Computer Graphics and Mathematics

Since its very existence as a separate field within computer science, computer graphics had to make extensive use of non-trivial mathematics, for example, projective geometry, solid modelling, and approximation theory. This interplay of mathematics and computer science is exciting, but also makes it difficult for students and researchers to assimilate or maintain a view of the necessary mathematics. The possibilities offered by an interdisciplinary approach are still not fully utilized. This book gives a selection of contributions to a workshop held near Genoa, Italy, in October 1991, where a group of mathematicians and computer scientists gathered to explore ways of extending the cooperation 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 Bézier 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.