Fractals and Solid Modeling
TL;DR: A new type of 3D objects is presented that accomplishes this combination in a specific way and can be incorporated into the CSG‐modeling technique (Constructive Solid Geometry) in two ways.
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Abstract: Trying to combine fractal geometry and solid modeling seems to be a contradiction in itself, In this paper a new type of 3D objects is presented that accomplishes this combination in a specific way. Objects with a fractal macro structure and a 3D solid micro structure can be specified and rendered efficiently by using context free, attribute, geometric grammars. This new object type can be incorporated into the CSG-modeling technique (Constructive Solid Geometry) in two ways: a) using CSG for the specification of the micro structure of the new object type, b) using these fractal like objects as a new type of primitive in the CSG model. Ray tracing is used for generating high quality images of these geometrically complex objects.
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Citations
•Book
Chaos and Fractals: A Computer Graphical Journey
Clifford A. Pickover
- 03 Aug 1998
TL;DR: Fractals and their applications in computer graphics and computer art are discussed in this article, where the author provides visual demonstrations of complicated and beautiful structures that can arise in systems, based on simple rules.
34
Generating languages of solid models
Jeff A. Heisserman,Robert Woodbury +1 more
- 01 Jun 1993
TL;DR: A formalism, boundary solid grammars, that allows complex geometric conditions and operations to be expressed using a logical reasoning mechanism, the construction of powerful rules, and the description of Grammars for generation of solid models that is appropriate for a variety of design domains is presented.
33
Modeling and rendering of nonlinear iterated function systems
TL;DR: Piecewise bilinear distortions of grids are used in this work to specify nonlinear Iterated Function Systems, characterized by a higher degree of flexibility and greater modeling capability than their linear counterparts.
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Fractals and Solid Modeling
TL;DR: A new type of 3D objects is presented that accomplishes this combination in a specific way and can be incorporated into the CSG‐modeling technique (Constructive Solid Geometry) in two ways.
ACC - lossless data compression of animation sequences
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References
•Book
The Fractal Geometry of Nature
Benoit B. Mandelbrot
- 01 Jan 1982
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
26.1K
The Fractal Geometry of Nature
Benoit B. Mandelbrot
- 01 Jul 1984
TL;DR: A blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) is presented in this article.
16.7K
•Book
Fractals Everywhere
Michael F. Barnsley
- 01 Jan 1988
TL;DR: Focusing on how fractal geometry can be used to model real objects in the physical world, this up-to-date edition featurestwo 16-page full-color inserts, problems and tools emphasizing fractal applications, and an answers section.
4.5K
•Book
The Algorithmic Beauty of Plants
Przemyslaw Prusinkiewicz,Aristid Lindenmayer +1 more
- 01 Jan 1990
TL;DR: Graphical modeling using L-systems and turtle interpretation of symbols for plant models and iterated function systems, and Fractal properties of plants.
Ray casting for modeling solids
TL;DR: This paper presents ray casting as the methodological basis for a CAD/CAM solid modeling system and presents new methods, accompanied by sample pictures and CPU times, to meet the challenge.
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