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[Myirci <>]

Thank you very much for the answer. I agree that (-4,2) to (-1,1) is CW but I used  (-4, -2) as a source point. I attached an image file to visualize the target and source points. According to this, could you please explain the output that I got with the sample code ?

Have a nice day

Murat

On Sat, Mar 9, 2013 at 5:48 PM, Efi Fogel <> wrote:

The parabolic arc from (-4,2) to (-1,1) is CW. If you choose CCW, you get the complement, which is divided at (0,0) into x-monotone arcs.

On Tue, Mar 5, 2013 at 2:44 PM, Myirci <> wrote:

Hi again,

No one has any idea? 

Have a nice week

Murat

On Thu, Feb 28, 2013 at 10:25 AM, Myirci <> wrote:

Hello,

I'm using conics arrangement and I've a difficulty to understand the orientation of the conics arcs. In the simple example below, I want to insert the parabola segment: { y² + x = 0, source (-4,-2), target(-1,1) } in to my arrangement. And according to my understanding, from source point to target, the direction must be CCW. However, in this case, the resultant arrangement has 3 vertices and 2 edges (which is unexpected for me). If I change the orientation to CW then, I get the expected output. Could you clarify my confusion? 

Output when orientation is CCW: 

3 vertices:

(-4 -2) - degree 1

(0 0) - degree 2

(-1 1) - degree 1

2 edges:

[{0*x^2 + -1*y^2 + 0*xy + -1*x + 0*y + 0} : (-4,-2) --ccw--> (0,0)]

[{0*x^2 + -1*y^2 + 0*xy + -1*x + 0*y + 0} : (0,0) --ccw--> (-1,1)]

Output when orientation is CW:

 

2 vertices:

(-4 -2) - degree 1

(-1 1) - degree 1

1 edges:

[{0*x^2 + 1*y^2 + 0*xy + 1*x + 0*y + 0} : (-4,-2) --cw--> (-1,1)]

Here is the code:

#include <CGAL/Cartesian.h>

#include <CGAL/CORE_algebraic_number_traits.h>

#include <CGAL/Exact_predicates_exact_constructions_kernel_with_sqrt.h>

#include <CGAL/Segment_Delaunay_graph_2.h>

#include <CGAL/Segment_Delaunay_graph_traits_2.h>

#include <CGAL/Arr_conic_traits_2.h>

#include <CGAL/Arrangement_2.h>

#include "print_arrangement.hpp" // same as the arr_print.h

typedef CGAL::CORE_algebraic_number_traits Nt_traits;

typedef Nt_traits::Rational Rational;

typedef Nt_traits::Algebraic Algebraic;

typedef CGAL::Cartesian<Rational> Rat_kernel;

typedef CGAL::Cartesian<Algebraic> Alg_kernel;

typedef CGAL::Arr_conic_traits_2<

Rat_kernel, Alg_kernel, Nt_traits> Traits_2;

typedef Traits_2::Point_2 Point_2;

typedef Traits_2::Curve_2 Conic_arc_2;

typedef CGAL::Arrangement_2<Traits_2> Arrangement_2;

int main() {

    Arrangement_2 conics_arr;

Conic_arc_2 parabola_arc(0, 1, 0, 1, 0, 0, CGAL::COUNTERCLOCKWISE,

Point_2(-4, -2), Point_2(-1, 1));

if(parabola_arc.is_valid()) {

CGAL::insert(conics_arr, parabola_arc);

print_arrangement(conics_arr);

}

else { std::cerr << "Conic arc is not valid! " << std::endl; }

return 0;

} 

--
Murat Yirci

--
Murat Yirci

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-- 
Murat Yirci

Attachment: parabola.png
Description: PNG image