Digital Geometry Processing
Exercise5-OpenMesh
Heng Liu, liu@inf.unibe.ch
Computer Graphics Group

OpenMesh

  • Features
    • Representation of arbitrary polygonal (the general case) and pure triangle meshes (providing more efficient, specialized algorithms)
    • Explicit representation of vertices, halfedges, edges and faces.
    • Fast neighbourhood access, especially the one-ring neighbourhood.
    • Highly customizable :
      • Choose your coordinate type (dimension and scalar type)
      • Attach user-defined elements/functions to the mesh elements.
      • Attach data at runtime using dynamic properties.

Halfedge data structure

  • Vertex
    • one outgoing halfedge
  • Halfedge
    • to vertex
    • incident face
    • previous/ next/ opposite halfedges
  • Face
    • one incident halfedge

Halfedge data structure

  • One-ring neighbourhood traversal

(1) start at a vertex

Halfedge data structure

  • One-ring neighbourhood traversal

(2) find outgoing halfedge

Halfedge data structure

  • One-ring neighbourhood traversal

(3) switch to opposite halfedge

Halfedge data structure

  • One-ring neighbourhood traversal

(4) next halfedge points to neighbouring vertex

TriMesh definition

  • Define with default traits
  typedef OpenMesh::TriMesh_ArrayKernelT<>  MyMesh;
  MyMesh mesh;
  • Define with customized traits
 struct TriTraits : public OpenMesh::DefaultTraits
 {
   /// Use double precision points
   typedef OpenMesh::Vec3d Point;
   /// Use double precision Normals
   typedef OpenMesh::Vec3d Normal;
   /// Use RGBA Color
   typedef OpenMesh::Vec4f Color;
 };
 typedef OpenMesh::TriMesh_ArrayKernelT<TriTraits>  MyMesh; 
 MyMesh mesh;

Mesh creation

  • Adding a vertex
   MyMesh mesh;
   ...
   OpenMesh::VertexHandle vh = mesh.add_vertex(MyMesh::Point(x,y,z));
  • Adding a face
MyMesh mesh;
OpenMesh::VertexHandle vh0, vh1, vh2;
...
OpenMesh::FaceHandle fh = mesh.add_face(vh0, vh1, vh2);

Access vertex geometry

  • Reading vertex positions
   MyMesh mesh;
   OpenMesh::VertexHandle vh;
   ...
   MyMesh::Point pos = mesh.point(vh);
  • Modifying vertex positions
   MyMesh mesh;
   OpenMesh::VertexHandle vh;
   MyMesh::Point new_pos;
   ...
   mesh.set_point(vh, new_pos);

Mesh elements traversal

  • How to modify all vertices?
 MyMesh mesh;
 //vertex iterators
 MyMesh::VertexIter v_it, v_begin, v_end;
 //range of iterators
 v_begin = mesh.vertices_begin();
 v_end = mesh.vertices_end();
 //iterate over all vertices
 for(v_it = v_begin; v_it != v_end; ++v_it){
     //get vertex handle
     OpenMesh::VertexHandle vh = *v_it;
     //process the vertex
     DoSomethingWithVertex(vh);
 }

Mesh elements traversal

  • Iterating over faces
    • MyMesh::VertexIter -> MyMesh::FaceIter
    • vertices_begin() -> faces_begin()
    • vertices_end() -> faces_end()
  • Similarly:
    • MyMesh::EdgeIter & MyMesh::HalfedgeIter

Enumerating incident elements

  • Iterate over all neighbouring vertices

      MyMesh mesh;
  OpenMesh::VertexHandle vh;
  //circulator around a vertex
  MyMesh::VertexVertexIter vv_it = mesh.vv_iter(vh);
  // circulate around the current vertex
  for(; vv_it.is_valid(); ++vv_it) {
      //process the neighbouring vertex
      DoSomethingWithVertex(*vv_it);
  }

Enumerating incident elements

  • The circulators around a vertex are:
    • VertexVertexIter: iterate over all neighboring vertices.
    • VertexIHalfedgeIter: iterate over all incoming halfedges.
    • VertexOHalfedgeIter: iterate over all outgoing halfedges.
    • VertexEdgeIter: iterate over all incident edges.
    • VertexFaceIter: iterate over all adjacent faces.

Enumerating incident elements

  • The circulators around a face are:
    • FaceVertexIter: iterate over the face’s vertices.
    • FaceHalfedgeIter: iterate over the face’s halfedges.
    • FaceEdgeIter: iterate over the face’s edges.
    • FaceFaceIter: iterate over all edge-neighboring faces.

Element count functions

  • Query entity number
MyMesh mesh;
unsigned int n1 = mesh.n_vertices(), 
n2 = mesh.n_faces(),
n3 = mesh.n_edges(),
n4 = mesh.n_halfedges();

Using properties

  • Template based properties
MyMesh mesh;
//define a property type, e.g edge property in float
typedef OpenMesh::EPropHandleT<float> edge_length;
//add the property to mesh and name it(optional)
mesh.add_property(edge_length, "edge length");
OpenMesh::EdgeHandle eh;
float L, LL;
//write to the property
mesh.property(edge_length, eh) = L;
//read the property
LL = mesh.property(edge_length, eh);
//remove the property
mesh.remove_property(edge_length);

Connectivity Query

  • Getting the connectivity information
MyMesh mesh; 
OpenMesh::HalfedgeHandle heh;
OpenMesh::VertexHandle vh_from = mesh.from_vertex_handle(heh),
OpenMesh::VertexHandle vh_to = mesh.to_vertex_handle(heh);
OpenMesh::FaceHandle fh = mesh.face_handle(heh);
OpenMesh::HalfedgeHandle heh_next = mesh.next_halfedge_handle(heh);
OpenMesh::HalfedgeHandle heh_prev= mymesh.prev_halfedge_handle(heh);
OpenMesh::HalfedgeHandle heh_opp = mymesh.opposite_halfedge_handle(heh);

Intergrated vector operations

  • Using the integrated vector operations
MyMesh::Point x, y, a, b, c, d;
...
//arithmetic operations
a = x + y;
b = x - y;
c = x * 0.5;
d = y / 3.0;
...

Intergrated vector operations

  • Using the integrated vector operations
MyMesh::Point x, y, a, b, c, d;
...
//dot product
Scalar dot = OpenMesh::dot(x, y); //Scalar dot = x | y;
//compute the norm
Scalar norm = x.norm();
//normalize 
a = x.normalize();
//cross product 
MyMesh::Point cross = OpenMesh::cross(x, y); //Scalar b = x % y;
...

Reference