A deviation space as used in  is shown in figure
4(a). The error vectors (representing the geometric deviation
between the original and the simplified mesh) are bounded by a volume consisting
of a sphere and two cones. In this implementation the deviation spaces are ``clipped''
at a sphere large enough to contain all error vectors (figure 4(b)).
Thus the tops of the cones are cut off resulting in less detail drawn without
exceeding the screen-space error tolerance.
Approximation of the error volume by different deviation spaces
After a vertex vs is created by an edge collapse operation, for all
leaf nodes of the hierarchy tree below vs (vertices of the original
mesh) their nearest neighbor on Nvs (all faces adjacent to vs)
is computed. The error vectors are the deviations between a leaf vertex and
its nearest neighbor on Nvs. By descending the PM hierarchy it
is also guaranteed that only topological corresponding regions are considered
(as in ).