我尝试使用CGAL来查找三角形网格内部的点。 （即不在其边界上的点集。对于使用CGAL :: Side_of_triangle_mesh＆lt;＆gt;函数的3D网格有similar example here。任何人都可以帮助/建议如何为2D修改它三角测量？
我的测试代码只创建了两个正方形，一个在另一个内部，然后将种子放在原点（形成一个洞），然后执行2D Delaunay三角剖分。当我打电话给side_of_triangle_mesh＆lt;＆gt;上课：
Point_2 p = points2D[i];
CGAL::Bounded_side res = inside2D(p);
我收到错误：
/usr/local/include/CGAL/Side_of_triangle_mesh.h:164:16: Candidate function not viable: no known conversion from 'Point_2' (aka 'Point_2<CGAL::Epick>') to 'const Point' (aka 'const Point_3<CGAL::Epick>') for 1st argument
这是否意味着side_of_triangle_mesh仅适用于3D Polyhedron_3网格？如果是这样，任何人都可以为2D网格建议一种方法吗？
我的测试代码如下：谢谢
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Delaunay_mesh_vertex_base_2.h>
#include <CGAL/Delaunay_mesh_face_base_2.h>
#include <CGAL/Delaunay_mesh_size_criteria_2.h>
#include <CGAL/Side_of_triangle_mesh.h>
#include <vector>
#include <CGAL/Delaunay_mesher_2.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Point_2 Point_2;
typedef CGAL::Triangle_2<K> triangle;
typedef CGAL::Delaunay_mesh_vertex_base_2<K> Vb;
typedef CGAL::Delaunay_mesh_face_base_2<K> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, Tds> CDT;
typedef CDT::Vertex_handle Vertex_handle;
typedef CGAL::Delaunay_mesh_size_criteria_2<CDT> Criteria;
int main(int argc, char* argv[])
{
// Create a vector of the points
//
std::vector<Point_2> points2D ;
points2D.push_back(Point_2(-5.0, -5.0)); // ----------
points2D.push_back(Point_2( 5.0, -5.0)); // | OUTER
points2D.push_back(Point_2( 5.0, 5.0)); // | SQUARE
points2D.push_back(Point_2(-5.0, 5.0)); // ----------
points2D.push_back(Point_2(-2.5, -2.5)); // ----------
points2D.push_back(Point_2( 2.5, -2.5)); // | INNER
points2D.push_back(Point_2( 2.5, 2.5)); // | SQUARE
points2D.push_back(Point_2(-2.5, 2.5)); // ----------
size_t numTestPoints = points2D.size();
// Create a constrained delaunay triangulation and add the points
//
CDT cdt;
std::vector<Vertex_handle> vhs;
for (unsigned int i=0; i<numTestPoints; ++i){
vhs.push_back(cdt.insert(points2D[i]));
}
// Creare constraints of the sides of the mesh
//
cdt.insert_constraint(vhs[0],vhs[1]);
cdt.insert_constraint(vhs[1],vhs[2]);
cdt.insert_constraint(vhs[2],vhs[3]);
cdt.insert_constraint(vhs[3],vhs[0]);
cdt.insert_constraint(vhs[4],vhs[5]);
cdt.insert_constraint(vhs[5],vhs[6]);
cdt.insert_constraint(vhs[6],vhs[7]);
cdt.insert_constraint(vhs[7],vhs[4]);
// Create a seed to make sure the inner square is a hole
//
std::list<Point_2> list_of_seeds;
list_of_seeds.push_back(Point_2(0, 0));
// Refine the mesh into triangles of max side length '1' and ensuring seeds are 'holes'
//
CGAL::refine_Delaunay_mesh_2(cdt, list_of_seeds.begin(), list_of_seeds.end(),
Criteria(0.125, 1),false);
// Call side_of_triangle_mesh
//
CGAL::Side_of_triangle_mesh<CDT, K> inside2D(cdt) ;
int n_inside = 0;
int n_boundary = 0;
for(unsigned int i=0; i<numTestPoints; ++i)
{
Point_2 p = points2D[i];
CGAL::Bounded_side res = inside2D(p);
// ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
// NO MATCHING FUNCTION Call
if (res == CGAL::ON_BOUNDED_SIDE) { ++n_inside; }
if (res == CGAL::ON_BOUNDARY) { ++n_boundary; }
}
std::cerr << "2D results for query size: " << cdt.number_of_vertices() << std::endl;
std::cerr << " " << n_inside << " points inside " << std::endl;
std::cerr << " " << n_boundary << " points on boundary " << std::endl;
return 0 ;
}
答案 0 :(得分：1)
感谢@sloriot，我深究了这一点。底线是你不能使用CGAL :: Side_of_triangle_mesh＆lt;＆gt;对于2D Delaunay网格。相反，您需要做的是遍历网格中的所有顶点，并通过查看顶点周围的所有相邻面来测试每个顶点。如果任何面在域外，则顶点或点位于网格的边缘。
以下是更正后的代码：
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Delaunay_mesh_vertex_base_2.h>
#include <CGAL/Delaunay_mesh_face_base_2.h>
#include <CGAL/Delaunay_mesh_size_criteria_2.h>
#include <vector>
#include <CGAL/Delaunay_mesher_2.h>
typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef K::Point_2 Point_2;
typedef CGAL::Delaunay_mesh_vertex_base_2<K> Vb;
typedef CGAL::Delaunay_mesh_face_base_2<K> Fb;
typedef CGAL::Triangulation_data_structure_2<Vb, Fb> Tds;
typedef CGAL::Constrained_Delaunay_triangulation_2<K, Tds> CDT;
typedef CDT::Vertex_handle Vertex_handle;
typedef CGAL::Delaunay_mesh_size_criteria_2<CDT> Criteria;
typedef CDT::Vertex_iterator Vertex_iterator;
typedef CDT::Vertex Vertex;
typedef CDT::Face Face ;
typedef Face::Face_handle Face_handle ;
typedef CDT::Face_circulator Face_circulator ;
int main(int argc, char* argv[])
{
// Create a vector of the points
//
std::vector<Point_2> points2D ;
points2D.push_back(Point_2(-5.0, -5.0)); // ----------
points2D.push_back(Point_2( 5.0, -5.0)); // | OUTER
points2D.push_back(Point_2( 5.0, 5.0)); // | SQUARE
points2D.push_back(Point_2(-5.0, 5.0)); // ----------
points2D.push_back(Point_2(-2.5, -2.5)); // ----------
points2D.push_back(Point_2( 2.5, -2.5)); // | INNER
points2D.push_back(Point_2( 2.5, 2.5)); // | SQUARE
points2D.push_back(Point_2(-2.5, 2.5)); // ----------
size_t numTestPoints = points2D.size();
// Create a constrained delaunay triangulation and add the points
//
CDT cdt;
std::vector<Vertex_handle> vhs;
for (unsigned int i=0; i<numTestPoints; ++i){
vhs.push_back(cdt.insert(points2D[i]));
}
// Creare constraints of the sides of the mesh
//
cdt.insert_constraint(vhs[0],vhs[1]);
cdt.insert_constraint(vhs[1],vhs[2]);
cdt.insert_constraint(vhs[2],vhs[3]);
cdt.insert_constraint(vhs[3],vhs[0]);
cdt.insert_constraint(vhs[4],vhs[5]);
cdt.insert_constraint(vhs[5],vhs[6]);
cdt.insert_constraint(vhs[6],vhs[7]);
cdt.insert_constraint(vhs[7],vhs[4]);
// Create a seed to make sure the inner square is a hole
//
std::list<Point_2> list_of_seeds;
list_of_seeds.push_back(Point_2(0, 0));
// Refine the mesh into triangles of max side length '1' and ensuring seeds are 'holes'
//
CGAL::refine_Delaunay_mesh_2(cdt, list_of_seeds.begin(), list_of_seeds.end(),
Criteria(0.125, 1.5),false);
// The mesh is now created. The next bit swings around each vertex point checking that
// all faces around it are in the domain. If any are not then the vertex is on the
// edge of the mesh.
// thanks to @sloriot for this
//
Vertex v ;
std::vector<Point_2> interior_points ;
std::vector<Point_2> boundary_points ;
CDT::Locate_type loc = CDT::Locate_type::VERTEX ;
int li;
Vertex_iterator vit = cdt.vertices_begin(), beyond = cdt.vertices_end() ;
while (vit != beyond) {
v = *vit ;
Point_2 query = vit->point();
Face_handle f = cdt.locate(query, loc, li);
bool current_face_in_domain ;
Face_handle start = f ;
do {
current_face_in_domain = f->is_in_domain() ;
Vertex_handle vh = f->vertex(li);
f = f->neighbor(cdt.ccw(li));
li = f->index(vh) ;
}
while(current_face_in_domain && f != start) ;
if (f == start) {
interior_points.push_back(query) ;
}else{
boundary_points.push_back(query) ;
}
++vit ;
}
printf("Boundary points:\n");
for(auto p = boundary_points.begin(); p != boundary_points.end(); ++p){
printf("%f,%f\n",p->x(), p->y()) ;
}
printf("interior points:\n");
for(auto p = interior_points.begin(); p != interior_points.end(); ++p){
printf("%f,%f\n",p->x(), p->y()) ;
}
return 0 ;
}
当你运行它时你会得到类似的东西： This
答案 1 :(得分：0)
您必须使用locate功能。它将返回包含查询点的面部句柄。
然后，您需要使用is_in_domain()成员函数检查面部是否在域中。
请注意，如果您要执行多个查询，则应首先将所有查询点放在容器中，然后使用hilbert_sort对其进行排序
并使用前一个点的位置作为定位函数的第二个参数。
以下是如何在边界情况下获取事件面的示例代码：
CDT_2 mesh;
CGAL::Locate_type loc;
int li;
Point_2 query;
Face_handle f = mesh.locate(query, loc, li);
switch(loc)
{
case FACE:
f->is_in_domain();
break;
case EDGE:
{
bool face_1_in_domain = f->is_in_domain(); // first incident face status
bool face_2_in_domain = f->neighbor(li)->is_in_domain(); // second incident face status
break;
}
case VERTEX:
{
// turn around f->vertex(li)
Face_handle start = f;
do{
bool current_face_in_domain = f->is_in_domain();
Vertex_handle v = f->vertex(mesh.cw(li));
f = f->neighbor(mesh.ccw(li));
li = f->index(v);
}
while(f!=current);
break;
}
default:
// outside of the domain.
}