3 About Kernels and Traits Classes_kernel traits-优快云博客

If you look at the manual page of the function convex_hull_2() and the other 2D convex hull algorithms, you see that they come in two versions. In the examples we have seen so far the function that takes two iterators for the range of input points and an output iterator for writing the result to. The second version has an additional template parameter Traits, and an additional parameter of this type.

template<class InputIterator , class OutputIterator , class Traits >
OutputIterator 
convex_hull_2(InputIterator first,
              InputIterator beyond,
              OutputIterator result,
              const Traits & ch_traits)

What are the geometric primitives a typical convex hull algorithm uses? Of course, this depends on the algorithm, so let us consider what is probably the simplest efficient algorithm, the so-called "Graham/Andrew Scan". This algorithm first sorts the points from left to right, and then builds the convex hull incrementally by adding one point after another from the sorted list. To do this, it must at least know about some point type, it should have some idea how to sort those points, and it must be able to evaluate the orientation of a triple of points.

And that is where the template parameter Traits comes in. For ch_graham_andrew() it must provide the following nested types:

Traits::Point_2
Traits::Less_xy_2
Traits::Left_turn_2
Traits::Equal_2

As you can guess, Left_turn_2 is responsible for the orientation test, while Less_xy_2 is used for sorting the points. The requirements these types have to satisfy are documented in full with the concept ConvexHullTraits_2 .

 
 template < 
 class InputIterator, 
 class OutputIterator, 
  class Po 
 int_2, 
 class Less_xy_2, 
  class Left_turn_2, 
 class Equal_2> 

 
 OutputIterator 

 
 ch_graham_andrew( 
  InputIterator first, 

 
 InputIterator beyond, 

 
 OutputIterator result); 

#include <iostream>
#include <iterator>
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Projection_traits_yz_3.h>
#include <CGAL/convex_hull_2.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K3;
typedef CGAL::Projection_traits_yz_3<K3> K;
typedef K::Point_2 Point_2;
int main()
{
  std::istream_iterator< Point_2 >  input_begin( std::cin );
  std::istream_iterator< Point_2 >  input_end;
  std::ostream_iterator< Point_2 >  output( std::cout, "\n" );
  CGAL::convex_hull_2( input_begin, input_end, output, K() );
  return 0;
}