Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

In presenting the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, the authors show how implicit objects can easily describe smooth, intricate, and shapes that articulate.


Implicit objects have gained increasing importance in geometric modeling, visualisation, animation, and computer graphics, because their geometric properties provide a good alternative to traditional parametric objects. This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces, and shows how implicit objects can easily describe smooth, intricate, and articulatable shapes, and hence why they are being increasingly used in graphical applications. Divided into two parts, the first introduces the mathematics of implicit curves and surfaces, as well as the data structures suited to store their sampled or discrete approximations, and the second deals with different computational methods for sampling implicit curves and surfaces, with particular reference to how these are applied to functions in 2D and 3D spaces.

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

Klappentext
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.

Inhalt
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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