Game Development Reference
Figure 14.15 Types of triangle configurations
Figure 14.16 Deletion of a vertex from a mesh
Figure 14.17 Deletion of an edge from a mesh, known as edge collapse method
type of algorithm can also be used when we want to refine a mesh). The first operator
simply removes a vertex, as shown in figure 14.16. However, a large number of degrees
of freedom remain on this operator: the re-triangulation shown in the figure is just one
example of triangulation.
To compensate this disadvantage, there is another type of operator, called edge
collapse, shown in figure 14.17. In this way, the only freedom that remains on the
operator is the place of the new vertex, which can be anywhere on the edge that was
deleted. A standard solution consists of choosing one of the two vertices of this edge;
it is called restricted edge collapse . These operators do not modify the topology of
the mesh, the non-convex regions of the mesh remain the same. There are also the
operators that modify the topology of the mesh, either by connecting the parts of the
mesh which were originally not connected or by reversing the edges, which can make
it possible to apply the previous operators in certain cases.
All these operators are applicable only to the internal vertices of the mesh. In
case of meshes that do not represent solid objects, the boundary vertices should be
processed with special precautions: Here it involves approximating the border of a
polyhedron. The standard algorithms can also be used by maintaining the perimeter
of the polyhedron, for example.