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#include "Viewer.h"
#include <CGAL/point_generators_3.h>
#include <CGAL/squared_distance_3.h>
#include <CGAL/Exact_spherical_kernel_3.h>
#include <vector>
template <class Kernel>
void Viewer::draw_circle_on_unit_sphere(const typename CGAL::Point_3<Kernel>& center) const {
const typename Kernel::Point_3 origin(0,0,0);
const typename Kernel::Plane_3 plane(center, center-origin);
typename Kernel::Vector_3 base1=plane.base1();
typename Kernel::Vector_3 base2=plane.base2();
base1=base1/CGAL::sqrt(base1.squared_length());
base2=base2/CGAL::sqrt(base2.squared_length());
const double radius=CGAL::sqrt( CGAL::to_double( 1 - CGAL::squared_distance(origin,center) ) );
const double nb_pt_per_circle=100;
const double step=2 * CGAL_PI / nb_pt_per_circle;
::glDisable(GL_LIGHTING);
::glBegin(GL_LINE_LOOP);
for (double theta = 0; theta < 2 * CGAL_PI ; theta += step) {
const typename Kernel::Point_3 point=center + ( radius*cos(theta)*base1 + radius*sin(theta)*base2 );
::glVertex3f( point.x(),point.y(),point.z() );
}
::glEnd();
::glEnable(GL_LIGHTING);
}
void Viewer::draw()
{
const int sphere_res=30;
//draw central sphere
::glPushMatrix();
::glColor3f(1,1,1);
::gluSphere(qsphere,0.999,sphere_res,sphere_res);
::glCallList(dl_nb);
::glCallList(dl_nb+1);
::glPopMatrix();
}
void Viewer::init()
{
// Restore previous viewer state.
restoreStateFromFile();
//init quadric to store sphere.
qsphere=gluNewQuadric();
gluQuadricOrientation(qsphere,GLU_OUTSIDE);
//code for antialiasing
::glEnable(GL_BLEND);
::glEnable(GL_LINE_SMOOTH);
::glEnable(GL_POINT_SMOOTH);
::glHint(GL_LINE_SMOOTH_HINT, GL_NICEST);
::glBlendFunc(GL_SRC_ALPHA, GL_ONE_MINUS_SRC_ALPHA);
//set intersection point size
::glPointSize(5);
//random generator of points within a sphere
typedef CGAL::Creator_uniform_3<EPIC::FT,EPIC::Point_3> Creator;
CGAL::Random_points_in_sphere_3<EPIC::Point_3, Creator> gen;
const unsigned nb_circles=20;
//vector to store input points
std::vector<EPIC::Point_3> points;
points.reserve(nb_circles);
//disable lighting before drawing segments and points
::glEnable(GL_LIGHTING);
//init call lists
dl_nb=::glGenLists(2);
//store circles in a display list
::glNewList(dl_nb,GL_COMPILE);
::glColor3f(1,0,0);
for (unsigned i=0;i<nb_circles;++i){
EPIC::Point_3 p=*++gen;
//prevent great circles
while (p.x()==0 && p.y()==0 && p.z()==0) { p=*++gen; }
draw_circle_on_unit_sphere(p);
points.push_back(p);
}
::glEndList();
std::vector<EPIC::Point_3> intersections;
naive_compute_intersection_points(points,std::back_inserter(intersections));
::glNewList(dl_nb+1,GL_COMPILE);
::glColor3f(0,1,0);
//draw points as small spheres
for (std::vector<EPIC::Point_3>::const_iterator it=intersections.begin();it!=intersections.end();++it){
glPushMatrix();
glTranslatef(it->x(),it->y(),it->z());
gluSphere(qsphere,0.005,10,10);
glPopMatrix();
}
::glEndList();
//lighting
::glEnable(GL_LIGHT0);
::glEnable(GL_LIGHTING);
float lpos[4] = { -.2f, .2f, .9797958971f, 0.0f };
::glLightfv(GL_LIGHT0,GL_POSITION,lpos);
::glLightModelf(GL_LIGHT_MODEL_TWO_SIDE, 1.0f);
::glEnable(GL_NORMALIZE);
::glShadeModel(GL_SMOOTH);
}
template<class Output_iterator>
void Viewer::naive_compute_intersection_points(const std::vector<EPIC::Point_3>& points,Output_iterator out) const {
typedef CGAL::Exact_spherical_kernel_3 SK;
SK::Sphere_3 sphere(SK::Point_3(0,0,0),1);
//converter point to exact SK point type
CGAL::Cartesian_converter<EPIC,SK> to_exact;
std::vector<SK::Circle_3> circles;
//create circles from points: need to use a converter to change floating points coordinates into an exact NT.
for (std::vector<EPIC::Point_3>::const_iterator it=points.begin();it!=points.end();++it){
const SK::Point_3 center=to_exact(*it);
circles.push_back( SK::Circle_3(sphere,SK::Plane_3(center,center-CGAL::ORIGIN) ) );
}
//Look for intersection points among pair of circles: use a naive and quadratic way
for (std::vector<SK::Circle_3>::const_iterator it_f=circles.begin();it_f!=--circles.end();++it_f){
std::vector<SK::Circle_3>::const_iterator it_s=it_f;
++it_s;
for (;it_s!=circles.end();++it_s){
std::vector <CGAL::Object> intersections;
//ensure_circles are different
CGAL_precondition(*it_s!=*it_f);
CGAL::intersection(*it_f,*it_s,std::back_inserter(intersections));
if (!intersections.empty()){
for (std::vector <CGAL::Object>::const_iterator it_pt=intersections.begin();it_pt!=intersections.end();++it_pt){
const std::pair<SK::Circular_arc_point_3,unsigned>* pt=
CGAL::object_cast< std::pair<SK::Circular_arc_point_3,unsigned> > (&(*it_pt));
assert(pt!=NULL);
*out++=EPIC::Point_3( CGAL::to_double(pt->first.x()),
CGAL::to_double(pt->first.y()),
CGAL::to_double(pt->first.z())
);
}
}
}
}
}
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