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Computer Science - Theoretical Computer Science | Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Gomes, A., Voiculescu, I., Jorge, J., Wyvill, B., Galbraith, C.

2009, XIV, 351 p.

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  • The first book to provide a general framework for both implicit curves and surfaces including their mathematical foundations, data structures, computational methods and algorithms
  • Includes both static and dynamic classes of implicit surfaces

Implicit techniques are a powerful tool that make it easier to describe smooth, intricate, and articulatable shapes via blending and solid geometry, and are becoming the technique of choice in an increasing number of graphics applications.

The mathematics, computational methods and data structures, as well as the algorithms required to render implicit curves and surfaces form the central theme of this book. The increasing importance of implicit objects in geometric modelling stems from the advantages these give over traditional modelling methods; the use of implicit techniques can help simplify complex actions such as point membership classification, which enables the detection of collisions in virtual environments and computer game scenarios.

Graduate students, researchers and developers in computer graphics, geometric modelling, virtual reality and computer games will find this an excellent resource and reference source for modelling and rendering complex geometric objects. The book can also be used as a core textbook for graduate level courses on implicit geometric modelling.

Content Level » Research

Keywords » 3D graphics - Animation - Dynamic Surfaces - Implicit Curves and Surfaces - Level Sets - Numerical Methods - Special Effects - computer graphics - modeling

Related subjects » Image Processing - Theoretical Computer Science

Table of contents 

Mathematics and Data Structures.- Mathematical Fundamentals.- Spatial Data Structures.- Sampling Methods.- Root Isolation Methods.- Interval Arithmetic.- Root-Finding Methods.- Reconstruction and Polygonisation.- Continuation Methods.- Spatial Partitioning Methods.- Implicit Surface Fitting.- Designing Complex Implicit Surface Models.- Skeletal Implicit Modelling Techniques.- Natural Phenomenae-I: Static Modelling.- Natural Phenomenae-II: Animation.

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