Gomes A.J.P., Voiculescu I., Jorge J., Wyvill B., Galbraith C. Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Springer, 2009. — 338 p.This book presents the mathematics, computational methods and data structures, as well as the algorithms needed to render implicit curves and surfaces. Implicit objects have gained an increasing importance in geometric modelling, visualisation, animation, and computer graphics due to their nice geometric properties which give them some advantages over traditional modelling methods. For example, the point membership classification is trivial using implicit representations of geometric objects - a very useful property for detecting collisions in virtual environments and computer game scenarios. The ease with which implicit techniques can be used to describe smooth, intricate, and articulatable shapes through blending and constructive solid geometry show us how powerful they are and why they are finding use in a growing number of graphics applications.
The book is mainly directed towards graduate students, researchers and developers in computer graphics, geometric modelling, virtual reality and computer games. Nevertheless, it can be useful as a core textbook for a graduate-level course on implicit geometric modelling or even for general computer graphics courses with a focus on modelling, visualisation and animation. Finally, and because of the scarce number of textbooks focusing on implicit geometric modelling, this book may also work as an important reference for those interested in modelling and rendering complex geometric objects.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