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.

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.