Deviation spaces

A deviation space as used in [6] is shown in figure

Figure 4: Approximation of the error volume by different deviation spaces

[HOPPE ([6])] [extended]

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.

After a vertex v_s is created by an edge collapse operation, for all leaf nodes of the hierarchy tree below v_s (vertices of the original mesh) their nearest neighbor on N_vs (all faces adjacent to v_s) is computed. The error vectors are the deviations between a leaf vertex and its nearest neighbor on N_vs. By descending the PM hierarchy it is also guaranteed that only topological corresponding regions are considered (as in [11]).