Chapter 5
Extensible Kernel

This manual section describe how users can plug user defined geometric classes in existing CGAL kernels. This is best illustrated by an example.

5.1   Introduction

CGAL defines the concept of a geometry kernel. Such a kernel provides types, construction objects and generalized predicates. Most implementations of Computational Geometry algorithms and data structures in the basic library of CGAL were done in a way that classes or functions can be parametrized with a geometric traits class.

In most cases this geometric traits class must be a model of the CGAL geometry kernel concept (but there are some exceptions).

5.2   An Extensive Example

Assume you have the following point class, where the coordinates are stored in an array of doubles, where we have another data member color, which shows up in the constructor.

class MyPointC2 {

  double vec[2];
  int col;


    : col(0)
    *vec = 0;
    *(vec+1) = 0;

  MyPointC2(const double x, const double y, int c)
    : col(c)
    *vec = x;
    *(vec+1) = y;

  const double& x() const  { return *vec; }

  const double& y() const { return *(vec+1); }

  double & x() { return *vec; }

  double& y() { return *(vec+1); }

  int color() const { return col; }

  int& color() { return col; }
  bool operator==(const MyPointC2 &p) const
    return ( *vec == *(p.vec) )  && ( *(vec+1) == *(p.vec + 1) && ( col == p.col) );

  bool operator!=(const MyPointC2 &p) const
      return !(*this == p);


As said earlier the class is pretty minimalistic, for example it has no bbox() method. One might assume that a basic library algorithm which computes a bounding box (e.g, to compute the bounding box of a polygon), will not compile. Luckily it will, because it does not use of member functions of geometric objects, but it makes use of the functor Kernel::Construct_bbox_2.

To make the right thing happen with MyPointC2 we have to provide the following functor.

template <class ConstructBbox_2>
class MyConstruct_bbox_2 : public ConstructBbox_2 {
  CGAL::Bbox_2 operator()(const typename MyPointC2& p) const {
    return CGAL::Bbox_2(p.x(), p.y(), p.x(), p.y());

Things are similar for random access to the Cartesian coordinates of a point. As the coordinates are stored in an array of doubles we can use double* as random access iterator.

class MyConstruct_coord_iterator {
  const double* operator()(const MyPointC2& p)
    return &p.x();

  const double* operator()(const MyPointC2& p, int)
    const double* pyptr = &p.y();
    return pyptr;

The last functor we have to provide is the one which constructs points. That is you are not forced to add the constructor with the Origin as parameter to your class, nor the constructor with homogeneous coordinates, and at the same time you can pass the additional color argument to your point constructor. The functor is a kind of glue layer between the CGAL algorithms and your class.

 template <typename K>
  class MyConstruct_point_2
    typedef typename K::RT         RT;
    typedef typename K::Point_2    Point_2;
    typedef Point_2          result_type;
    typedef CGAL::Arity_tag< 1 >   Arity;

    operator()() const
    { return Point_2(); }

    operator()(CGAL::Origin o) const
    { return Point_2(0,0, 0); }

    operator()(const RT& x, const RT& y) const
    { return Point_2(x, y, 0); }

    // We need this one, as such a functor is in the Filtered_kernel
    operator()(const RT& x, const RT& y, const RT& w) const
      if(w != 1){
	return Point_2(x/w, y/w, 0); 
      } else {
	return Point_2(x,y, 0);

Now we are ready to put the puzzle together. We won't explain it in detail, but you see that there are typedefs to the new point class and the functors. All the other types are inherited.

#ifndef MYKERNEL_H
#define MYKERNEL_H

#include <CGAL/Cartesian.h>
#include "MyPointC2.h"
#include "MySegmentC2.h"

// K_ is the new kernel, and K_Base is the old kernel
template < typename K_, typename K_Base >
class MyCartesian_base
  : public K_Base::template Base<K_>::Type
  typedef typename K_Base::template Base<K_>::Type   OldK;
  typedef K_                                Kernel;
  typedef MyPointC2                         Point_2;
  typedef MySegmentC2<Kernel>               Segment_2;
  typedef MyConstruct_point_2<Kernel>       Construct_point_2;
  typedef const double*                     Cartesian_const_iterator_2;
  typedef MyConstruct_coord_iterator        Construct_cartesian_const_iterator_2;
  typedef MyConstruct_bbox_2<typename OldK::Construct_bbox_2> 

  template < typename Kernel2 >
  struct Base { typedef MyCartesian_base<Kernel2, K_Base>  Type; };

template < typename FT_ >
struct MyKernel
  : public MyCartesian_base<MyKernel<FT_>, CGAL::Cartesian<FT_> >

#endif // MYKERNEL_H

Finally, we give an example how this new kernel can be used. Predicates and constructions work with the new point, they can be a used to construct segments and triangles with, and data structures from the Basic Library, as the Delaunay triangulation work with them.

The kernel itself can be made robust by plugging it in the Filtered_kernel_adaptor. This class has the same functionality as the class Filtered_kernel with the only difference that it does not enforce type equality between Kernel::Point_2 and Point_2<Kernel>, which does not make sense in our case as our point does not offer the functionality of the latter.

// file: examples/Kernel_23/MyKernel.C

#include <CGAL/basic.h>
#include <CGAL/Filtered_kernel.h>
#include <CGAL/Delaunay_triangulation_2.h>
#include <CGAL/squared_distance_2.h>
#include <cassert>
#include "MyKernel.h"

typedef MyKernel<double>                   MK;
typedef CGAL::Filtered_kernel_adaptor<MK>  K;
typedef CGAL::Delaunay_triangulation_2<K>  Delaunay_triangulation_2;

typedef K::Point_2         Point;
typedef K::Segment_2       Segment;
typedef K::Ray_2           Ray;
typedef K::Line_2          Line;
typedef K::Triangle_2      Triangle;
typedef K::Iso_rectangle_2 Iso_rectangle;

const int RED= 1;
const int BLACK=2;

int main()
  Point a(0,0, RED), b(1,0, BLACK), c(1,1, BLACK), d(0,1, RED);

  Delaunay_triangulation_2 dt;

  K::Orientation_2 orientation;
  Point p(1,2, BLACK), q;
  p.color() = RED;
  q.color() = BLACK;
  std::cout << p << std::endl;

  K::Compute_squared_distance_2 squared_distance;

  std::cout << "squared_distance(a, b) == "
            << squared_distance(a, b) << std::endl;

  Segment s1(p,q), s2(a, c);

  K::Construct_midpoint_2 construct_midpoint_2;


  assert(s1.source().color() == RED);

  s1.source().color() = BLACK;

  assert(s1.source().color() == BLACK);

  K::Intersect_2 intersection;

  CGAL::Object o = intersection(s1, s2);

  K::Construct_cartesian_const_iterator_2 construct_it;
  K::Cartesian_const_iterator_2  cit = construct_it(a);
  assert(*cit == a.x());

  cit = construct_it(a,0);

  assert(*cit == a.y());

  Line l1(a,b), l2(p, q);

  intersection(l1, l2);

  intersection(s1, l1);

  Ray r1(d,b), r2(d,c);
  intersection(r1, r2);

  intersection(r1, l1);

  squared_distance(r1, r2);
  squared_distance(r1, l2);
  squared_distance(r1, s2);

  Triangle t1(a,b,c), t2(a,c,d);
  intersection(t1, t2);
  intersection(t1, l1);

  intersection(t1, s1);

  intersection(t1, r1);

  Iso_rectangle i1(a,c), i2(d,p);
  intersection(i1, i2);
  intersection(i1, s1);

  intersection(i1, r1);
  intersection(i1, l1);


  std::cout << s1.source() << std::endl;

  std::cout << t1.bbox() << std::endl;
  return 0;

5.3   Limitations

The point class must have member functions x() and y() (and z() for the 3d point). We will probably introduce function objects that take care of coordinate access.

Global functions operating on, for example CGAL::orientation(CGAL::MyKernel<double>::Point_2,CGAL::MyKernel<double>::Point_2,CGAL::MyKernel<double>::Point_2 will not work. Instead you have to use the functor MyKernel<double>::Orientation_2.

Rewriting the code is however straightforward: you can give the function object the same name as the global function.

K::Orientation_2 orientation_2;
K::Point_2 p(0,0,RED), q(1,1,BLACK), r(2,1, RED);

orientation(p, q, r);

We did not go through the entire kernel, to also make it possible to plug in user defined lines, rays or triangles.