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[Marco Feder <>]

Thanks Andreas for your prompt reply,

Unfortunately, I don’t see how this can be applied to my problem, since I need to find the coordinates of the intersections only, not to loop over faces. I’m trying to set up a minimal working example where I have the unit square [0,1]^2 cut by a straight line and the goal is to get the coords of the two intersection points. 

The following snippet is adapted from example Example 9.3 (https://doc.cgal.org/latest/Triangulation_2/index.html#Triangulation_2ExampleBuildingaTriangulated). So far I’ve only created the square and added the segment. How can I compute the two intersection points? Also, I don’t really see how to use Line_face_circulator.

#include <CGAL/Constrained_Delaunay_triangulation_2.h>

#include <CGAL/Constrained_triangulation_plus_2.h>

#include <CGAL/Exact_predicates_exact_constructions_kernel.h>

#include <CGAL/Polygon_2.h>

#include <vector>

typedef CGAL::Exact_predicates_exact_constructions_kernel K;

typedef CGAL::Polygon_2<K> Polygon_2;

typedef CGAL::Exact_intersections_tag Itag;

typedef CGAL::Constrained_Delaunay_triangulation_2<K, CGAL::Default, Itag> CDT;

typedef CGAL::Constrained_triangulation_plus_2<CDT> CDTP;

typedef CDTP::Point Point;

typedef CDTP::Constraint_id Cid;

typedef CDTP::Vertex_handle Vertex_handle;

void print(const CDTP &cdtp, Cid cid) {

std::cout << "Polyline constraint:" << std::endl;

for (Vertex_handle vh : cdtp.vertices_in_constraint(cid)) {

std::cout << vh->point() << std::endl;

}

}

int main() {

CDTP cdtp;

std::vector<Point> points;

points.push_back(Point(1, 1));

points.push_back(Point(0, 1));

points.push_back(Point(0, 0));

points.push_back(Point(1, 0));

Cid id1 = cdtp.insert_constraint(points.begin(), points.end()); //create square

Cid id2 = cdtp.insert_constraint(Point(0.2,-0.2),Point(0.5,1.1)); //insert segment

print(cdtp, id1);

return 0;

}

Best,

Marco

On 27 Jan 2022, at 10:40, Andreas Fabri <> wrote:

Hello,

You could use the Line_face_circulator

https://doc.cgal.org/latest/Triangulation_2/classCGAL_1_1Triangulation__2.html#a41a46211193d767f122504f2eb99189a

Best,

Andreas

On 1/27/2022 9:29 AM, Marco Feder ( via cgal-discuss Mailing List) wrote:

"> Hi everyone,

I’m trying to see if it’s possible to use CGAL to perform the intersection between a mesh and a (closed) curve inside it. This curve has co-dimension 1, and I’m assuming it’s just the union of segments given by straight lines connecting its support points, which I know of course. 

Basically my goal is to compute the coordinates of the blue points as in the attachment. As I am new to CGAL, I’d like to understand how you would attack the problem. Arrangement_2D cannot be used now because I do need the coordinates, so I was thinking to directly work with the 2D mesh package, even if I don’t see a straightforward way to get the result.

Best,

Marco

<cut_mesh_2.jpeg>

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-- 
Andreas Fabri, PhD
Chief Officer, GeometryFactory
Editor, The CGAL Project

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