Abstract
Amorphous shapes have always been a challenge to CG modelers. Apparently natural in look, their topology is hard to retrieve manually. Scientists from different backgrounds have tried to understand and model such phenomena. Fractals belong to the most representative solutions, but still are rare in 3D domain. Methods for generation of fractal objects use mainly quaternion representations for nonlinear systems in four dimensions. In such a case advanced volumetric graphics methods need to be applied to convey multidimensional information. In the paper, we propose a simple and effective approach to use four-dimensional escape-time fractals as automated shape generator. We extend general quadratic fractal maps to four dimensions. The algorithm results in diverse aesthetically balanced volumetric shapes delivered in real time on a modern PC.
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References
Sprott, J.C., Pickover, C.A.: Automatic generation of general quadratic map basins. Computers & Graphics 19(2), 309–313 (1995)
Nikiel, S., Goinski, A.: Generation of volumetric escape time fractals. Computers & Graphics 27(6), 977–982 (2003)
Wonka, P., Wimmer, M., Sillion, F., Ribarsky, W.: Instant architecture. ACM Transactions on Graphics 22(3), 669–677 (2003)
Parish, Y., Muller, P.: Procedural Modeling of Cities. In: Fiume, E. (ed.) Proceedings (SIGGRAPH 2001), pp. 301–308. ACM Press (2001)
Greuter, S., Parker, J., Stewart, N., Leach, G.: Real-time procedural generation of pseudo infinite cities. In: Proceedings (GRAPHITE 2003), pp. 87–95. ACM Press (2003)
Peytavie, A., Galin, E., Grosjean, J., Merrilou, S.: Arches: a Framework for Modelling Complex Terrains, Computer Graphics Forum. In: Proceedings EUROGRAPHICS, vol. 28(2), pp. 457–467 (2009)
Bouthors, A., Neyret, F.: Modelling Clouds Shape. In: Proceedings EUROGRAPHICS (2004)
Schpok, J., Simons, J., Ebert, D., Hansen, C.: A real-time cloud modeling, rendering, and animation system. In: Symposium on Computer Animation 2003, pp. 160–166 (2003)
Dobashi, Y., Kaneda, K., Yamashita, H., Okita, T., Nishita, T.: A simple, efficient method for realistic animation of clouds. In: Proceedings of ACM SIGGRAPH 2000, pp. 19–28 (2000)
Ebert, D.: Volumetric procedural implicit functions: A cloud is born. In: Whitted, T. (ed.) SIGGRAPH 97 Technical Sketches Program. ACM SIGGRAPH. Addison Wesley (1997) ISBN 0-89791-896-7
Elinas, P., Sturzlinger, W.: Real-time rendering of 3D clouds. Journal of Graphics Tools 5(4), 33–45 (2000)
Nishita, T., Nakamae, E., Dobashi, Y.: Display of clouds taking into account multiple anisotropic scattering and sky light. In: Rushmeier, H. (ed.) SIGGRAPH 96 Conference Proceedings, ACM SIGGRAPH, pp. 379–386. Addison Wesley (1996)
Harris, M.J., Lastra, A.: Real-time cloud rendering. Computer Graphics Forum 20(3), 76–84 (2001)
Gardner, G.Y.: Simulation of natural scenes using textured quadric surfaces. In: Christiansen, H. (ed.) Computer Graphics (SIGGRAPH 1984 Proceedings), vol. 18, pp. 11–20 (1984)
Gardner, G.Y.: Visual simulation of clouds. In: Barsky, B.A. (ed.) Computer Graphics (SIGGRAPH 1985 Proceedings), vol. 19, pp. 297–303 (1985)
Prusinkiewicz, P., Lindenmayer, A.: The Algorithmic Beauty of Plants, pp. 101–107. Springer (1991) ISBN 978-0387972978
Am Ende, B.A.: 3D Mapping of Underwater Caves. IEEE Computer Graphics Applications 21(2), 14–20 (2001)
Boggus, M., Crawfis, R.: Procedural Creation of 3D Solution Cave Models. In: Proceedings of the 20th IASTED International Conference on Modelling and Simulation, pp. 180–186 (2009)
Boggus, M., Crawfis, R.: Explicit Generation of 3D Models of Solution Caves for Virtual Environments. In: Proceedings of the 2009 International Conference on Computer Graphics and Virtual Reality, pp. 85–90 (2009)
Johnson, L., Yannakakis, G.N., Togelius, J.: Cellular Automata for Real-time Generation of Infinite Cave Levels. In: Proceedings of the 2010 Workshop on Procedural Content Generation in Games (PC Games 2010), pp. 1–4 (2010)
Schuchardt, P., Bowman, D.A.: The Benefits of Immersion for Spatial Understanding of Complex Underground Cave Systems. In: Proceedings of the 2007 ACM Symposium on Virtual Reality Software and Technology (VRST 2007), pp. 121–124 (2007)
Clempner, J.B., Poznyak, A.S.: Convergence method, properties and computational complexity for Lyapunov games. The International Journal of Applied Mathematics and Computer Science 21(2), 349–361 (2011)
Di Trapani, L.J., Inanc, T.: NTGsim, A graphical user interface and a 3D simulator for nonlinear trajectory generation methodology. The International Journal of Applied Mathematics and Computer 20(2), 305–316 (2010)
Norton, A.: Generation and display of geometric fractals in 3D. Computer Graphics (16), 61–67 (1982)
Kantor, I.L.: Hypercomplex Numbers. Springer, New York (1989)
Bedding, S., Briggs, K.: Iteration of quaternion maps. Int.Journal Bif. and Chaos, Appl. Sci. Eng. (5), 887–891 (1995)
Holbrook, J.A.R.: Quaternionic Fatou-Julia Sets. Annals Sci. Math., Quebcec (11), 79–94 (1987)
Rochon, D.: A generalized Mandelbrot set for bicomplex numbers. Fractals 8(2), 355–368 (2000)
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Goiński, A., Zawadzki, T., Nikiel, S. (2012). Automatic Shape Generation Based on Quadratic Four-Dimensional Fractals. In: Bolc, L., Tadeusiewicz, R., Chmielewski, L.J., Wojciechowski, K. (eds) Computer Vision and Graphics. ICCVG 2012. Lecture Notes in Computer Science, vol 7594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33564-8_9
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DOI: https://doi.org/10.1007/978-3-642-33564-8_9
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