collinear ?
cc = CGAL::ORIGIN +
( 0.25*Vector
(
a[0]+b[0]+c[0]+d[0],
a[1]+b[1]+c[1]+d[1],
a[2]+b[2]+c[2]+d[2]
)
);
if(cc == CGAL::ORIGIN) cerr << "<dg_vp : returning cc as ORIGIN>" << endl;
return cc;
}
float
sdf( const Point& q, const Mesh &mesh, const vector<double>& weights,
KdTree& kd_tree, const Triangulation& triang )
{
VECTOR3 query (CGAL::to_double(q.x()),
CGAL::to_double(q.y()),
CGAL::to_double(q.z()));
kd_tree.queryPosition(query);
// Initialize the search structure, and search all N points
int n_vid = kd_tree.getNeighbourPositionIndex(0);
if(n_vid == -1) throw std::runtime_error("No nearest neighbor. MDS empty?");
CGAL_assertion( ! mesh.vert_list[n_vid].iso());
MVertex nv = mesh.vert_list[n_vid];
double min_sq_d = HUGE;
int n_fid = -1;
for(int i = 0; i < nv.num_inc_face; i ++)
{
MFace f = mesh.face_list[nv.inc_face(i)];
Point p[3] = {mesh.vert_list[f.get_corner(0)].point(),
mesh.vert_list[f.get_corner(1)].point(),
mesh.vert_list[f.get_corner(2)].point()};
Triangle_3 t (p[0], p[1], p[2]);
Plane_3 H (p[0], p[1], p[2]);
Point _q = H.projection(q);
// check if _q is inside t.
if( t.has_on(_q) )
{
double sq_d = CGAL::to_double((q-_q)*(q-_q));
if( sq_d < min_sq_d ) { min_sq_d = sq_d; n_fid = nv.inc_face(i); }
}
else
{
for(int j = 0; j < 3; j ++)
{
double _d = CGAL::to_double(CGAL::squared_distance(_q,Segment(p[j], p[(j+1)%3])));
double sq_d = CGAL::to_double((q-_q)*(q-_q)) + _d;
if( sq_d < min_sq_d ) { min_sq_d = sq_d; n_fid = nv.inc_face(i); }
}
}
}
// locate the query point in the triang which is already tagged
// with in-out flag by the reconstruction.
bool is_q_outside = false;
Triangulation::Locate_type lt;
int u = -1, v = -1;
Cell_handle c = triang.locate(q, lt, u, v);
if( lt == Triangulation::OUTSIDE_AFFINE_HULL )
{
is_q_outside = true;
cerr << "Point " << q << " is outside the affine hull." << endl;
}
else if( lt == Triangulation::OUTSIDE_CONVEX_HULL )
is_q_outside = true;
else
{
if( lt == Triangulation::CELL )
{
if( c->outside )
is_q_outside = true;
else
is_q_outside = false;
}
else if( lt == Triangulation::FACET )
{
Cell_handle _c = c->neighbor(u);
if( c->outside && _c->outside )
is_q_outside = true;
else
is_q_outside = false;
}
else if( lt == Triangulation::EDGE )
{
if( is_outside_VF(triang, Edge(c, u, v)) )
is_q_outside = true;
else
is_q_outside = false;
}
else
{
CGAL_assertion( lt == Triangulation::VERTEX );
is_q_outside = false;
}
}
double w;
if(weights.size() && mesh.face_list[n_fid].label != -1) w = weights[mesh.face_list[n_fid].label];
else w = 1.0;
// double w = mesh.face_list[n_fid].w;
double gen_sdf = 0;
if( is_q_outside ) gen_sdf = w*sqrt(min_sq_d);
else gen_sdf = -w*min_sq_d;
#if 0
double MAX = 10, MIN = -10;
if( gen_sdf > MAX ) gen_sdf = MAX;
if( gen_sdf < MIN ) gen_sdf = MIN;
#endif
return gen_sdf;
}