Computational geometry: an introduction
Computational geometry: an introduction
Fractals everywhere
Approximations of fractal sets
Journal of Computational and Applied Mathematics
Efficient antialiased rendering of 3-D linear fractals
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Spatial bounding of self-affine iterated function system attractor sets
GI '96 Proceedings of the conference on Graphics interface '96
Computational geometry in C (2nd ed.)
Computational geometry in C (2nd ed.)
Determining the minimum-area encasing rectangle for an arbitrary closed curve
Communications of the ACM
Bounding Recursive Procedural Models Using Convex Optimization
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Chaos and Fractals
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
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We present an algorithm for approximating convex hulls of affine iterated function system (IFS) attractors in R^2 at any accuracy required. The algorithm is based on the gift-wrapping technique. However, in order to make the computation efficient and with low memory requirements, we take advantage of self-similarity of IFS attractors. To accomplish this we engage the adaptive-cut approach in the process of the convex hull computation. In effect, the convex hull of an IFS attractor is approximated efficiently (our algorithm appears to run in expected O(hN) time) with the guaranteed O(logN) storage, where h is the number of the approximate hull vertices, and N is the number of points of an @e-approximation of the attractor. Since the convex hull is the most ubiquitous structure in computational geometry, our algorithm opens the door to solving many geometrical problems concerning IFS attractors. As instances of possible applications in computer graphics we show how to compute the diameter of an IFS attractor and the smallest oriented rectangle to bound the attractor.