将Nef多面体保存为polyhedron_3或Surface_mesh会得到不同的结果

Question

我想把一个Nef多面体保存到一个OFF文件中，以便对其进行可视化。正如CGALNef多面体用户手册中所写的那样(见第5.4和5.5段(，Nef多面体可以转换为polyhedron_3或Surface_mesh。

然而，我注意到，当转换到这些结构，然后将其保存到OFF文件中时，结果是不同的。

在这里，我报告了一个最小示例的代码：

#include <list>
#include <iostream>
#include <fstream>
#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/Nef_polyhedron_3.h>
#include <CGAL/IO/Nef_polyhedron_iostream_3.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/boost/graph/convert_nef_polyhedron_to_polygon_mesh.h>    
typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
typedef Kernel::Point_3 Point_3;
typedef CGAL::Surface_mesh<Point_3> Mesh;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron_3;
typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;
typedef Kernel::Vector_3 Vector_3;
typedef Kernel::Aff_transformation_3 Aff_transformation_3;
int convertStlToOff(const char* inputFilename, const char* outputFilename)
{
//read 80 bytes and put in std::cerr
std::ifstream obj(inputFilename, std::ios::in | std::ios::binary);
for (int i = 0; i < 80; i++) {
boost::uint8_t c;
obj.read(reinterpret_cast<char*>(&c), sizeof(c));
std::cerr << c;
}
std::cerr << std::endl;
//read 4 bytes and initialize number of triangles
boost::uint32_t N32;
obj.read(reinterpret_cast<char*>(&N32), sizeof(N32));
unsigned int N = N32;
std::cerr << N << " triangles" << std::endl;
//reserve space for N faces
std::vector<Point_3> points;
std::map<Point_3, int> pmap;
typedef boost::tuple<int, int, int> Face;
std::vector<Face> faces;
faces.reserve(N);
//read all faces
int number_of_points = 0;
int number_of_snapped_points = 0;
for (int i = 0; i < N; i++)
{
//read face normal (it is ignored)
float normal[3];
obj.read(reinterpret_cast<char*>(&normal[0]), sizeof(normal[0]));
obj.read(reinterpret_cast<char*>(&normal[1]), sizeof(normal[1]));
obj.read(reinterpret_cast<char*>(&normal[2]), sizeof(normal[2]));
//read coordinates of all 3 points
int index[3];
for (int j = 0; j < 3; j++)
{
float x, y, z;
obj.read(reinterpret_cast<char*>(&x), sizeof(x));
obj.read(reinterpret_cast<char*>(&y), sizeof(y));
obj.read(reinterpret_cast<char*>(&z), sizeof(z));
Point_3 p(x, y, z);
if (pmap.find(p) == pmap.end())
{
// check brute force if there is a close point
bool found_close_point = false;
/*for (int k = 0; k < points.size(); k++)
{
if (sqrt(CGAL::squared_distance(p, points[k])) < 0.00001)
{
index[j] = k;
found_close_point = true;
number_of_snapped_points++;
}
}*/
if (!found_close_point)
{
points.push_back(p);
index[j] = number_of_points;
pmap[p] = number_of_points++;
}
}
else {
index[j] = pmap[p];
}
}
faces.push_back(boost::make_tuple(index[0], index[1], index[2]));
//read two additional bytes, and ignore them
char c;
obj.read(reinterpret_cast<char*>(&c), sizeof(c));
obj.read(reinterpret_cast<char*>(&c), sizeof(c));
}
std::cerr << number_of_snapped_points << " snapped points" << std::endl;
std::ofstream outputFile(outputFilename);
outputFile.precision(20);
outputFile << "OFFn" << points.size() << " " << faces.size() << " 0" << std::endl;
for (int i = 0; i < points.size(); i++)
{
outputFile << points[i] << std::endl;
}
for (int i = 0; i < faces.size(); i++)
{
outputFile << "3 " << boost::get<0>(faces[i]) << " " << boost::get<1>(faces[i]) << " " << boost::get<2>(faces[i]) << std::endl;
}
return 0;
}
void fill_cube_1(Polyhedron_3 & poly)
{
std::string input =
"OFFn
8 12 0n
-1 -1 -1n
-1 1 -1n
1 1 -1n
1 -1 -1n
-1 -1 1n
-1 1 1n
1 1 1n
1 -1 1n
3  0 1 3n
3  3 1 2n
3  0 4 1n
3  1 4 5n
3  3 2 7n
3  7 2 6n
3  4 0 3n
3  7 4 3n
3  6 4 7n
3  6 5 4n
3  1 5 6n
3  2 1 6";
std::stringstream ss;
ss << input;
ss >> poly;
}
enum savingModality
{
SAVE_AS_POLYHEDRON_3 = 0,
SAVE_AS_SURFACE_MESH = 1,
};
int saveNefObjectInOffFile(Nef_polyhedron offObject, const char* filename, savingModality modality)
{
if (!offObject.is_simple())
{
printf("Object is not simple. Cannot convert to mesh or polyhedronn");
return 1;
}
std::ofstream outStream;
outStream.open(filename);
if (modality == SAVE_AS_POLYHEDRON_3)
{
Polyhedron_3 outputPolyhedron;
offObject.convert_to_Polyhedron(outputPolyhedron);
outStream << outputPolyhedron;
}
else if (modality == SAVE_AS_SURFACE_MESH)
{
Mesh outputMesh;
CGAL::convert_nef_polyhedron_to_polygon_mesh(offObject, outputMesh);
outStream << outputMesh;
}
outStream.close();
return 0;
}
int main()
{
int ret;
//construct nef object #1
Polyhedron_3 cube1;
fill_cube_1(cube1);
Nef_polyhedron nefObject1(cube1);
//construct nef object #2
Nef_polyhedron nefObject2(cube1);
Aff_transformation_3 scale2(1, 0, 0,
0, 1, 0,
0, 0, 1,
2);
nefObject2.transform(scale2);
Aff_transformation_3 translation2(CGAL::TRANSLATION, Vector_3(-0.5, -0.5, -0.5));
nefObject2.transform(translation2);
//construct nef object #3
Nef_polyhedron nefObject3;
nefObject3 = nefObject1 - nefObject2;
//save results into .off file
ret = saveNefObjectInOffFile(nefObject3, "out1.off", SAVE_AS_POLYHEDRON_3);
ret = saveNefObjectInOffFile(nefObject3, "out2.off", SAVE_AS_SURFACE_MESH);
return 0;
}

以及两个文件的可视化屏幕截图：另存为Polyhedron_3和另存为Surface_mesh。正如你所看到的，似乎有些面孔不见了。

我的问题是："为什么结果看起来不同？">

Answer 1

对Polyhedron_3的输出进行三角测量，而对Surface_mesh的输出则不进行三角测量。我想meshlab中有一个显示非凸面的错误。

看看文档，你会发现有一个布尔参数可以触发或不触发三角测量。