\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Circular Geometry Kernel

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Circular_kernel_2/functor_has_on_2.cpp
#include <CGAL/Exact_circular_kernel_2.h>
#include <CGAL/point_generators_2.h>
typedef CGAL::Exact_circular_kernel_2 Circular_k;
typedef CGAL::Point_2<Circular_k> Point_2;
typedef CGAL::Circular_arc_2<Circular_k> Circular_arc_2;
int main()
{
int n = 0;
Circular_arc_2 c = Circular_arc_2(Point_2(10,0), Point_2(5,5), Point_2(0, 0));
for(int i = 0; i <= 10; i++) {
for(int j = 0; j <= 10; j++) {
Point_2 p = Point_2(i, j);
if(Circular_k().has_on_2_object()(c,p)) {
n++;
std::cout << "(" << i << "," << j << ")" << std::endl;
}
}
}
std::cout << "There are " << n << " points in the [0,..,10]x[0,..,10] "
<< "grid on the circular" << std::endl
<< " arc defined counterclockwisely by the points (0,0), (5,5), (10,0)"
<< std::endl << "See the points above." << std::endl;
return 0;
}