Graphics Reference
In-Depth Information
mesh type produces redundancies. Moreover, because polygon meshes do not have adjacency
information, mesh traversal is not efficient.
Vertex-polygon mesh:
To alleviate the redundancy problem of the polygon mesh, the vertices
of the mesh are stored in a separate table. Rather than the actual vertices being stored in the
polygon table, their indices to the vertex table are stored instead. Nevertheless, this mesh type
stores no adjacency information.
Simple adjacency mesh:
In this mesh type, three tables are used to store vertices, edges, and
polygons. Along with each individual element, the indices to all incident elements are stored.
This mesh enables an efficient traversal but requires extra storage (compared with other mesh
types), more processing power, and care during manipulation (e.g., split or merge operations)
to maintain mesh consistency.
Partial adjacency mesh:
This mesh is similar to the simple adjacency mesh with the excep-
tion that not all adjacency information is stored, hence reducing the demand for memory
and storage. The unprovided adjacency information can be efficiently inferred from the one
provided; thus, the mesh is efficiently traversable, particularly if the facets are constrained to
be triangular (as in the case of a triangular mesh).
Triangular mesh:
As previously mentioned, the polygons in this mesh are triangles, and it
is the most widely used mesh representation because of its simplicity. The triangular mesh
usually stores the vertices and the triangles with indices to all neighboring vertices and triangles
in separate tables. The edge information is implicit and can be inferred at any vertex (defined
by the neighboring vertices) or triangle (its edges).
Winged-edge mesh:
The adjacency information in this mesh is centered around the edges,
and the mesh is traversed on an edge-by-edge basis. Along with each edge, indices point to
the two incident polygons (left and right) and four other edges; the first encountered edges in
the clock wise (CW) and the counter-clock wise (CCW) directions at both vertices of the edge
(see Figure 2.3). The split-and-merge operations are flexible and efficient for the winged-edge
mesh.
3D meshes can store (or refer to) data pertaining to local mesh elements such as texture
(as with point cloud pointers to texture maps are used), normals and curvatures. They can
also be customized to better suit (from the point of view of flexibility and/or efficiency)
the applications at hand. For more variants and extensive discussions of 3D meshes and
mesh operations, the reader is refered to the SIGGRAPH course notes by Botsch et al.
(2007). Well-thought of designs of data structures for 3D polygonal meshes are provided by
Kettner (1999).
Range Image Representation
×
A range image can be defined as a partial binary function,
r
:
, that maps to the
range (depth) of a surface point relative to a reference Cartesian frame (often the frame of
the 3D acquisition digitizer). The domain of the range image
R
can be the azimuth
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