CGAL users discussion list

[Issha Kayo <>]

Hi Manuel and everyone,

> See also the reference documentation:
> http://www.cgal.org/Manual/last/doc_html/cgal_manual/Periodic_3_triangulation_3_ref/Class_Periodic_3_triangulation_3.html

Oh, yes! Your advise is exactly what I wanted and it works!
Thank you for the information. It has solved most of my simple problem,
but I still have a silly question.

Assume a point at (0.01 0.5 0.5) might be in a cell, one of whose
vertices is out of the original cube. In this case I expect
point(Periodic_point) to return the position of the vertex, say, (-0.05,
0.5, 0.5). The actual return, however, seems to be (0.95, 0.5, 0.5).

As an example, please see the following code. I can easily imagine I'm
doing something very silly ....

Thank you,
Issha

-------------
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Periodic_3_triangulation_traits_3.h>
#include <CGAL/Periodic_3_Delaunay_triangulation_3.h>

#include <iostream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Periodic_3_triangulation_traits_3<K> GT;
typedef CGAL::Periodic_3_Delaunay_triangulation_3<GT> PDT;
typedef PDT::Point                  Point;

int main()
{
  PDT T;

  // Input point grid (27 points)
  for (double x=0.1 ; x < .9 ; x += 0.33) {
    for (double y=0.1 ; y < .9 ; y += 0.33) {
      for (double z=0.1 ; z < .9 ; z += 0.33) {
        T.insert(Point(x,y,z)); 
  } } }

  Point p(0.05, 0.5, 0.5);
  PDT::Cell_handle c;
  c=T.locate(p);

  T.convert_to_1_sheeted_covering();

  std::cout << T.point(T.periodic_point(c,0)) << std::endl;
  std::cout << T.point(T.periodic_point(c,1)) << std::endl;
  std::cout << T.point(T.periodic_point(c,2)) << std::endl;
  std::cout << T.point(T.periodic_point(c,3)) << std::endl;

  return 0;
}
-----------------------------

The resulting output is

1.1 0.43 0.43   <--- If 0.1 0.43 0.43, I'm happy.
1.1 0.76 0.43   <--- If 0.1 0.76 0.43, I'm happ..
0.76 0.76 0.76  <--- If -0.24 0.76 0.76, I'm hap...
1.1 0.43 0.76   <--- If 0.1 0.43 0.76, ..