增量式重网格化

AMCAX::Meshing::Remeshing::TriMesh_IncrementalRemeshing 实现对输入网格进行各向同性重网格化。当输入三维网格的点和面以及参数 Params 时，便会输出 incremental remesh（尽可能生成正三角形）后的点和面。

Params 中可以设置的参数：

Max_error：与原网格的最大误差，用于计算自适应长度，参数越大，自适应长度会越长，默认值 0.0005
targetEdgeLength：目标边长与原网格所有边的平均长度的比值，默认值 0.5。长度范围是 [0.3*targetEdgeLength*meanLength，3*targetEdgeLength*meanLength]
isAdaptive：是否自适应，true 自适应，false 不自适应，默认值 false
featurePreserved：是否保持特征，true 保持，false 不保持，默认值 false
tolAngle：判断特征的角度阈值，弧度制，默认值 0.7854
iterNum：迭代次数，默认值 5，一般迭代 10 次足够

Incremental remesh主要步骤：

输入网格的点和面，可以根据实际情况自行读入某种格式 (obj/stl) 的文件
设置参数
初始化 reference mesh 和 variable mesh 的点和面
执行 remesh
输出为需要的文件格式 (obj/stl)

std::string inputfilename = "./data/32770_sf.obj";
// Define mesh input/output options 
AMCAX::Meshing::Mesh::IOOptions io_options;
// Option: Vertices include coordinate information
io_options.vertex_has_point = true;
 
// Create OBJ file reader and read triangle soup from the file
AMCAX::Meshing::Mesh::OBJReader<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> reader;
reader.read(inputfilename, io_options);
// Move read vertex data and triangle data
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Points input_points = std::move(reader.m_points);
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Triangles input_triangles = std::move(reader.m_triangles);
 
// Create incremental mesh remesher
AMCAX::Meshing::Remeshing::TriMesh_IncrementalRemeshing<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> remesher;
// Configure remeshing parameters
AMCAX::Meshing::Remeshing::TriMesh_IncrementalRemeshing<AMCAX::Meshing::Mesh::TriSoupTraits_Coord>::Params params;
//Initialize output_points and output_triangles
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Points output_points = input_points;
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Triangles output_triangles = input_triangles;
 
// Parameter
params.featurePreserved = true;
params.isAdaptive = true;
params.iterNum = 10;
params.Max_error = 0.0002;
params.targetEdgeLength = 0.2;
params.tolAngle = 60. / 180. * AMCAX::Constants::pi;
 
// Set reference mesh
remesher.setReferenceMesh(input_points, input_triangles);
// Set variable mesh
remesher.setVariableMesh(output_points, output_triangles);
//Remeshing
remesher.remesh(params);
 
std::string outputfilename =
    "incrementalRemeshing" + std::to_string(params.iterNum) + ".obj";
// Create OBJ file writer
AMCAX::Meshing::Mesh::OBJWriter<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> writer;
writer.m_points = std::move(output_points);
writer.m_triangles = std::move(output_triangles);
// Write remeshed mesh to file with 15 decimal places precision
writer.write(outputfilename, io_options, 15);

网格切割与网格参数化

AMCAX::Meshing::TriMeshCut::GreedyCut< Traits >::cut 实现对封闭的曲面网格进行切割，使其与圆盘拓扑同胚，并尽可能的降低参数化扭曲，为参数化算法提供支持。需要注意的是网格切割算法具有随机性，因此每一次切割并不一致。
以下分别为切割后的网格（图中绿色线条为网格边界）：

将切割网格作为参数化算法的输入，便得到参数化网格（参数化网格是一个平面的，不会自相交）：

对 3D 曲面网格进行参数化，得到低扭曲、低自相交的平面参数化网格，为纹理贴图等应用提供支持。需要注意的是输入网格需要保证有切割的边界，并且无非流行结构（网格必须是 2 维流形网格），另外 stl 文件会在一定的误差范围内对点进行合并，所以需要在调用算法前对输入网格进行确认。

// Define mesh input/output options  
AMCAX::Meshing::Mesh::IOOptions io_options;
// Option: Vertices include coordinate information
io_options.vertex_has_point = true;
// Create OBJ reader and writer
AMCAX::Meshing::Mesh::OBJReader<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> obj_reader;
AMCAX::Meshing::Mesh::OBJWriter<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> obj_writer;
 
std::string in_filename = "./data/cow.obj";
std::string out_cut_filename = "bunny_cut.obj";
std::string out_para_filename = "bunny_parameterization.obj";
 
// Read the object file
obj_reader.read(in_filename, io_options);
 
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Points    i_points = std::move(obj_reader.m_points);
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Triangles i_triangles = std::move(obj_reader.m_triangles);
 
// Perform mesh cut
AMCAX::Meshing::TriMeshCut::GreedyCut<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> mesh_cut(
    i_points, i_triangles, true);
 
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Points    cut_points;
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Triangles cut_triangles;
 
mesh_cut.cut(cut_points, cut_triangles);
 
// Write the cut mesh to a new file
obj_writer.m_points = cut_points;
obj_writer.m_triangles = cut_triangles;
obj_writer.write(out_cut_filename, io_options, 10);
obj_writer.clear();
 
AMCAX::Meshing::Mesh::TriSoupTraits_Coord::Points para_points;
 
// Perform bijective parameterization on the cut mesh
AMCAX::Meshing::Parameterization::BijectivePara<AMCAX::Meshing::Mesh::TriSoupTraits_Coord> para(
    cut_points, cut_triangles, para_points, true);
para.parameterization();
 
// Write the parameterized cut mesh to a new file
obj_writer.m_points = std::move(para_points);
obj_writer.m_triangles = std::move(cut_triangles);
obj_writer.write(out_para_filename, io_options, 10);