We propose a concise approximate description, and a method for efficiently obtaining this description, via adaptive random sampling of the performance (running time, memory consumption, or any other profileable numerical quantity) of a given algorith
m on some low-dimensional rectangular grid of inputs. The formal correctness is proven under reasonable assumptions on the algorithm under consideration; and the approachs practical benefit is demonstrated by predicting for which observer positions and viewing directions an occlusion culling algorithm yields a net performance benefit or loss compared to a simple brute force renderer.
For a fixed virtual scene (=collection of simplices) S and given observer position p, how many elements of S are weakly visible (i.e. not fully occluded by others) from p? The present work explores the trade-off between query time and preprocessing s
pace for these quantities in 2D: exactly, in the approximate deterministic, and in the probabilistic sense. We deduce the EXISTENCE of an O(m^2/n^2) space data structure for S that, given p and time O(log n), allows to approximate the ratio of occluded segments up to arbitrary constant absolute error; here m denotes the size of the Visibility Graph--which may be quadratic, but typically is just linear in the size n of the scene S. On the other hand, we present a data structure CONSTRUCTIBLE in O(n*log(n)+m^2*polylog(n)/k) preprocessing time and space with similar approximation properties and query time O(k*polylog n), where k<n is an arbitrary parameter. We describe an implementation of this approach and demonstrate the practical benefit of the parameter k to trade memory for query time in an empirical evaluation on three classes of benchmark scenes.
