Implicit curves and surfaces: mathematics, data structures and algorithms

Abel J. P. Gomes, Irina Voiculescu, Joaquim Jorge, Brian Wyvill, Callum Galbraith (eds.)9781848824058, 184882405X

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.

Table of contents :
Front Matter….Pages I-XIV
Mathematical Fundamentals….Pages 7-40
Spatial Data Structures….Pages 41-62
Root Isolation Methods….Pages 67-87
Interval Arithmetic….Pages 89-115
Root-Finding Methods….Pages 117-140
Continuation Methods….Pages 145-186
Spatial Partitioning Methods….Pages 187-225
Implicit Surface Fitting….Pages 227-262
Skeletal Implicit Modelling Techniques….Pages 267-285
Natural Phenomenae-I: Static Modelling….Pages 287-302
Natural Phenomenae-II: Animation….Pages 303-317
Back Matter….Pages 319-351