ptdist - Nanyang Technological University

Fig. 12. Periodograms of Poisson disk distributions generated with dual Poisson-disk tiles (a-f) and dart throwing (g).
where Rmax is an upper bound of the Poisson disk radius given the total surface area and the
distribution density, whereas r is the Poisson disk radius we have in the generated Poisson disk
distribution.
Rmax = (2 √ 3K/S) −1/2 ,
where S is the total surface area and K/S is the distribution density. Here r is half of the shortest
distance among neighboring point pairs distributed on the object surface. Furthermore, radius
statistics measure the ratio ρ = r/Rmax to estimate the regularity of the generated distributions.
A small ρ indicates an uneven distribution, while a large ρ indicates a regular distribution.
According to Section 3.1 in [32], Poisson disk distributions should have a relative radius that
is large (ρ > 0. 65), but not too large (ρ > 0. 90). Furthermore, it is worth noting that since the
equation for estimating Rmax is originally for 2D planar domain, we have to assume sufficiently
large point sets in our experiments, so that Rmax can serve as a good upper bound approximation
even on non-planar surfaces. In practice, we can obtain ρ values of around 0. 3 to 0. 6 (on surfaces)
after the tiling depending on the quality of the surface parameterization, and can quickly optimize
ρ to be around 0. 7 to 0. 8 after distribution refinement. Table III presents some related results
for HOLES3, BUNNY, and LAURANA before and after relaxation, while Figure 13 shows the
generated distributions on BUNNY before and after relaxation. Note that we also compute mbefore
February 2, 2008 MINOR REVISION
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