Providing a comprehensive introduction to the upper envelope problem, this book is perfect for anyone interested in computational geometry, topology, and algorithms. With clear explanations, insightful examples, and rigorous proofs, Edelsbrunner, Guibas, and Sharir provide deep insights into the subject and cutting-edge techniques for solving this classic problem.
Focusing on computational geometry and topology, this monograph begins with Voronoi diagrams and Delaunay triangulations, then explores alpha complexes significant in biological contexts. The core of the text delves into homology theory and its computational aspects, particularly persistence theory, which is vital for applications like shape reconstruction. Aimed at researchers and practitioners in mathematics, biology, neuroscience, and computer science, it also serves as a valuable resource for graduate students in these disciplines.
Combining geometry, topology, algorithms, and engineering, this graduate text emphasizes essential and practical topics. It serves as a comprehensive resource for students, focusing on foundational concepts that are applicable in various fields, making it both accessible and valuable for advanced study.
This book explores the interplay between computational geometry and combinatorial geometry, highlighting their mutual benefits. It is divided into three parts: combinatorial, computational, and applications. The author emphasizes fundamental algorithms and geometric transforms that reveal connections between different problems, structuring the field effectively.