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[Mael Rouxel-Labbé <>]

Hello,

In the package Periodic_3_mesh_3, the canonical domain must currently be a cube, and not a cuboid.

There is on-going work on periodic triangulations capable of handling cuboids (and even more generic domains), which will be available in an upcoming release. A stable "alpha" version is available in the branch https://github.com/MaelRL/cgal/tree/Generic_Periodic_Triangulations and it might be possible to adjust the code of Periodic_3_mesh_3 to make it work with those generic periodic triangulations too, but I have not looked into it yet.

Best,
Mael

On 30/04/2021 17:02, Nicolas Renaud ( via cgal-discuss Mailing List) wrote:

Dear CGAL community,

Thanks for all the work developing and maintaining CGAL !

I'm very new to CGAL and I'm trying to mesh an  non-periodic function using `Periodic_3_mesh_3` with a `Periodic_3_function_wrapper` following the documentation for the sphere (https://doc.cgal.org/latest/Periodic_3_mesh_3/index.html#title4).

Most of the times everything works fine. However for some dimensions of the canonical cube I get the following error :

```terminate called after throwing an instance of 'CGAL::Assertion_exception'
  what():  CGAL ERROR: assertion violation!
File: /home/nico/anaconda3/include/CGAL/Mesh_3/Refine_facets_3.h
Line: 1486
Explanation: Mesh_3 ERROR: A facet is not in conflict with its refinement point!```

This is for example the case in the example below where the cube is specified as (0, 0, 0, 1, 1, 0.85). But for a cube of (0, 0, 0, 1, 1, 1) the meshing succeeds.

I don't understand what I'm doing wrong and I would gladly welcome any help !

Thanks for your help !

Nico

#include <CGAL/Periodic_3_mesh_3/config.h>

#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>

#include <CGAL/make_periodic_3_mesh_3.h>

#include <CGAL/optimize_periodic_3_mesh_3.h>

#include <CGAL/Periodic_3_mesh_3/IO/File_medit.h>

#include <CGAL/Periodic_3_mesh_triangulation_3.h>

#include <CGAL/Periodic_3_function_wrapper.h>

#include <CGAL/Labeled_mesh_domain_3.h>

#include <CGAL/Mesh_complex_3_in_triangulation_3.h>

#include <CGAL/Mesh_criteria_3.h>

#include <CGAL/number_type_config.h> // CGAL_PI

#include <cmath>

#include <iostream>

#include <fstream>

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;

typedef K::FT FT;

typedef K::Point_3 Point;

typedef K::Iso_cuboid_3 Iso_cuboid;

// Domain

typedef FT (Function)(const Point&);

typedef CGAL::Labeled_mesh_domain_3<K> Periodic_mesh_domain;

// Triangulation

typedef CGAL::Periodic_3_mesh_triangulation_3<Periodic_mesh_domain>::type Tr;

typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;

// Criteria

typedef CGAL::Mesh_criteria_3<Tr> Periodic_mesh_criteria;

typedef CGAL::Periodic_3_function_wrapper<Function, K> Periodic_function;

// To avoid verbose function and named parameters call

using namespace CGAL::parameters;

// Implicit function

// A sphere centered on (0.5, 0.5, 0.5) with radius sqrt(0.2)

FT sphere_function (const Point& p) {

return CGAL::squared_distance(p, Point(0.5, 0.5, 0.5)) - 0.2;

}

int main(int argc, char** argv)

{

// 'int' because the 'schwarz_p' function is periodic over the domain only if

// the length of the side of the domain is an integer.

int domain_size = (argc > 1) ? atoi(argv[1]) : 1;

int number_of_copies_in_output = (argc > 2) ? atoi(argv[2]) : 4; // can be 1, 2, 4, or 8

bool verbose = true;

Iso_cuboid canonical_cube(0, 0, 0, 1, 1, 0.85);

Periodic_mesh_domain domain =

Periodic_mesh_domain::create_implicit_mesh_domain(

Periodic_function(sphere_function, canonical_cube), canonical_cube);

Periodic_mesh_criteria criteria(facet_angle = 30,

facet_size = 0.035 * domain_size,

facet_distance = 0.025 * domain_size,

cell_radius_edge_ratio = 2.,

cell_size = 0.05);

// Mesh generation

if (!verbose) {

// suppress output

std::cerr.setstate(std::ios_base::failbit);

}

// Mesh generation

C3t3 c3t3 = CGAL::make_periodic_3_mesh_3<C3t3>(domain, criteria);

if (!verbose) {

std::cerr.clear();

}

std::ofstream medit_file("output_implicit_shape.mesh");

CGAL::output_periodic_mesh_to_medit(medit_file, c3t3, number_of_copies_in_output);

std::cout << "EXIT SUCCESS" << std::endl;

return 0;

}

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