Realistic rendering 3D IFS fractals in real-time with graphics accelerators

Martyn, Tomasz

doi:10.1016/j.cag.2009.10.001

Cited by 14 publications

(4 citation statements)

References 13 publications

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“…For example, Martyn [20] has developed an algorithm for approximating the rectangular convex hulls of 2D affine IFS fractals, ensuring a given accuracy. Martyn [19] has developed an approach to realistic real-time rendering of 3-D IFS fractals that requires both approximations of convex hulls of IFS fractal subsets and estimations of normals on a fractal surface. Mishkinis et al [21] have developed an algorithm for approximating the curvilinear convex hulls of 2D IFS fractals preserving the desired accuracy.…”

Section: Related Workmentioning

confidence: 99%

A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

Chang¹,

Shih²

2014

Computer-Aided Design and Applications

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This study deals with the design for manufacturing (DFM) of fractals created by a random walk called iterated function system (IFS). In particular, the DFM of an IFS-created fractal called Barnsley's fern-leaf is considered. The IFS dedicated for creating virtual models of a fern-leaf uses a set of four strictlycontracting affine mappings in the onto manner. The interactions among these mappings are studied in detail in order to identify some data structures. Based on the identified data structures, a DFM procedure is proposed. In the proposed DFM procedure, three out of the four mappings are employed in both the onto and one-to-one manner. The proposed DFM procedure is applied to the redesign of the shape (fern-leaf). Physical models of the redesigned fern-leaf are manufactured using both additive and subtractive manufacturing technologies (3-D printing and milling). The factors affecting accuracy of the physical models are also described. Although this study is limited to the shape of the fern-leaf, other IFS-created shapes can be redesigned using the proposed DFM procedure. Nevertheless, this study sheds some light on our understanding of how to develop more accurate physical models of IFS-created fractals.

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Section: Related Workmentioning

confidence: 99%

A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

Chang¹,

Shih²

2014

Computer-Aided Design and Applications

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“…The process of building a fractal model is rapid as it is based on recursive algorithms. For instance, an array of 50000 pixels requires less than 8 seconds to be built using the IFS method and rendering algorithms for various FM methods are constantly optimized for productivity (Gröller, 1994;Karam and Nakajima, 2001;Martyn, 2010).…”

Section: Introduction Of a Fractal Classification Of Enps Aggregate Smentioning

confidence: 99%

Improving the prediction of environmental fate of engineered nanomaterials by fractal modelling

Avilov

Lamon

Hristozov

et al. 2017

Environment International

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A critical analysis of the available engineered nanomaterials (ENMs) environmental fate modelling approaches indicates that existing tools do not satisfactorily account for the complexities of nanoscale phenomena. Fractal modelling (FM) can complement existing kinetic fate models by including more accurate interpretations of shape and structure, density and collision efficiency parameters to better describe homo- and heteroaggregation. Pathways to including hierarchical symmetry concepts and a route to establishing a structural classification of nanomaterials based on FM are proposed.

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“…9 In the context of computer graphics and in other areas, fractals have been used to generate very complex and beautiful patterns. [10][11][12] While fractal patterns are very complex, only a small amount of information is needed to generate them; e.g., in the IFS, only information about a finite number of contractive mappings is needed. In the literature, there are many methods of generating fractal patterns, including the deterministic algorithm and random iteration algorithm, 2 the escape time algorithm, 13 and even the IFS ray tracing algorithm.…”

Section: Introductionmentioning

confidence: 99%

Star-Shaped Set Inversion Fractals

Gdawiec

2014

Fractals

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In the paper, we generalized the idea of circle inversion to star-shaped sets and used the generalized inversion to replace the circle inversion transformation in the algorithm for the generation of the circle inversion fractals. In this way, we obtained the star-shaped set inversion fractals. The examples that we have presented show that we were able to obtain very diverse fractal patterns by using the proposed extension and that these patterns are different from those obtained with the circle inversion method. Moreover, because circles are star-shaped sets, the proposed generalization allows us to deform the circle inversion fractals in a very easy and intuitive way.

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Realistic rendering 3D IFS fractals in real-time with graphics accelerators

Cited by 14 publications

References 13 publications

A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

A Hybrid Approach of Dynamic Programming and Genetic Algorithm for Multi-criteria Optimization on Sustainable Architecture design

Improving the prediction of environmental fate of engineered nanomaterials by fractal modelling

Star-Shaped Set Inversion Fractals

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