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 ;
}
std::string pp(const Segment_3& segment)
{
std::stringstream out;
out << std::setprecision(pp_precision);
out << "[" << pp(segment.source()) << ", " << pp(segment.target()) << "]";
return out.str();
}
std::string pp_id(const Segment_3& segment)
{
std::stringstream out;
size_t a = segment.source().id();
size_t b = segment.target().id();
if (a > b)
swap(a, b);
out << a << "--" << b;
return out.str();
}
double errorOfLineInPlane(Segment_3 &l, Eigen::Vector3d& point, Eigen::Vector3d& normal)
{
Plane_3 plane( Point_3(point.x(), point.y(), point.z()),
Vector_3(normal.x(), normal.y(), normal.z()) );
double dist1 = squared_distance(plane, l.point(0));
double dist2 = squared_distance(plane, l.point(1));
return 0.5*(sqrt(dist1)+sqrt(dist2));
}
void Viewer::draw()
{
if( m_pScene == NULL ) return;
QFont fontPrompt("Arial", 14);
if( m_showAxis ) {
qglColor(::Qt::black);
drawAxis( sceneRadius() );
}
/* Draw vertices */
if ( m_showVertex && m_pScene->m_dt.number_of_vertices()>0 ) {
for(QList<Vertex_handle>::iterator vit = m_pScene->m_vhArray.begin();
vit < m_pScene->m_vhArray.end(); ++vit) {
if( m_curMode == SELECT && (*vit)->isSeled() ) continue;
if( (*vit) == m_nearestNb ) continue;
drawVertex( (*vit)->point(), m_colorVertex, m_fSizeVertex );
}//end-for-points
}//end-if-points
/* Draw all points during incremental mode */
if( !m_incrementalPts.isEmpty() ) {
/* draw the rest to-be-inserted vertices */
for(QList<Point_3>::iterator pit=m_incrementalPts.begin();
pit < m_incrementalPts.end(); ++pit) {
drawVertex( (*pit), ::Qt::gray, m_fSizeVertex );
}
switch( m_curStep ) {
case NEWPT:
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( 10, 20, tr("Highlight the next-to-insert point"), fontPrompt );
/* Highlight the next-to-insert point */
drawVertex( m_curIncPt, ::Qt::red, m_fSizeVertex );
break;
case CELL: // show the tetrahedron that contains the point
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( 10, 20, tr("Show the tetrahedron containing the point"), fontPrompt );
drawText( 10, 40, tr("(Only finite facets are drawn)"), fontPrompt );
/* Highlight the next-to-insert vertex */
drawVertex( m_curIncPt, ::Qt::red, m_fSizeVertex );
/* Draw the cell containing that point */
for(int i=0; i<4; ++i) {
if( m_pScene->m_dt.is_infinite(m_cellContain, i) ) continue;
drawFacet( m_pScene->m_dt.triangle( m_cellContain, i ), m_colorFacet );
}//end-for-facets
break;
case CONFLICT: // show the conflict region
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( 10, 20, tr("Show the conflict region"), fontPrompt );
/* Highlight the next-to-insert vertex */
drawVertex( m_curIncPt, ::Qt::red, m_fSizeVertex );
/* Draw conflict region */
for(QList<Facet>::iterator fit = m_boundaryFacets.begin();
fit < m_boundaryFacets.end(); ++fit) {
if( m_pScene->m_dt.is_infinite(*fit) ) continue;
drawFacet( m_pScene->m_dt.triangle(*fit), QColor(215, 80, 0, 96) ); //semi-transparent purple
}//end-for-facets
break;
default:
break;
}//end-of=switch
}//end-if-incpts
/* Draw Delaunay edges */
if( m_showDEdge ) {
for(edges_iterator eit = m_pScene->m_dt.finite_edges_begin();
eit != m_pScene->m_dt.finite_edges_end(); ++eit) {
Segment_3 seg = m_pScene->m_dt.segment(*eit);
drawEdge( seg.vertex(0), seg.vertex(1), m_colorDEdge, m_fSizeDEdge );
}//end-for-edges
}//end-if-dt
/* Draw Voronoi edges */
if( m_showVEdge ) {
for(facets_iterator fit = m_pScene->m_dt.finite_facets_begin();
fit != m_pScene->m_dt.finite_facets_end(); ++fit) {
Object_3 o = m_pScene->m_dt.dual(*fit);
if (const Segment_3 *s = CGAL::object_cast<Segment_3>(&o)) {
drawEdge( s->vertex(0), s->vertex(1), m_colorVEdge, m_fSizeVEdge );
} else if (const Ray_3 *r = CGAL::object_cast<Ray_3>(&o)) {
drawEdge( r->point(0), // the source of the ray
r->point(1), // another point on the ray, different from the source
m_colorVEdge, m_fSizeVEdge );
}
}//end-for-edges
}//end-if-vd
/* Draw facets */
if( m_showFacet ) {
for(facets_iterator fit = m_pScene->m_dt.finite_facets_begin();
fit != m_pScene->m_dt.finite_facets_end(); ++fit) {
drawFacet( m_pScene->m_dt.triangle(*fit), m_colorFacet );
}//end-for-facets
}//end-if-facets
/* Insert vertex mode */
if( m_curMode == INSERT_V ) {
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( width()-200, 20, tr("Shift+Left: Insert a vertex"), fontPrompt );
drawText( width()-200, 40, tr("Shift+Wheel: Resize trackball"), fontPrompt );
/* Draw the trackball */
drawSphere( m_fRadius, m_colorTrackball );
}//end-if-insv
/* Insert point mode */
else if( m_curMode == INSERT_PT ) {
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( width()-200, 20, tr("Shift+Left: Insert a point"), fontPrompt );
drawText( width()-200, 40, tr("Hold Left: Move the point"), fontPrompt );
drawText( width()-200, 60, tr("Return: Insert to DT"), fontPrompt );
drawText( width()-200, 80, tr("Escape: Cancel insertion"), fontPrompt );
drawText( width()-200, 100, tr("Shift+Wheel: Resize trackball"), fontPrompt );
/* Draw the trackball */
drawSphere( m_fRadius, m_colorTrackball );
if( m_hasNewPt ) {
/* Draw the newly inserted point */
drawVertex( m_newPt, ::Qt::red, m_fSizeVertex );
/* Draw conflict region */
for(QList<Facet>::iterator fit = m_boundaryFacets.begin();
fit < m_boundaryFacets.end(); ++fit) {
if( m_pScene->m_dt.is_infinite(*fit) ) continue;
drawFacet( m_pScene->m_dt.triangle(*fit), QColor(215, 80, 0, 96) ); //semi-transparent purple
}//end-for-facets
}//end-if-shown
}//end-if-inspt
/* Select mode */
else if( m_curMode == SELECT) {
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( width()-200, 20, tr("Shift+Left: Select"), fontPrompt );
drawText( width()-200, 40, tr("Ctrl+Left: Add selection"),
QFont("Arial", 14) );
drawText( width()-200, 60, tr("Escape: Cancel selection"), fontPrompt );
drawText( width()-200, 80, tr("DEL: Delete selected"), fontPrompt );
/* Highlight the selected vertices */
for(QList<int>::iterator vit=m_vidSeled.begin(); vit<m_vidSeled.end(); ++vit) {
drawVertex( m_pScene->m_vhArray.at(*vit)->point(), ::Qt::red, m_fSizeVertex );
}//end-for-seledpts
/* Draw the multiple selection window */
if( m_isPress ) {
::glDisable( GL_LIGHTING );
startScreenCoordinatesSystem();
qglColor( QColor(80, 180, 180, 64) );
::glBegin(GL_QUADS);
::glVertex2i(m_rectSel.left(), m_rectSel.top());
::glVertex2i(m_rectSel.right(), m_rectSel.top());
::glVertex2i(m_rectSel.right(), m_rectSel.bottom());
::glVertex2i(m_rectSel.left(), m_rectSel.bottom());
::glEnd();
stopScreenCoordinatesSystem();
::glEnable( GL_LIGHTING );
}//end-if-press
}//end-if-sel
/* Move mode */
else if( m_curMode == MOVE ) {
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( width()-200, 20, tr("Left Click: Select"), fontPrompt );
if( m_isMoving ) {
drawText( width()-200, 40, tr("Shift+Wheel: Resize trackball"), fontPrompt );
/* Draw the trackball */
drawSphere( m_fRadius, m_colorTrackball );
/* Highlight the moving point */
drawVertex( m_pScene->m_vhArray.at( m_vidMoving )->point(), ::Qt::red, m_fSizeVertex );
}//end-if-v
}//end-if-move
/* FindNb mode */
else if( m_curMode == FINDNB ) {
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( width()-200, 20, tr("Shift+Left: Place query point"), fontPrompt );
drawText( width()-200, 40, tr("Shift+Wheel: Resize trackball"), fontPrompt );
/* Draw the trackball */
drawSphere( m_fRadius, m_colorTrackball );
/* Draw the nearest neighbor */
if( m_nearestNb != NULL ) {
drawVertex( m_queryPt, ::Qt::red, m_fSizeVertex );
drawVertex( m_nearestNb->point(), ::Qt::red, m_fSizeVertex );
}
}//end-if-findnb
/* EmptySphere mode */
else if( m_curMode == EMPTYSPH ) {
/* Show prompt messages */
qglColor( ::Qt::black );
drawText( width()-200, 20, tr("Shift+Left: Place query point"), fontPrompt );
drawText( width()-200, 40, tr("Press S: Show/Hide trackball"), fontPrompt );
drawText( width()-200, 60, tr("Shift+Wheel: Resize trackball"), fontPrompt );
/* Draw the trackball */
if( m_showTrackball )
drawSphere( m_fRadius, m_colorTrackball );
if( m_hasEmptyS ) {
/* Draw the query point */
drawVertex( m_queryPt, ::Qt::red, m_fSizeVertex );
/* Draw the cell containing that point */
for(int i=0; i<4; ++i) {
if( m_pScene->m_dt.is_infinite(m_cellContain, i) ) continue;
drawFacet( m_pScene->m_dt.triangle( m_cellContain, i ), m_colorFacet );
}//end-for-facets
/* Draw the sphere */
drawSphere( m_fREmptyS, m_colorEmptySphere, m_centerPt );
}
}//end-if-emptyS
}
Segment_2 project_2(const Segment_3& s)
{
return Segment_2(s.source().point_2(), s.target().point_2());
}
Segment_3 lexicographically_ordered(const Segment_3& s)
{
if (CGAL::lexicographically_xyz_smaller(s.source(), s.target()))
return s;
return s.opposite();
}
void Viewer::compute_elements()
{
//glColor3f(1.0f, 0.72f, 0.06f);
pos_points.resize(0);
pos_lines.resize(0);
pos_8lines.resize(0);
pos_8lines2D.resize(0);
for(Periodic_point_iterator ppit
= scene->periodic_triangulation.periodic_points_begin(
P3DT3::UNIQUE) ;
ppit != scene->periodic_triangulation.periodic_points_end(P3DT3::UNIQUE);
++ppit){
Point_3 p(scene->periodic_triangulation.point(*ppit));
pos_points.push_back(p.x()); pos_points.push_back(p.y()); pos_points.push_back(p.z());
}
//glColor3f(0.27f, 0.51f, 0.7f);
for (Periodic_triangle_iterator ptit
= scene->periodic_triangulation.periodic_triangles_begin(
P3DT3::UNIQUE);
ptit != scene->periodic_triangulation.periodic_triangles_end(
P3DT3::UNIQUE);
++ptit) {
for (int i=0 ; i<4 ; i++) {
Segment_3 dual = scene->periodic_triangulation.construct_segment(
scene->periodic_triangulation.dual(*(ptit.get_facet())));
FT sz = dual.source().z();
FT tz = dual.target().z();
if (scene->two_dimensional && ((sz-tz > 0.5) || (sz-tz < -0.5))) continue;
if (scene->two_dimensional) { sz = 0.; tz = 0.; }
FT sx = dual.source().x();
FT tx = dual.target().x();
FT sy = dual.source().y();
FT ty = dual.target().y();
pos_lines.push_back(sx); pos_lines.push_back(sy); pos_lines.push_back(sz);
pos_lines.push_back(tx); pos_lines.push_back(ty); pos_lines.push_back(tz);
Iso_cuboid_3 d = scene->periodic_triangulation.domain();
pos_8lines2D.push_back(sx+0.); pos_8lines2D.push_back(sy+d.ymax()-d.ymin()); pos_8lines2D.push_back(sz+0.);
pos_8lines2D.push_back(tx+0.); pos_8lines2D.push_back(ty+d.ymax()-d.ymin()); pos_8lines2D.push_back(tz+0.);
pos_8lines2D.push_back(sx+d.xmax()-d.xmin()); pos_8lines2D.push_back(sy+0.); pos_8lines2D.push_back(sz+0.);
pos_8lines2D.push_back(tx+d.xmax()-d.xmin()); pos_8lines2D.push_back(ty+0.); pos_8lines2D.push_back(tz+0.);
pos_8lines2D.push_back(sx+d.xmax()-d.xmin()); pos_8lines2D.push_back(sy+d.ymax()-d.ymin()); pos_8lines2D.push_back(sz+0.);
pos_8lines2D.push_back(tx+d.xmax()-d.xmin()); pos_8lines2D.push_back(ty+d.ymax()-d.ymin()); pos_8lines2D.push_back(tz+0.);
pos_8lines.push_back(sx+0.); pos_8lines.push_back(sy+0.); pos_8lines.push_back(sz+d.zmax()-d.zmin());
pos_8lines.push_back(tx+0.); pos_8lines.push_back(ty+0.); pos_8lines.push_back(tz+d.zmax()-d.zmin());
pos_8lines.push_back(sx+0.); pos_8lines.push_back(sy+d.ymax()-d.ymin()); pos_8lines.push_back(sz+d.zmax()-d.zmin());
pos_8lines.push_back(tx+0.); pos_8lines.push_back(ty+d.ymax()-d.ymin()); pos_8lines.push_back(tz+d.zmax()-d.zmin());
pos_8lines.push_back(sx+d.xmax()-d.xmin()); pos_8lines.push_back(sy+0.); pos_8lines.push_back(sz+d.zmax()-d.zmin());
pos_8lines.push_back(tx+d.xmax()-d.xmin()); pos_8lines.push_back(ty+0.); pos_8lines.push_back(tz+d.zmax()-d.zmin());
pos_8lines.push_back(sx+d.xmax()-d.xmin()); pos_8lines.push_back(sy+d.ymax()-d.ymin()); pos_8lines.push_back(sz+d.zmax()-d.zmin());
pos_8lines.push_back(tx+d.xmax()-d.xmin()); pos_8lines.push_back(ty+d.ymax()-d.ymin()); pos_8lines.push_back(tz+d.zmax()-d.zmin());
}
}
}
void
Viewer::gl_draw_surface()
{
::glColor3f(1.0f, 0.72f, 0.06f);
::glDisable(GL_LIGHTING);
::glEnable(GL_BLEND);
::glEnable(GL_POINT_SMOOTH);
::glHint(GL_POINT_SMOOTH_HINT, GL_NICEST);
::glEnable(GL_LINE_SMOOTH);
::glHint(GL_LINE_SMOOTH_HINT, GL_NICEST);
::glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
::glPointSize(5);
::glBegin(GL_POINTS);
for(Periodic_point_iterator ppit
= scene->periodic_triangulation.periodic_points_begin(
P3DT3::UNIQUE) ;
ppit != scene->periodic_triangulation.periodic_points_end(P3DT3::UNIQUE);
++ppit){
Point_3 p(scene->periodic_triangulation.point(*ppit));
::glVertex3d(p.x(), p.y(), p.z());
}
::glEnd();
::glBegin(GL_LINES);
::glColor3f(0.27f, 0.51f, 0.7f);
for (Periodic_triangle_iterator ptit
= scene->periodic_triangulation.periodic_triangles_begin(
P3DT3::UNIQUE);
ptit != scene->periodic_triangulation.periodic_triangles_end(
P3DT3::UNIQUE);
++ptit) {
for (int i=0 ; i<4 ; i++) {
Segment_3 dual = scene->periodic_triangulation.segment(
scene->periodic_triangulation.dual(*(ptit.get_facet())));
FT sz = dual.source().z();
FT tz = dual.target().z();
if (scene->two_dimensional && ((sz-tz > 0.5) || (sz-tz < -0.5))) continue;
if (scene->two_dimensional) { sz = 0.; tz = 0.; }
FT sx = dual.source().x();
FT tx = dual.target().x();
FT sy = dual.source().y();
FT ty = dual.target().y();
::glVertex3d(sx,sy,sz); ::glVertex3d(tx,ty,tz);
Iso_cuboid_3 d = scene->periodic_triangulation.domain();
if (scene->eight_copies) {
::glColor3f(0.69f, 0.77f, 0.87f);
::glVertex3d(sx+0.,sy+d.ymax()-d.ymin(),sz+0.);
::glVertex3d(tx+0.,ty+d.ymax()-d.ymin(),tz+0.);
::glVertex3d(sx+d.xmax()-d.xmin(),sy+0.,sz+0.);
::glVertex3d(tx+d.xmax()-d.xmin(),ty+0.,tz+0.);
::glVertex3d(sx+d.xmax()-d.xmin(),sy+d.ymax()-d.ymin(),sz+0.);
::glVertex3d(tx+d.xmax()-d.xmin(),ty+d.ymax()-d.ymin(),tz+0.);
if (!scene->two_dimensional) {
::glVertex3d(sx+0.,sy+0.,sz+d.zmax()-d.zmin());
::glVertex3d(tx+0.,ty+0.,tz+d.zmax()-d.zmin());
::glVertex3d(sx+0.,sy+d.ymax()-d.ymin(),sz+d.zmax()-d.zmin());
::glVertex3d(tx+0.,ty+d.ymax()-d.ymin(),tz+d.zmax()-d.zmin());
::glVertex3d(sx+d.xmax()-d.xmin(),sy+0.,sz+d.zmax()-d.zmin());
::glVertex3d(tx+d.xmax()-d.xmin(),ty+0.,tz+d.zmax()-d.zmin());
::glVertex3d(sx+d.xmax()-d.xmin(),sy+d.ymax()-d.ymin(),sz+d.zmax()-d.zmin());
::glVertex3d(tx+d.xmax()-d.xmin(),ty+d.ymax()-d.ymin(),tz+d.zmax()-d.zmin());
}
::glColor3f(0.27f, 0.51f, 0.7f);
}
}
}
::glEnd();
::glEnable(GL_LIGHTING);
}
bool Boundary_slice_chords::retired(const Segment_3& chord)
{
return (_retired.find(chord) != _retired.end() || _retired.find(chord.opposite()) != _retired.end());
}