Game Development Reference

In-Depth Information

Figure 16.5 Removing an edge.

There is a limitation to the edge contraction-based technique where an

unconnected mesh is involved. Because we only allow for edge

contraction, the model can change dramatically in the volumes perceived.

In a low polygon game, the perceived volumes are the most important

aspect of the display. A useful way to avoid the problem of changing

volume when reducing polygons is to allow for two vertices that are close

together to be regarded in the same way as an edge. The human eye

works in much the same way, with distant detail merging together.

Determining the limiting distance for such vertex pairs has to be handled

with care, but the resulting models hold their volume much more

effectively.

Deciding who can stay and who must go

The algorithm we use must determine an error for the removal of an edge.

If by removing the edge we retain a similar shape to the original, after this

contraction then this edge can be safely removed. We do this by

calculating a quadric matrix,
Q
, for each vertex. The error at a vertex is

then given by
v
T
Q
v
. When calculating the effect of merging two vertices,

we create a new matrix by using the sum of the matrices for each

vertex:

Q

=
Q
1
+
Q
2

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