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An efficient algorithm for terrain simplification

Conference ·
OSTI ID:471668
;  [1]
  1. Duke Univ., Durham, NC (United States)
Given a set S of n points in {Re}{sup 3}, sampled from an unknown bivariate function f (x, y) (i.e., for each point p {element_of} S, z{sub p} = f (x{sub p}, y{sub p})), a piecewise-linear function g(x, y) is called an {epsilon}-approximation of f (x, y) if for every p {element_of} S, {vert_bar}f (x, y) - g (x, y){vert_bar} {le} {epsilon}. The problem of computing an {epsilon}-approximation with the minimum number of vertices is NP-Hard. We present a randomized algorithm that computes an {epsilon}-approximation of size O(c{sup 2} log{sup 2} c) in O(n{sup 2+{delta}} + c{sup 3} log{sup 2}c log n/c) expected time, where c is the size of the {epsilon}-approximation with the minimum number of vertices and {delta} is any arbitrarily small positive number. Under some reasonable assumptions, the size of the output is close to O(c log c) and the expected running time is O(n{sup 2+{delta}}). We have implemented a variant of this algorithm and include some empirical results.
OSTI ID:
471668
Report Number(s):
CONF-970142--; CNN: Grant CCR-93-01259; Grant DAAH04-96-1-0013
Country of Publication:
United States
Language:
English

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