Game Development Reference

In-Depth Information

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.

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