Computer Graphics and Mathematics [Paperback]

Since its very existence as a separate field within computerscience, computer graphics had to make extensive use ofnon-trivial mathematics, for example, projective geometry,solid modelling, and approximation theory. This interplay ofmathematics and computer science is exciting, but also makesit difficult for students and researchers to assimilate ormaintain a view of the necessary mathematics. Thepossibilities offered by an interdisciplinary approach arestill not fully utilized. This book gives a selection ofcontributions to a workshop held near Genoa, Italy, inOctober 1991, where a group of mathematicians and computerscientists gathered to explore ways of extending thecooperation between mathematics and computer graphics.1 Integer Approximation to the Intersection of Three Planes with Planar Constraints.- 2 Approximate C1-blending with Triangular Cubic Patches.- 3 A Geometric Approach to B?zier Curves.- 4 Representing and Modeling of Cyclide Patches using NURBS.- 5 Local Parametrization of Space Curves at Singular Points.- 6 Shape of Curves and Surfaces: the Combinatorics.- 7 Two Surfaces Suffice.- 8 Does a Trigonometric Curve Cross an Algebraic Surface?.- 9 Incidence Relationships: Kernel Concept in Combinatorical Topology.- 10 A Taxonomy on Geometric and Topological Models.- 11 Multilevel Generation of Fractal Images Using the Associated Markov Process.- 12 Statistical Color Quantization for Minimum Distortion.- 13 Minimizing the Absolute Value Energy Function: An Application to Geometrical Constraint-Solving.- 14 Geometric Constraint Propagation with Quantum Labels.- 15 Computer Vision, Descriptive Geometry, and Classical Mechanics.- 16 Discrete Surface Models: Constraint-based Generation and Understanding.- 17 Visualization of Depth Maps.- 18 An Analysis of Digitalization Algorithms for Non-linear Curves.- 19 Visualizing Hyperbolic Space.- List of Contributors.This book gives a selection of cl³'