Overview

The A48 library is intended for applications in which shape information is known independently of the mesh. Typically in such applications, the following requirements are satisfied:

• There is a base domain where the surface geometry is defined;
• It is possible to compute samples of points on the surface.

The library takes care of maintaining an adaptive variable resolution mesh, but storing only the current mesh and providing a simple interface.

The user must provide the topology and geometry of an initial base polyhedron, together with a means to sample and adapt the underlying surface.

The library API, related to mesh construction and adaptation is composed of only two functions:

• Mesh(Surface* surf) -- this function is the mesh constructor. It takes as a parameter an object that represents the surface.

• Mesh::adapt()| -- this function adapts the mesh according to the user defined criteria provided by surf.

The function adapt performs both refinement and simplifications of the current mesh. Two additional functions, adapt_refine and adapt_simplify, are also exposed by the library API, in case the application needs to do only refinement or simplification.

The above API requires that the application supplies four functions through the surface object: a procedure to construct the {base polyhedron}; a {sampling function} to evaluate the geometry of the surface at vertex of the mesh; a {refinement test} and a {simplification test} to determine if the mesh needs further subdivision or coarsening, respectively.

Therefore, the Surface object class has to implement the following minimum functionality:

class Surface {
  void base_mesh(int nv, Point pts[][], int nt, int tris[][]);
  void sample(Edge e, Vertex &v);
  float refine_rank(Hedge e);
  float simplif_rank(Vertex v); 
}

In addition to the API above, the library also provides the standard operators for querying and navigating topological data structures.

The library data structure does not include any apriori geometric data. This is supplied by the application through attribute classes. The library deals only with topological issues. Therefore, the application has full control of geometry aspects through the face, edge and vertex attribute classes and the sampling function.

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