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本节内容主要涉及形状检测（Shape Detection）与形状重建（Shape Reconstruction），具体算法步骤会在后续章节介绍。CGAL在6.0重点更新了形状重建部分的一些模块——动态空间分割与动态形状重建等，也会在后续详细介绍。官网上的效果和问题缺陷测试还需要一些时间验证，以及算法效率的实际测试。
题外话
泊松，前进，尺度这些重建算法本身都有相应的局限性，用CGAL测试或者其他任意的第三方库测试这些方法的时候我想也发现了，一些重建结果不理想或者出现问题是很容易发生的，所以需要嵌入0-3维的一些几何特征，之后也会介绍如何把这些与神经网络相结合，以及一些混合建模手段，比如多项式连续与离散结合，各种几何算子融合诸如此类等。
理论部分
形状检测
- 区域增长法
- 点云形状检测的高效ransac
形状重建
从点云重建多边形曲面
源码编译相关问题
- 添加形状检测头文件会报错
#include <CGAL/Shape_detection/Efficient_RANSAC.h>
报错：
问题在模版定义部分有重复，注释掉这部分重复的代码即可
-
c++常见模版问题
-
多边形曲面重建部分需要SCIP/GLPK库，否则不能用。关于scip的库用2022编译好了，可以看：
网盘 提取码：0212
里面有zlib,tbb，soplex，scip，scip只编译了涉及的这部分相关的，其他的关联依赖自行编译
例子
#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
#include <CGAL/IO/read_points.h>
#include <CGAL/property_map.h>
#include <CGAL/Surface_mesh.h>
#include <CGAL/Shape_detection/Efficient_RANSAC.h>
#include <CGAL/Polygonal_surface_reconstruction.h>#include <CGAL/Polygon_mesh_processing/orientation.h>#include <CGAL/Timer.h>#include <fstream>
#include <CGAL/IO/read_points.h>
#include <CGAL/property_map.h>
#include <CGAL/Point_with_normal_3.h>
#ifdef CGAL_USE_SCIP // defined (or not) by CMake scripts, do not define by hand#include <CGAL/SCIP_mixed_integer_program_traits.h>
typedef CGAL::SCIP_mixed_integer_program_traits<double> MIP_Solver;#elif defined(CGAL_USE_GLPK) // defined (or not) by CMake scripts, do not define by hand#include <CGAL/GLPK_mixed_integer_program_traits.h>
typedef CGAL::GLPK_mixed_integer_program_traits<double> MIP_Solver;#endifusing Kernel = CGAL::Exact_predicates_inexact_constructions_kernel;
using Point_3 = Kernel::Point_3;
using Mesh = CGAL::Surface_mesh<Kernel::Point_3>;
// Point with normal, and plane index
typedef boost::tuple<Point, Vector, int> PNI;
typedef std::vector<PNI> Point_vector;
typedef CGAL::Nth_of_tuple_property_map<0, PNI> Point_map;
typedef CGAL::Nth_of_tuple_property_map<1, PNI> Normal_map;
typedef CGAL::Nth_of_tuple_property_map<2, PNI> Plane_index_map;typedef CGAL::Shape_detection::Efficient_RANSAC_traits<Kernel, Point_vector, Point_map, Normal_map> Traits;typedef CGAL::Shape_detection::Efficient_RANSAC<Traits> Efficient_ransac;
typedef CGAL::Shape_detection::Plane<Traits> Plane;
typedef CGAL::Shape_detection::Point_to_shape_index_map<Traits> Point_to_shape_index_map;typedef CGAL::Polygonal_surface_reconstruction<Kernel> Polygonal_surface_reconstruction;
typedef CGAL::Surface_mesh<Point> Surface_mesh; void test()
{Point_vector points;const std::string input_file = CGAL::data_file_path("..\\data\\cube.pwn");if (!CGAL::IO::read_points(input_file.c_str(), std::back_inserter(points),CGAL::parameters::point_map(Point_map()).normal_map(Normal_map()))){std::cerr << "Error: cannot read file " << input_file << std::endl;return;}CGAL::Timer t;t.start();// Shape detectionEfficient_ransac ransac;ransac.set_input(points);ransac.add_shape_factory<Plane>();std::cout << "Extracting planes...";t.reset();ransac.detect();Efficient_ransac::Plane_range planes = ransac.planes();std::size_t num_planes = planes.size();std::cout << " Done. " << num_planes << " planes extracted. Time: " << t.time() << " sec." << std::endl;// Stores the plane index of each point as the third element of the tuple.Point_to_shape_index_map shape_index_map(points, planes);for (std::size_t i = 0; i < points.size(); ++i) {// Uses the get function from the property map that accesses the 3rd element of the tuple.int plane_index = get(shape_index_map, i);points[i].get<2>() = plane_index;}std::cout << "Generating candidate faces...";t.reset();Polygonal_surface_reconstruction algo(points,Point_map(),Normal_map(),Plane_index_map());std::cout << " Done. Time: " << t.time() << " sec." << std::endl;Mesh model;std::cout << "Reconstructing...";t.reset();if (!algo.reconstruct<MIP_Solver>(model)) {std::cerr << " Failed: " << algo.error_message() << std::endl;return ;}const std::string& output_file("without_input_planes_result.off");if (CGAL::IO::write_OFF(output_file, model))std::cout << " Done. Saved to " << output_file << ". Time: " << t.time() << " sec." << std::endl;else {std::cerr << " Failed saving file." << std::endl;return ;}// Also stores the candidate faces as a surface mesh to a fileMesh candidate_faces;algo.output_candidate_faces(candidate_faces);const std::string& candidate_faces_file("without_input_planes_cube_candidate_faces.off");std::ofstream candidate_stream(candidate_faces_file.c_str());if (CGAL::IO::write_OFF(candidate_stream, candidate_faces))std::cout << "Candidate faces saved to " << candidate_faces_file << "." << std::endl;}
结果
without_input_planes_result.off：
without_input_planes_cube_candidate_faces.off：