Fractal Deformation Using Displacement Vectors Based on Extended Iterated Shuffle Transformation
In this paper, we propose a framework of “fractal deformation” using displacement vectors based on “extended Iterated Shuffle Transformation (ext-IST)”. An ext-unit-IST is a one-to-one and onto mapping that is extended from a unit-IST, which we have proposed, and is basically defined on a code space...
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| Published in | Journal of the Society for Art and Science Vol. 1; no. 3; pp. 134 - 146 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English Japanese |
| Published |
The Society for Art and Science
2002
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1347-2267 1347-2267 |
| DOI | 10.3756/artsci.1.134 |
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| Abstract | In this paper, we propose a framework of “fractal deformation” using displacement vectors based on “extended Iterated Shuffle Transformation (ext-IST)”. An ext-unit-IST is a one-to-one and onto mapping that is extended from a unit-IST, which we have proposed, and is basically defined on a code space. When the mapping is applied on a geometric space, a fractal-like repeated structure, which is referred to as “local resemblance in space/scale directions”, is constructed on the relationship between points on the domain and those on the range. By applying the mapping to displacement vectors given on a geometric shape, the shape can be deformed in the fractal-like repeated manner. This fractal deformation is easy to control by changing the displacement vectors intuitively. In addition, a continuous transition between a continuous deformation and a fractal deformation can be realized. We demonstrate how the fractal deformation technique produces attractive results by showing various examples. |
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| AbstractList | In this paper, we propose a framework of “fractal deformation” using displacement vectors based on “extended Iterated Shuffle Transformation (ext-IST)”. An ext-unit-IST is a one-to-one and onto mapping that is extended from a unit-IST, which we have proposed, and is basically defined on a code space. When the mapping is applied on a geometric space, a fractal-like repeated structure, which is referred to as “local resemblance in space/scale directions”, is constructed on the relationship between points on the domain and those on the range. By applying the mapping to displacement vectors given on a geometric shape, the shape can be deformed in the fractal-like repeated manner. This fractal deformation is easy to control by changing the displacement vectors intuitively. In addition, a continuous transition between a continuous deformation and a fractal deformation can be realized. We demonstrate how the fractal deformation technique produces attractive results by showing various examples. |
| Author | Muraoka, Kazunobu Chiba, Norishige Fujimoto, Tadahiro Ohno, Yoshio |
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| Copyright | 2002 Fujimoto, Tadahiro, Ohno, Yoshio, Muraoka, Kazunobu and Chiba, Norishige |
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| References | [7] Fujimoto, T. and Ohno, Y., Formalization and Superposed Construction of Wrinkly Surface, Transactions of Information Processing Society of Japan, Vol.41, No.9, pp.2518-2535, 2000 (in Japanese). [17] Zair, C. E. and Tosan, E., Fractal Modeling Using Free Form Techniques, EUROGRAPHICS ′96, Vol.15, No.3, pp.269-278, 1996. [13] Massopust, P. R., Fractal Surfaces, Journal of Mathematical Analysis and Applications, 151, pp.275-290, 1990. [18] Zair, C. E. and Tosan, E., Unified IFS-based Model to Generate Smooth or Fractal Forms, Surface Fitting and Multiresolution Methods, Vanderbilt University Press, pp.345-354, 1997. [16] Sederberg, T. and Parry, S., Free-Form Deformation of Solid Geometric Models, Computer Graphics (SIGGRAPH ″86), Vol.20, No.4, pp.151-160, 1986. [9] Fujimoto, T., Ohno, Y., Muraoka, K., and Chiba, N., Fractal Deformation Based on Extended Iterated Shuffle Transformation, NICOGRAPH International 2002, pp.79-84, 2002. [5] Burch, B. and Hart, J. C., Linear Fractal Shape Interpolation, Graphics Interface ′97, pp.155-162, 1997. [14] Montiel, M. E., Aguado, A. S., and Zaluska, E. J., Topology in Fractals, Chaos, Solitons and Fractals, Vol.7, No.8, pp.1187-1207, 1996. [8] Fujimoto, T., Ohno, Y., Muraoka, K., and Chiba, N., Wrinkly Surface Generated on Irregular Mesh by Using IST Generalized on Code Space and Multi-Dimensional Space : Unification of Interpolation Surface and Fractal, IEICE Transactions on Information and Systems, to appear. [2] Barnsley, M. F., Jacquin, A., Malassenet, F., Reuter, L., and Sloan, A. D., Harnessing Chaos for Image Synthesis, Computer Graphics (SIGGRAPH ′88), Vol.22, No.4, pp.131-140, 1988. [19] Zair, C. E. and Tosan, E., Computer Aided Geometric Design with IFS Techniques, Fractal Frontiers (Proc. Fractals ′97), pp.443-452, 1997. [20] Zhao, N., Construction and Application of Fractal Interpolation Surfaces, The Visual Computer, 12, pp.132-146, 1996. [3] Barnsley, M. F., Fractals Everywhere, 2nd ed., Academic Press, Boston, 1993. [1] Barnsley, M. F., Fractal Functions and Interpolation, Constructive Approximation, 2, pp.303-329, 1986. [15] Peruggia, M., Discrete Iterated Function Systems, A K Peters, 1993. [11] Gomes, J., Darsa, L., Costa, B., and Velho, L., Warping and Morphing of Graphical Objects, Morgan Kaufmann, 1999. [10] Geronimo, J. S. and Hardin, D., Fractal Interpolation Surfaces and a Related 2-D Multiresolution Analysis, Journal of Mathematical Analysis and Applications, 176, pp.561-586, 1993. [4] Bowman, R. L., Fractal Metamorphosis: a Brief StudentTutorial, Computers & Graphics, Vol.19, No.1, pp.157-164, 1995. [6] Demko, S., Construction of Fractal Objects with Iterated Function Systems, Computer Graphics (SIGGRAPH ′85), Vol.19, No.3, pp.271-278, 1985. [12] Gonzalez, J. A., A Tutorial and Recipe for Moving Fractal Trees, Computers & Graphics, Vol.22, No.2-3, pp.301-305, 1998. 11 12 13 14 15 16 17 18 19 FUJIMOTO TADAHIRO (7) 2000; 41 1 2 3 4 5 6 8 9 20 10 |
| References_xml | – reference: [2] Barnsley, M. F., Jacquin, A., Malassenet, F., Reuter, L., and Sloan, A. D., Harnessing Chaos for Image Synthesis, Computer Graphics (SIGGRAPH ′88), Vol.22, No.4, pp.131-140, 1988. – reference: [9] Fujimoto, T., Ohno, Y., Muraoka, K., and Chiba, N., Fractal Deformation Based on Extended Iterated Shuffle Transformation, NICOGRAPH International 2002, pp.79-84, 2002. – reference: [1] Barnsley, M. F., Fractal Functions and Interpolation, Constructive Approximation, 2, pp.303-329, 1986. – reference: [20] Zhao, N., Construction and Application of Fractal Interpolation Surfaces, The Visual Computer, 12, pp.132-146, 1996. – reference: [16] Sederberg, T. and Parry, S., Free-Form Deformation of Solid Geometric Models, Computer Graphics (SIGGRAPH ″86), Vol.20, No.4, pp.151-160, 1986. – reference: [17] Zair, C. E. and Tosan, E., Fractal Modeling Using Free Form Techniques, EUROGRAPHICS ′96, Vol.15, No.3, pp.269-278, 1996. – reference: [8] Fujimoto, T., Ohno, Y., Muraoka, K., and Chiba, N., Wrinkly Surface Generated on Irregular Mesh by Using IST Generalized on Code Space and Multi-Dimensional Space : Unification of Interpolation Surface and Fractal, IEICE Transactions on Information and Systems, to appear. – reference: [11] Gomes, J., Darsa, L., Costa, B., and Velho, L., Warping and Morphing of Graphical Objects, Morgan Kaufmann, 1999. – reference: [12] Gonzalez, J. A., A Tutorial and Recipe for Moving Fractal Trees, Computers & Graphics, Vol.22, No.2-3, pp.301-305, 1998. – reference: [18] Zair, C. E. and Tosan, E., Unified IFS-based Model to Generate Smooth or Fractal Forms, Surface Fitting and Multiresolution Methods, Vanderbilt University Press, pp.345-354, 1997. – reference: [5] Burch, B. and Hart, J. C., Linear Fractal Shape Interpolation, Graphics Interface ′97, pp.155-162, 1997. – reference: [7] Fujimoto, T. and Ohno, Y., Formalization and Superposed Construction of Wrinkly Surface, Transactions of Information Processing Society of Japan, Vol.41, No.9, pp.2518-2535, 2000 (in Japanese). – reference: [10] Geronimo, J. S. and Hardin, D., Fractal Interpolation Surfaces and a Related 2-D Multiresolution Analysis, Journal of Mathematical Analysis and Applications, 176, pp.561-586, 1993. – reference: [13] Massopust, P. R., Fractal Surfaces, Journal of Mathematical Analysis and Applications, 151, pp.275-290, 1990. – reference: [3] Barnsley, M. F., Fractals Everywhere, 2nd ed., Academic Press, Boston, 1993. – reference: [15] Peruggia, M., Discrete Iterated Function Systems, A K Peters, 1993. – reference: [14] Montiel, M. E., Aguado, A. S., and Zaluska, E. J., Topology in Fractals, Chaos, Solitons and Fractals, Vol.7, No.8, pp.1187-1207, 1996. – reference: [4] Bowman, R. L., Fractal Metamorphosis: a Brief StudentTutorial, Computers & Graphics, Vol.19, No.1, pp.157-164, 1995. – reference: [19] Zair, C. E. and Tosan, E., Computer Aided Geometric Design with IFS Techniques, Fractal Frontiers (Proc. Fractals ′97), pp.443-452, 1997. – reference: [6] Demko, S., Construction of Fractal Objects with Iterated Function Systems, Computer Graphics (SIGGRAPH ′85), Vol.19, No.3, pp.271-278, 1985. – ident: 3 – ident: 18 – ident: 16 doi: 10.1145/15886.15903 – ident: 1 doi: 10.1007/BF01893434 – ident: 5 – ident: 17 doi: 10.1111/1467-8659.1530269 – ident: 11 – ident: 19 – ident: 15 doi: 10.1201/9781439864708 – ident: 14 – ident: 12 doi: 10.1016/S0097-8493(98)00014-4 – ident: 10 doi: 10.1006/jmaa.1993.1232 – ident: 4 doi: 10.1016/0097-8493(94)00131-H – ident: 9 – ident: 13 doi: 10.1016/0022-247X(90)90257-G – ident: 8 – volume: 41 start-page: 2518 issn: 0387-5806 issue: 9 year: 2000 ident: 7 – ident: 20 doi: 10.1007/s003710050053 – ident: 2 doi: 10.1145/378456.378502 – ident: 6 doi: 10.1145/325165.325245 |
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| Title | Fractal Deformation Using Displacement Vectors Based on Extended Iterated Shuffle Transformation |
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