Curve and Surface Reconstruction: Algorithms with Mathematical Analysis

This book presents algorithms for the problem of reconstructing a curve or a surface from a sample its points, and includes a mathematical analysis of these algorithms. Reconstruction from points is an important problem in practice because of the existence of affordable 3d scanners.

The book contains much interesting geometry and shows how it relates to the design of efficient reconstruction algorithms. Underlying these are the Voronoi diagram and the Delaunay triangulation, the main classical objects of computational geometry.

The book can serve as a basis for a graduate course on computational geometry or geometric modeling and will probably become a standard reference for researchers interested in reconstruction from points.

Luiz Henrique de Figueiredo is a researcher at IMPA in Rio de Janeiro, Brazil. His main interests are numerical methods in computer graphics, but he remains an algebraist at heart. He is also one of the designers of the Lua language.