Curve and Surface Reconstruction Algorithms with Mathematical Analysis
Curve and Surface Reconstruction Algorithms with Mathematical Analysis by Tamal K. Dey, published by Cambridge University Press on October 16, 2006, is a comprehensive resource that explores the computation of digital models from point samples generated by advanced scanning technology. This edition, consisting of 232 pages, delves into the fundamentals of sampling theory and its relationship to geometric and topological properties, providing a foundation for understanding the reconstruction of physical objects in various scientific and engineering contexts.
Readers will find a detailed examination of a range of algorithms designed for surface reconstruction, addressing challenges such as inadequate density and noise in samples. The book covers techniques based on Voronoi and Delaunay methods, implicit surface approaches, and Morse theory, making it a valuable reference for professionals in fields like drug design, medical imaging, and computer-aided design. This work serves as an essential introduction to the algorithms and mathematical analysis involved in reconstructing digital models from real-world data.
Official synopsis Publisher
Many applications in science and engineering require a digital model of a real physical object. Advanced scanning technology has made it possible to scan such objects and generate point samples on their boundaries. This book, first published in 2007, shows how to compute a digital model from this point sample. After developing the basics of sampling theory and its connections to various geometric and topological properties, the author describes a suite of algorithms that have been designed for the reconstruction problem, including algorithms for surface reconstruction from dense samples, from samples that are not adequately dense and from noisy samples. Voronoi- and Delaunay-based techniques, implicit surface-based methods and Morse theory-based methods are covered. Scientists and engineers working in drug design, medical imaging, CAD, GIS, and many other areas will benefit from this first book on the subject.
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