Abstract
Cross sections of Julia sets in the quaternions are highly complicated 3-dimen-sional objects, which may serve as qualified test objects for surface construction and rendering algorithms. Boundary tracking methods generate the surfaces as lists of primitives such that rotation or repositioning requires only re-rendering. The main disadvantage of early boundary tracking approaches is the amount of storage they require. Ray-tracing methods, although adapted to the fractal setting, are time consuming since the objects have to be generated anew for each rendering. The Chain of Cubes algorithm used in this article is a boundary tracking method which uses a minimum of storage to generate a polygonal approximation of an iso-valued surface.
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References
EX. Allgower, P.H. Schmidt: An Algorithm for Piecewise Linear Approximation of an Implicit Defined Manifold, SIAM J. Numer. Anal. 22, 322–346, 1985
EX. Allgower, S. Gnutzmann: An Algorithm for Piecewise Linear Approximation of Implicitly Defined Two-Dimensional Surfaces, SIAM J. Numer. Anal. 24, 452–469, 1987
EX. Allgower, K. Georg: Introduction to Numerical Continuation Methods, Springer-Verlag, New York, 1990
J.C. Hart, D.J. Sandin, L.H. Kauffman: Ray Tracing Deterministic 3-D Fractals, Computer Graphics (Proc. SIGGRAPH) 23(3), 289–296, 1989
H. Jürgens: Optimierte Oberflächenabtastung mit orientierten Kubusketten, in H. Jürgens, D. Saupe (Eds.): Visualisierung in Mathematik und Naturwissenschaften, 53–66, Springer-Verlag, Heidelberg, 1989
R. Lichtenberger: Visualisierung von Fraktalen mit Raytracing, Diplomarbeit, Universität Bremen, 1991
W.E. Lorensen, H.E. Cline: Marching Cubes: a High Resolution 3D Surface Construction Algorithm, Computer Graphics (Proc. SIGGRAPH) 21(4), 163–169, 1987
B.B. Mandelbrot: The Fractal Geometry of Nature, Freeman, San Francisco, 1982
A. Norton: Generation and Display of Geometric Fractals in 3-D, Computer Graphics (Proc. SIGGRAPH) 16(3), 61–66, 1982
A. Norton: Julia Sets in the Quaternions, Computers & Graphics 13(2), 267–278, 1989
H.-O. Peitgen, P. Richter: The Beauty of Fractals, Springer-Verlag, New York, 1986
M. Rümpf et al.: GRAPE GRAphics Programming Environment, Institut für Angewandte Mathematik der Universität Bonn, SFB 256, 1991
G. Wyvill, C. McPheeters, B. Wyvill: Data Structure for Soft Objects, Visual Computer 2(4), 227–234, 1986
C. Zahlten: Piecewise Linear Approximation of Isovalued Surfaces, to appear in the Proceedings of the 2nd Eurographics Workshop on Visualization in Scientific Computing, Delft, The Netherlands, 22-24 April, 1991
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© 1992 Springer-Verlag Berlin Heidelberg
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Zahlten, C. (1992). Boundary Tracking of Complicated Surfaces with Applications to 3-D Julia Sets. In: Encarnação, J.L., Sakas, G., Peitgen, HO., Englert, G. (eds) Fractal Geometry and Computer Graphics. Beiträge zur Graphischen Datenverarbeitung. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-95678-2_8
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DOI: https://doi.org/10.1007/978-3-642-95678-2_8
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