Abstract
For producing numerous frames as in computer animation, the direct application of the Mandelbrot theory of fractals is very expensive. The recursive midpoint subdivision is much more efficient although it sacrifices mathematical purity for execution speed. In our implementation, fractal polygons are created using subdivisions of meshes of triangles. But the midpoint is randomly generated inside a revolution volume where the axis is the edge itself. Based on this implementation, we study the impact of three geometric parameters for controlling this algorithm: the edge threshold, the eccentricity of the smallest cylinder surrounding the revolution volume and the displacement of the revolution volume towards the segment center. Several examples are provided. The subdivision algorithm is also applied to generate textures by perturbation of the normal length.
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References
Blinn JF (1978) Simulation of wrinkled surfaces. Proc SIGGRAPH'78, Comput Graph 12(3):286–292
Burgess (1987) Introduction of texture in the MIRA-SHADING language (in French). MSc Thesis MIRALab, Université de Montréal
Fournier A, Fussell D, Carpenter L (1982) Computer rendering of stochastic models. Commun ACM 25(6):371–384
Haruyama S, Barsky BA (1984) Using stochastic modeling for texture generation. IEEE Comput Graph Appl 4(3):7–19
Magnenat-Thalmann N, Thalmann D, Fortin M (1985) MIRANIM: An Extensible Director-Oriented System for the Animation of Realistic Images. IEEE Comput Graph Appl 5(3):61–73
Mandelbrot B (1975) Stochastic models for the earth's relief, the shape and fractal dimension of coastlines, and the number area rule for islands. Proc Natl Acad Sci 72(10):2825–2828
Mandelbrot B (1977) Fractals: form, chance and dimension. WH Freeman, San Francisco
Mandelbrot B (1982a) The fractal geometry of nature, WH Freeman, San Francisco
Mandelbrot B (1982b) Comment on computer rendering of fractal stochastic models. Commun ACM 25(3):581–582
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Magnenat-Thalmann, N., Burgess, M., Forest, L. et al. A geometric study of parameters for the recursive midpoint subdivision. The Visual Computer 3, 145–151 (1987). https://doi.org/10.1007/BF01962895
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DOI: https://doi.org/10.1007/BF01962895