## Fast Rendering of Subdivision Surfaces: Slide 10 of 15.

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The fact that two triangles can be combined into a quadrangle allows
us to simply store the vertices into a square 2D array. The gray color
shows the proper triangles surrounded by the support edges and
vertices. With this representation, we don't need any pointers for
finding neighbors, and we store explicitly only the vertices --- no
edges or faces --- so we get rid of almost all of the overhead usually
associated with storing a polygonal mesh. We can find all such
information, even the edge and vertex types, by consulting the
original message and the location within the square array.

A straightforward implementation of subdividing a level at a time
would require memory on the order of the number of vertices at the
final level. However, this number grows up really fast: each
successive level has about 4 times as many vertices as the previous
one.