半边数据结构与OpenMesh中的处理

参考：https://blog.csdn.net/jialong_chen/article/details/118497495

《Springer.3D Mesh Processing and Character Animation.With Examples Using OpenGL, OpenMesh and Assimp》

1. 半边数据结构的基本假设

1）三维模型包含顶点、边、面片三部分结构，在空间中分别是0维、1维和2维的。面即为物体表面的某一多边形区域，边是相邻两个面的交线段或一个面的边缘，顶点为相邻边的交点。
2）每条边只与最多两个面相邻
3）每个面片均有自己的朝向，以区分内侧和外侧
4）两个相邻的面片朝向相同

2.数据结构

半边数据结构中包含了三种对象：顶点、半边和面片。每个对象均为固定长度，并包含了指向其他对象的指针。

2.OpenMesh中的相关函数

2.1 拓扑关联对象

// Type declarations for handles:
OpenMesh::VertexHandle verH;
OpenMesh::FaceHandle facH;
OpenMesh::HalfedgeHandle hedH, hedH_n, hedH_p;
OpenMesh::Vec3d point;

// Half-edge operations:
half-edge → vert: verH = mesh.to_vertex_handle(hedH);
half-edge→ pair→vert:verH = mesh.from_vertex_handle(hedH);
half-edge→ next:hedH_n = mesh.next_halfedge_handle(hedH);
half-edge→pair:hedH_p=mesh.opposite_halfedge_handle(hedH);
half-edge → face: facH = mesh.face_handle(hedH);
face → half-edge: hedH = mesh.halfedge_handle(facH);
vert → half-edge: hedH = mesh.halfedge_handle(verH);
vert coordinates: point = mesh.point(verH);

2.2 遍历

// vertex iterator

typedef OpenMesh::TriMesh_ArrayKernelT<> MyMesh;
MyMesh mesh;
OpenMesh::VertexHandle verH;
MyMesh::VertexIter vit;
OpenMesh::Vec3d p;
int valence;
OpenMesh::IO::read_mesh(mesh, "cube.off")
for (vit = mesh.vertices_begin(); vit != mesh.vertices_end(); vit++)
{
    verH = *vit;
    p = mesh.point(verH);
    valence = mesh.valence(verH);
    cout << p[0] << " " << p[1] << " " << p[2] << " " << valence << endl;
}

// face iterator

typedef OpenMesh::TriMesh_ArrayKernelT<> MyMesh;
MyMesh mesh;
OpenMesh::FaceHandle facH;
MyMesh::FaceIter fit;
int nvert;
OpenMesh::IO::read_mesh(mesh, "cube.off")
for (fit = mesh.faces_begin(); fit != mesh.faces_end(); fit++)
{
    facH = *fit;
    nvert = mesh.valence(facH);
    cout << "Number of vertices = " << nvert << endl;
}

// edge iterator

typedef OpenMesh::TriMesh_ArrayKernelT<> MyMesh;
MyMesh mesh;
OpenMesh::EdgeHandle edgH;
MyMesh::EdgeIter eit;
float len, angle;
OpenMesh::IO::read_mesh(mesh, "cube.off")
for (eit = mesh.edges_begin(); eit != mesh.edges_end(); eit++)
{
    edgH = *eit;
    len = mesh.calc_edge_length(edgH);
    angle = mesh.calc_dihedral_angle(edgH);
    cout << "Edge length = " << len <<" Dihedral angle = " << angle << endl;
}

2.3 邻接查询