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 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.
• Provides fundamentals of point cloud data processing • Algorithms with correctness proofs are presented • Many figures, a set of exercises, and a brief history for each chapter
Contents
1. Basics; 2. Curve reconstruction; 3. Surface samples; 4. Surface reconstruction; 5. Undersampling; 6. Watertight reconstructions; 7. Noisy samples; 8. Noise and reconstruction; 9. Implicit surface based reconstructions; 10. Morse theoretic reconstructions.
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