DOC - Using and understanding OpenMesh
DOC - Using and understanding OpenMesh
目錄
- DOC - Using and understanding OpenMesh
- Features and Goals of OpenMesh
- The Halfedge Data Structure
- Mesh Iterators and Circulators
- How to navigate on mesh
- Read and write meshes from files
- Some basic operations: Flipping and collapsing edge
- Collapsing edges
- Conceptual Class Hierarchy
- Specifying your MyMesh
- Specifying an OpenMesh using Eigen3 vectors
本文是對OpenMesh文件中《Using and understanding OpenMesh》一節的學習摘錄。
Features and Goals of OpenMesh
資料結構主要特徵是:
- 並不受限於三角形網格,可處理一般的多邊形網格;
- 頂點,半邊,邊,面的明確表示;
- 高效的訪問一個頂點的鄰域;
- 能夠處理非流形頂點(如兩個面,共享一個頂點)。
The Halfedge Data Structure
半邊資料結構中是將一條邊,劃分成了兩條方向相對的半邊,不同元素之間的連線關係,如下圖所示:
- 每個頂點儲存了從它出發的半邊,圖中為1;
- 每個面儲存了周圍的一條半邊,圖中為2;
- 每個半邊儲存了以下handle:
- 指向的頂點,圖中為3;
- 屬於哪個面,圖中為4;
- 共享面的下一個半邊(逆時針方向),圖中為5;
- 相對的半邊,圖中為6;
- 可選的,共享面的上一個半邊,圖中為7。
通過上面構建的關係,可以很方便的,對一個面周圍的半邊,頂點,相鄰面進行遍歷。
Mesh Iterators and Circulators
網格提供了迭代器,用來訪問vertices,halfedges,edges,faces。所有的迭代器定義在OpenMesh::Iterators
名稱空間中,在具體使用的時候,可以用mesh內部的迭代器MyMesh::VertexIter
取代OpenMesh::Iterators::VertexIterT<MyMesh>
的形式。
迭代器的使用示例如下:
MyMesh mesh;
// iterate over all vertices
for (MyMesh::VertexIter v_it=mesh.vertices_begin(); v_it!=mesh.vertices_end(); ++v_it)
...; // do something with *v_it, v_it->, or *v_it
// iterate over all halfedges
for (MyMesh::HalfedgeIter h_it=mesh.halfedges_begin(); h_it!=mesh.halfedges_end(); ++h_it)
...; // do something with *h_it, h_it->, or *h_it
// iterate over all edges
for (MyMesh::EdgeIter e_it=mesh.edges_begin(); e_it!=mesh.edges_end(); ++e_it)
...; // do something with *e_it, e_it->, or *e_it
// iterator over all faces
for (MyMesh::FaceIter f_it=mesh.faces_begin(); f_it!=mesh.faces_end(); ++f_it)
...; // do something with *f_it, f_it->, or *f_it
刪除的元素
如果mesh中沒有元素被標記為刪除,idx()
返回的值依次從0到number of elements - 1
。
但是如果有元素被標記為刪除,同時沒有執行垃圾回收(OpenMesh::ArrayKernel::garbage_collection() ),有效的idx
並不是按順序依次排列的。執行完垃圾回收之後,順序會被重新調整。
OpenMesh使用惰性刪除方案,以避免不必要的資料結構更新。 半邊資料結構將始終直接進行更新,以確保以下演算法具有正確的迭代器設定。
如果你刪除一個面,這個面本身是存在的,但是位於hole的半邊會更新,這意味著相鄰頂點上的迴圈器將不再碰到該面。
如果刪除了一條邊,相鄰的面也將被刪除(標記它們已刪除並更新周圍的半邊)。 邊本身也將標記為已刪除。 同樣,迴圈器將不再看到刪除的元素。
對於頂點,將使用上述方案刪除所有相鄰的面和邊,並將頂點標記為已刪除。
此時,迭代器仍然能夠訪問到所有的元素(包括,標記為刪除的)。如果你使用skipping iterators,將會跳過刪除的元素。
skipping iterators如下:
vertices_sbegin()
;edges_sbegin()
;halfedges_sbegin()
;faces_sbegin()
;
Circulators
用來快速訪問鄰域的迭代器。如,VertexVertexIter
用來訪問頂點的1-ring頂點;FaceHalfedgeIter
用來訪問屬於這個面的半邊;CenterItem_AuxiliaryInformation_TargetItem_Iter
用來訪問中心元素周圍的所有相鄰元素。主要有:
VertexVertexIter
: 頂點的所有1-ring頂點;VertexIHalfedgeIter
: 頂點的所有入半邊;VertexOHalfedgeIter
: 頂點的所有出半邊;VertexEdgeIter
: 頂點的所有相鄰邊;VertexFaceIter
: 頂點的所有相鄰面;FaceVertexIter
:面上的頂點;FaceHalfedgeIter
:面上的半邊;FaceEdgeIter
:面上的邊;FaceFaceIter
: 面的相鄰面;HalfedgeLoopIter
: 順序連結的半邊;
獲取以上迭代器的函式如下(defined in OpenMesh::PolyConnectivity):
/**************************************************
* Vertex circulators
**************************************************/
// Get the vertex-vertex circulator (1-ring) of vertex _vh
VertexVertexIter OpenMesh::PolyConnectivity::vv_iter (VertexHandle _vh);
// Get the vertex-incoming halfedges circulator of vertex _vh
VertexIHalfedgeIter OpenMesh::PolyConnectivity::vih_iter (VertexHandle _vh);
// Get the vertex-outgoing halfedges circulator of vertex _vh
VertexOHalfedgeIter OpenMesh::PolyConnectivity::voh_iter (VertexHandle _vh);
// Get the vertex-edge circulator of vertex _vh
VertexEdgeIter OpenMesh::PolyConnectivity::ve_iter (VertexHandle _vh);
// Get the vertex-face circulator of vertex _vh
VertexFaceIter OpenMesh::PolyConnectivity::vf_iter (VertexHandle _vh);
/**************************************************
* Face circulators
**************************************************/
// Get the face-vertex circulator of face _fh
FaceVertexIter OpenMesh::PolyConnectivity::fv_iter (FaceHandle _fh);
// Get the face-halfedge circulator of face _fh
FaceHalfedgeIter OpenMesh::PolyConnectivity::fh_iter (FaceHandle _fh);
// Get the face-edge circulator of face _fh
FaceEdgeIter OpenMesh::PolyConnectivity::fe_iter (FaceHandle _fh);
// Get the face-face circulator of face _fh
FaceFaceIter OpenMesh::PolyConnectivity::ff_iter (FaceHandle _fh);
使用示例:
MyMesh mesh;
// (linearly) iterate over all vertices
for (MyMesh::VertexIter v_it=mesh.vertices_sbegin(); v_it!=mesh.vertices_end(); ++v_it)
{
// circulate around the current vertex
for (MyMesh::VertexVertexIter vv_it=mesh.vv_iter(*v_it); vv_it.is_valid(); ++vv_it)
{
// do something with e.g. mesh.point(*vv_it)
}
}
How to navigate on mesh
對半邊進行順序訪問:
[...]
TriMesh::HalfedgeHandle heh, heh_init;
// Get the halfedge handle assigned to vertex[0]
heh = heh_init = mesh.halfedge_handle(vertex[0].handle());
// heh now holds the handle to the initial halfedge.
// We now get further on the boundary by requesting
// the next halfedge adjacent to the vertex heh
// points to...
heh = mesh.next_halfedge_handle(heh);
// We can do this as often as we want:
while(heh != heh_init) {
heh = mesh.next_halfedge_handle(heh);
}
[...]
判斷邊界相關的函式(OpenMesh::PolyConnectivity::is_boundary().):
// Test if a halfedge lies at a boundary (is not adjacent to a face)
bool is_boundary (HalfedgeHandle _heh) const
// Test if an edge lies at a boundary
bool is_boundary (EdgeHandle _eh) const
// Test if a vertex is adjacent to a boundary edge
bool is_boundary (VertexHandle _vh) const
// Test if a face has at least one adjacent boundary edge.
// If _check_vertex=true, this function also tests if at least one
// of the adjacent vertices is a boundary vertex
bool is_boundary (FaceHandle _fh, bool _check_vertex=false) const
獲取邊的from,to頂點:
// Get the handle of the to vertex
OpenMesh::Concepts::KernelT::to_vertex_handle();
// Get the handle of the from vertex
OpenMesh::Concepts::KernelT::from_vertex_handle();
Read and write meshes from files
示例如下:
#include <OpenMesh/Core/IO/MeshIO.hh>
MyMesh mesh;
if (!OpenMesh::IO::read_mesh(mesh, "some input file"))
{
std::cerr << "read error\n";
exit(1);
}
// do something with your mesh ...
if (!OpenMesh::IO::write_mesh(mesh, "some output file"))
{
std::cerr << "write error\n";
exit(1);
}
Some basic operations: Flipping and collapsing edge
Flipping edges
TriMesh mesh;
// Add some vertices
TriMesh::VertexHandle vhandle[4];
vhandle[0] = mesh.add_vertex(MyMesh::Point(0, 0, 0));
vhandle[1] = mesh.add_vertex(MyMesh::Point(0, 1, 0));
vhandle[2] = mesh.add_vertex(MyMesh::Point(1, 1, 0));
vhandle[3] = mesh.add_vertex(MyMesh::Point(1, 0, 0));
// Add two faces
std::vector<TriMesh::VertexHandle> face_vhandles;
face_vhandles.push_back(vhandle[2]);
face_vhandles.push_back(vhandle[1]);
face_vhandles.push_back(vhandle[0]);
mesh.add_face(face_vhandles);
face_vhandles.clear();
face_vhandles.push_back(vhandle[2]);
face_vhandles.push_back(vhandle[0]);
face_vhandles.push_back(vhandle[3]);
mesh.add_face(face_vhandles);
// Now the edge adjacent to the two faces connects
// vertex vhandle[0] and vhandle[2].
// Find this edge and then flip it
for(TriMesh::EdgeIter it = mesh.edges_begin(); it != mesh.edges_end(); ++it) {
if(!mesh.is_boundary(*it)) {
// Flip edge
mesh.flip(*it);
}
}
// The edge now connects vertex vhandle[1] and vhandle[3].
Collapsing edges
將from_vertex塌陷成to_vertex。
PolyMesh mesh;
// Request required status flags
mesh.request_vertex_status();
mesh.request_edge_status();
mesh.request_face_status();
// Add some vertices as in the illustration above
PolyMesh::VertexHandle vhandle[7];
vhandle[0] = mesh.add_vertex(MyMesh::Point(-1, 1, 0));
vhandle[1] = mesh.add_vertex(MyMesh::Point(-1, 3, 0));
vhandle[2] = mesh.add_vertex(MyMesh::Point(0, 0, 0));
vhandle[3] = mesh.add_vertex(MyMesh::Point(0, 2, 0));
vhandle[4] = mesh.add_vertex(MyMesh::Point(0, 4, 0));
vhandle[5] = mesh.add_vertex(MyMesh::Point(1, 1, 0));
vhandle[6] = mesh.add_vertex(MyMesh::Point(1, 3, 0));
// Add three quad faces
std::vector<PolyMesh::VertexHandle> face_vhandles;
face_vhandles.push_back(vhandle[1]);
face_vhandles.push_back(vhandle[0]);
face_vhandles.push_back(vhandle[2]);
face_vhandles.push_back(vhandle[3]);
mesh.add_face(face_vhandles);
face_vhandles.clear();
face_vhandles.push_back(vhandle[1]);
face_vhandles.push_back(vhandle[3]);
face_vhandles.push_back(vhandle[5]);
face_vhandles.push_back(vhandle[4]);
mesh.add_face(face_vhandles);
face_vhandles.clear();
face_vhandles.push_back(vhandle[3]);
face_vhandles.push_back(vhandle[2]);
face_vhandles.push_back(vhandle[6]);
face_vhandles.push_back(vhandle[5]);
mesh.add_face(face_vhandles);
// Now find the edge between vertex vhandle[2]
// and vhandle[3]
for(PolyMesh::HalfedgeIter it = mesh.halfedges_begin(); it != mesh.halfedges_end(); ++it) {
if( mesh.to_vertex_handle(*it) == vhandle[3] &&
mesh.from_vertex_handle(*it) == vhandle[2])
{
// Collapse edge
mesh.collapse(*it);
break;
}
}
// Our mesh now looks like in the illustration above after the collapsing.
Conceptual Class Hierarchy
概念相關類的繼承關係如下(大多通過模板引數的形式實現整合):
Specifying your MyMesh
自定義一個mesh,需要有如下步驟:
- 明確是三角網格,還是多邊形網格;(通常情況下選擇三角網格)
- 選擇mesh kernel;mesh kernel特例化了mesh 屬性在內部的儲存形式。預設的kernel是ArrayKernelT。
- 使用
Traits
類,引數化mesh。可以向網格項新增任意items,如標量,點,法線和顏色型別,並使用預定義屬性,例如Attributes :: Normal和Attributes :: Color。 - 使用自定義型別,動態繫結資料到mesh,或者是mesh的entities(vertex,(half-)edge,face)。
Mesh Traits
下面需要使用者自定義實現,需要提供的型別有:
- point和scalar型別:
MyMesh::Point
和MyMesh::Scalar
; - mesh items:
MyMesh::Vertex,MyMesh::Halfedge,MyMesh::Edge,MyMesh::Face
; - handle型別:
MyMesh::VertexHandle,MyMesh::HalfedgeHandle,MyMesh::EdgeHandle,MyMesh::FaceHandle
。
預設的traits類似如下:
struct DefaultTraits
{
typedef Vec3f Point;
typedef Vec3f Normal;
typedef Vec2f TexCoord;
typedef Vec3uc Color;
VertexTraits {};
HalfedgeTraits {};
EdgeTraits {};
FaceTraits {};
VertexAttributes(0);
HalfedgeAttributes(Attributes::PreHalfedge);
EdgeAttributes(0);
FaceAttributes(0);
};
建立自定義traits的時候需要從上面繼承建立。如果需要改變point的型別,可以進行如下操作:
struct MyTraits : public OpenMesh::DefaultTraits
{
typedef OpenMesh::Vec3d Point;
};
Adding Predefined Attributes
有一些預定義的attributes可以新增到mesh items中。這些全域性的屬性定義在OpenMesh::Attributes.命名看空間中。如果想要向頂點新增法向量和顏色,向面上新增法向量,那麼可以如下操作:
struct MyTraits : public OpenMesh::DefaultTraits
{
VertexAttributes( OpenMesh::Attributes::Normal | OpenMesh::Attributes::Color);
FaceAttribtues(OpenMesh::Attributes::Normal);
};
對於屬性提供執行時檢測,和編譯時檢測,執行時檢測如下:
if (OM_Check_Attrib(MyMesh::Vertex, Normal))
do_something_with_normals();
編譯時檢測如下:
#include <OpenMesh/Core/Utils/GenProg.hh>
// draw a face normal if we have one
void drawFaceNormal(const MyMesh::Face& _f) {
drawFaceNormal(_f, GenProg::Bool2Type<OM_Check_Attrib(MyMesh::Face, Normal)>());
}
// normal exists -> use it
void drawFaceNormal(const MyMesh::Face& _f, GenProg::Bool2Type<true>) {
glNormal3fv(_f.normal());
}
// empty dummy (no normals)
void drawFaceNormal(const MyMesh::Face& _f, GenProg::Bool2Type<false>){}
Adding User-Defined Elements
struct MyTraits : public OpenMesh::DefaultTraits
{
VertexTraits
{
int some_additional_index;
};
};
// 巨集定義展開後得到如下形式:
struct MyTraits : public OpenMesh::DefaultTraits
{
template <class Base, class Refs> struct VertexT : public Base
{
int some_additional_index;
};
};
Final Implementation Example
#include <OpenMesh/Core/Mesh/TriMesh_ArrayKernelT.hh>
// define traits
struct MyTraits : public OpenMesh::DefaultTraits
{
// use double valued coordinates
typedef OpenMesh::Vec3d Point;
// use vertex normals and vertex colors
VertexAttributes( OpenMesh::DefaultAttributer::Normal |
OpenMesh::DefaultAttributer::Color );
// store the previous halfedge
HalfedgeAttributes( OpenMesh::DefaultAttributer::PrevHalfedge );
// use face normals
FaceAttributes( OpenMesh::DefaultAttributer::Normal );
// store a face handle for each vertex
VertexTraits
{
typename Base::Refs::FaceHandle my_face_handle;
};
};
// Select mesh type (TriMesh) and kernel (ArrayKernel)
// and define my personal mesh type (MyMesh)
typedef OpenMesh::TriMesh_ArrayKernelT<MyTraits> MyMesh;
int main(int argc, char **argv)
{
MyMesh mesh;
// -------------------- Add dynamic data
// for each vertex an extra double value
OpenMesh::VPropHandleT< double > vprop_double;
mesh.add_property( vprop_double );
// for the mesh an extra string
OpenMesh::MPropHandleT< string > mprop_string;
mesh.add_property( mprop_string );
// -------------------- do something
...;
}
Specifying an OpenMesh using Eigen3 vectors
#include <OpenMesh/Core/Geometry/EigenVectorT.hh>
struct EigenTraits : OpenMesh::DefaultTraits {
using Point = Eigen::Vector3d;
using Normal = Eigen::Vector3d;
using TexCoord2D = Eigen::Vector2d;
};
using EigenTriMesh = OpenMesh::TriMesh_ArrayKernelT<EigenTraits>;
EigenTriMesh mesh;