目录
1、使用曲面网格的示例
2、使用默认多面体的示例
3、使用丰富多面体的示例
主要对1、使用曲面网格的示例 进行深度研究
CGAL编译与安装CGAL安装到验证到深入_cgal测试代码-CSDN博客
参考资料CGAL 5.4.5 - Triangulated Surface Mesh Simplification: User Manual
meshlab下载打开off文件MeshLab
1、使用曲面网格的示例
下面的例子说明了如何简化曲面网格。未指定的代价策略默认为 Lindstrom-Turk。
预览源文件 cube-meshed.off
stop_ratio 0.1代表只有之前10%的边量
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/Surface_mesh_simplification/edge_collapse.h>
#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h>
#include <chrono>
#include <fstream>
#include <iostream>
typedef CGAL::Simple_cartesian<double> Kernel;
typedef Kernel::Point_3 Point_3;
typedef CGAL::Surface_mesh<Point_3> Surface_mesh;
namespace SMS = CGAL::Surface_mesh_simplification;
int main(int argc, char** argv)
{
Surface_mesh surface_mesh;
const std::string filename =CGAL::data_file_path(R"(C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\cube-meshed.off)");
std::ifstream is(filename);
if (!is || !(is >> surface_mesh))
{
std::cerr << "Failed to read input mesh: " << filename << std::endl;
return EXIT_FAILURE;
}
if (!CGAL::is_triangle_mesh(surface_mesh))
{
std::cerr << "Input geometry is not triangulated." << std::endl;
return EXIT_FAILURE;
}
std::chrono::steady_clock::time_point start_time = std::chrono::steady_clock::now();
// In this example, the simplification stops when the number of undirected edges
// drops below 10% of the initial count
double stop_ratio = 0.1;
SMS::Count_ratio_stop_predicate<Surface_mesh> stop(stop_ratio);
int r = SMS::edge_collapse(surface_mesh, stop);
std::chrono::steady_clock::time_point end_time = std::chrono::steady_clock::now();
std::cout << "\nFinished!\n" << r << " edges removed.\n" << surface_mesh.number_of_edges() << " final edges.\n";
std::cout << "Time elapsed: " << std::chrono::duration_cast<std::chrono::milliseconds>(end_time - start_time).count() << "ms" << std::endl;
CGAL::IO::write_polygon_mesh(R"(C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\out.off)", surface_mesh, CGAL::parameters::stream_precision(17));
return EXIT_SUCCESS;
} 
2、使用默认多面体的示例
下面的示例展示了使用默认顶点、半边和面简化多面体_3 的过程。未指定的代价策略默认为 Lindstrom-Turk。
C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\small_cube.off 1000 C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\small_cube_out.off#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_3.h>
// Simplification function
#include <CGAL/Surface_mesh_simplification/edge_collapse.h>
// Stop-condition policy
#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_stop_predicate.h>
#include <iostream>
#include <fstream>
typedef CGAL::Simple_cartesian<double> Kernel;
typedef CGAL::Polyhedron_3<Kernel> Surface_mesh;
namespace SMS = CGAL::Surface_mesh_simplification;
int main(int argc, char** argv)
{
Surface_mesh surface_mesh;
const std::string filename = (argc > 1) ? argv[1] : CGAL::data_file_path("meshes/small_cube.off");
std::ifstream is(filename);
if (!is || !(is >> surface_mesh))
{
std::cerr << "Failed to read input mesh: " << filename << std::endl;
return EXIT_FAILURE;
}
if (!CGAL::is_triangle_mesh(surface_mesh))
{
std::cerr << "Input geometry is not triangulated." << std::endl;
return EXIT_FAILURE;
}
// This is a stop predicate (defines when the algorithm terminates).
// In this example, the simplification stops when the number of undirected edges
// left in the surface mesh drops below the specified number (1000)
const std::size_t edge_count_treshold = (argc > 2) ? std::stoi(argv[2]) : 1000;
SMS::Count_stop_predicate<Surface_mesh> stop(edge_count_treshold);
// This the actual call to the simplification algorithm.
// The surface mesh and stop conditions are mandatory arguments.
// The index maps are needed because the vertices and edges
// of this surface mesh lack an "id()" field.
std::cout << "Collapsing edges of Polyhedron: " << filename << ", aiming for " << edge_count_treshold << " final edges..." << std::endl;
int r = SMS::edge_collapse(surface_mesh, stop,
CGAL::parameters::vertex_index_map(get(CGAL::vertex_external_index, surface_mesh))
.halfedge_index_map(get(CGAL::halfedge_external_index, surface_mesh)));
std::cout << "\nFinished!\n" << r << " edges removed.\n"
<< (surface_mesh.size_of_halfedges() / 2) << " final edges.\n";
std::ofstream os(argc > 3 ? argv[3] : "out.off");
os.precision(17);
os << surface_mesh;
return EXIT_SUCCESS;
}
点和面一样
3、 使用丰富多面体的示例
下面的示例等同于上一个示例，但使用的是丰富多面体，其半边支持 id 字段，用于存储算法所需的边索引。
C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\small_cube.off 0.1 C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\small_cube_out.off#include <CGAL/Simple_cartesian.h>
#include <CGAL/Polyhedron_3.h>
// Extended polyhedron items which include an id() field
#include <CGAL/Polyhedron_items_with_id_3.h>
#include <CGAL/Surface_mesh_simplification/edge_collapse.h>
#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h>
#include <iostream>
#include <fstream>
typedef CGAL::Simple_cartesian<double> Kernel;
typedef Kernel::Point_3 Point;
// Setup an enriched polyhedron type which stores an id() field in the items
typedef CGAL::Polyhedron_3<Kernel, CGAL::Polyhedron_items_with_id_3> Surface_mesh;
typedef boost::graph_traits<Surface_mesh>::vertex_descriptor vertex_descriptor;
typedef boost::graph_traits<Surface_mesh>::halfedge_descriptor halfedge_descriptor;
namespace SMS = CGAL::Surface_mesh_simplification;
int main(int argc, char** argv)
{
Surface_mesh surface_mesh;
const std::string filename = (argc > 1) ? argv[1] : CGAL::data_file_path("meshes/small_cube.off");
std::ifstream is(filename);
if (!is || !(is >> surface_mesh))
{
std::cerr << "Failed to read input mesh: " << filename << std::endl;
return EXIT_FAILURE;
}
if (!CGAL::is_triangle_mesh(surface_mesh))
{
std::cerr << "Input geometry is not triangulated." << std::endl;
return EXIT_FAILURE;
}
// The items in this polyhedron have an "id()" field
// which the default index maps used in the algorithm
// need to get the index of a vertex/edge.
// However, the Polyhedron_3 class doesn't assign any value to
// this id(), so we must do it here:
int index = 0;
for (halfedge_descriptor hd : halfedges(surface_mesh))
hd->id() = index++;
index = 0;
for (vertex_descriptor vd : vertices(surface_mesh))
vd->id() = index++;
// In this example, the simplification stops when the number of undirected edges
// drops below xx% of the initial count
const double ratio = (argc > 2) ? std::stod(argv[2]) : 0.1;
SMS::Count_ratio_stop_predicate<Surface_mesh> stop(ratio);
// The index maps are not explicitelty passed as in the previous
// example because the surface mesh items have a proper id() field.
// On the other hand, we pass here explicit cost and placement
// function which differ from the default policies, ommited in
// the previous example.
std::cout << "Collapsing edges of mesh: " << filename << ", aiming for " << 100 * ratio << "% of the input edges..." << std::endl;
int r = SMS::edge_collapse(surface_mesh, stop);
std::cout << "\nFinished!\n" << r << " edges removed.\n"
<< (surface_mesh.size_of_halfedges() / 2) << " final edges.\n";
std::ofstream os((argc > 3) ? argv[3] : "out.off");
os.precision(17);
os << surface_mesh;
return EXIT_SUCCESS;
}
主要对1、使用曲面网格的示例 进行深度研究
曲面网格简化是指在尽可能保留整体形状、体积和边界的前提下，减少曲面网格中使用的面的数量。它与细分相反。
本文介绍的算法可以使用一种称为 "边缘折叠 "的方法，简化任何具有任意数量连接组件、有或无边界（边界或孔）和手柄（任意种属）的定向 2-manifold曲面。粗略地说，这种方法包括用一个顶点迭代替换一条边，每次折叠删除 2 个三角形。
边的折叠优先级由用户提供的成本函数决定，替换顶点的坐标由另一个用户提供的放置函数决定。当满足用户提供的停止谓词（如达到所需的边数）时，算法终止。
这里实现的算法是通用的，因为它不要求曲面网格是特定类型的，而要求它是可变曲面图（MutableFaceGraph）和半边列表图（HalfedgeListGraph）概念的模型。我们给出了 Surface_mesh、Polyhedron_3 和 OpenMesh 的示例。
计算折叠成本和顶点位置的具体方法称为成本策略。用户可以选择不同的策略，以策略和相关参数的形式传递给算法。
当前版本的软件包提供了一组实现三种策略的策略：默认的 Lindstrom-Turk 策略、Garland-Heckbert 策略，以及由边长成本和可选的中点放置（速度更快，但精度较低）组成的策略。
文献[4]、[5]中介绍的策略的主要特点是，简化后的曲面网格在每一步都不会与原始曲面网格（或前一步的曲面网格）进行比较，因此无需保留额外的信息，如原始曲面网格或局部变化的历史记录。因此被称为无记忆简化。
与 Lindstrom-Turk 策略一样，[2] 中提出的 Garland-Heckbert 策略不将生成的网格与原始网格进行比较，也不依赖于局部变化的历史。相反，它通过为每个顶点分配四元矩阵来编码与原始网格的近似距离。
关键函数
/*
surface_mesh : 要简化的曲面网格
stop_predicate : 表示何时必须完成简化的策略
vertex_index_map(vimap)：赋予每个顶点唯一整数索引的属性映射
edge_index_map(eimap)：赋予每条边唯一整数索引的属性图
edge_is_constrained_map(ebmap)：指定一条边是否为受约束边的属性图
get_cost(cf)：计算折叠成本的函数对象
get_placement(pf)：计算剩余顶点位置的函数对象
filter(filter)：用于拒绝下一条折叠边的候选对象的函数对象
visitor(vis) : 跟踪简化过程的函数对象
*/
int r = edge_collapse(surface_mesh, stop_predicate、
CGAL::parameters::vertex_index_map(vimap)
.edge_index_map(eimap)
.edge_is_border_map(ebmap)
.get_cost(cf)
.get_placement(pf)
.filter(filter
.visitor(vis))；
这里读取的数据是off文件，如果需要读取其他文件例如ply,obj则需要转换位Surface_mesh格式，先解析一下这个格式
Surface_mesh surface_mesh;
const std::string filename = CGAL::data_file_path(R"(C:\chenqi\ThridParty\CGAL-5.4.3\data\meshes\bear.off)");
std::ifstream is(filename);
if (!is || !(is >> surface_mesh))
{
std::cerr << "Failed to read input mesh: " << filename << std::endl;
return EXIT_FAILURE;
}- 下载的obj网站：Borderlands角色扮演 | 免费3D模型 | 专业3D扫描方案 (artec3d.cn)
读取obj进行网格简化，已经测试，这份代码只可以处理网格，不可以处理带纹理的
#include <CGAL/Simple_cartesian.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/IO/OBJ.h>
#include <CGAL/Surface_mesh_simplification/edge_collapse.h>
#include <CGAL/Surface_mesh_simplification/Policies/Edge_collapse/Count_ratio_stop_predicate.h>
#include <fstream>
typedef CGAL::Simple_cartesian<double> Kernel;
typedef Kernel::Point_3 Point;
typedef CGAL::Surface_mesh<Point> Surface_Mesh;
namespace SMS = CGAL::Surface_mesh_simplification;
int main() {
Surface_Mesh surface_mesh;
std::string input_filename = R"(C:\Users\Administrator\Desktop\OBJ\borderlands_cosplay-obj\out.obj)"; // Replace with your input OBJ file path
std::string output_filename = R"(C:\Users\Administrator\Desktop\OBJ\borderlands_cosplay-obj\out2.obj)"; // Replace with your desired output OBJ file path
// Read the mesh from OBJ file
if (!CGAL::IO::read_polygon_mesh(input_filename, surface_mesh)) {
std::cerr << "Failed to read input mesh: " << input_filename << std::endl;
return EXIT_FAILURE;
}
// Perform edge collapse simplification
double stop_ratio = 0.5; // Adjust this ratio as needed
SMS::Count_ratio_stop_predicate<Surface_Mesh> stop(stop_ratio);
SMS::edge_collapse(surface_mesh, stop);
// Write the simplified mesh to OBJ file
if (!CGAL::IO::write_polygon_mesh(output_filename, surface_mesh)) {
std::cerr << "Failed to write output mesh: " << output_filename << std::endl;
return EXIT_FAILURE;
}
return EXIT_SUCCESS;
}
至于实现纹理贴图自动更新，需要自己额外实现塌陷策略、停止的标准。目前代码是已经有一部分了，还需要完善，后续会更新。
在简化前记录纹理坐标：在开始网格简化之前，记录下每个顶点的纹理坐标。
自定义边缘坍塌操作：实现一个自定义的边缘坍塌策略，在边缘坍塌的同时更新相关顶点的纹理坐标。这可能涉及计算坍塌操作中涉及的顶点的新纹理坐标。
简化网格：使用自定义策略来简化网格。
输出简化后的网格和纹理坐标：在简化过程完成后，输出简化后的网格和更新后的纹理坐标到 OBJ 文件。
参考文章：网格简化 QEM 方法详解 - 知乎 (zhihu.com)
