Gomes A.J.P. et al. Implicit Curves and Surfaces: Mathematics, Data Structures and Algorithms

Springer, 2009. – 336 p. – 130 illus., 107 in color – ISBN: 184882405X, 9781848824065Implicit 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.
Keywords » Animation - Dynamic Surfaces - Implicit Curves and Surfaces - Level Sets - Numerical Methods - Special EffectsMathematics 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 Modeling Techniques.
Natural Phenomenae-I Static Modeling.
Natural Phenomenae-II Animation.