A Short Course in Computational Geometry and Topology

• Main Author: Edelsbrunner, Herbert (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: SpringerBriefs in Applied Sciences and Technology,
• Subjects: Mathematics.; Computer mathematics.; Manifolds (Mathematics).; Complex manifolds.; Biomathematics.; Biomedical engineering.; Computational Science and Engineering.; Manifolds and Cell Complexes (incl. Diff.Topology).; Biomedical Engineering.; Mathematical and Computational Biology.

With the aim to bring the subject of Computational Geometry and Topology closer to the scientific audience, this book is written in thirteen ready-to-teach sections organized in four parts: TESSELLATIONS, COMPLEXES, HOMOLOGY, PERSISTENCE. To speak to the non-specialist, detailed formalisms are often...

Table of Contents:

• Roots of Geometry and Topology
• Voronoi and Delaunay Diagrams
• Weighted Diagrams
• Three Dimensions
• Alpha Complexes
• Holes
• Area Formulas
• Topological Spaces
• Homology Groups
• Complex Construction
• Filtrations
• PL Functions
• Matrix Reduction
• Epilogue.