Polygon Mesh Processing

Geometry processing, or mesh processing, is a fast-growing area of research that uses concepts from applied mathematics, computer science, and engineering to design efficient algorithms for the acquisition, reconstruction, analysis, manipulation, simulation, and transmission of complex 3D models. Applications of geometry processing algorithms already cover a wide range of areas from multimedia, entertainment, and classical computer-aided design, to biomedical computing, reverse engineering, and scientific computing. Over the last several years, triangle meshes have become increasingly popular, as irregular triangle meshes have developed into a valuable alternative to traditional spline surfaces. This book discusses the whole geometry processing pipeline based on triangle meshes. The pipeline starts with data input, for example, a model acquired by 3D scanning techniques. This data can then go through processes of error removal, mesh creation, smoothing, conversion, morphing, and more. The authors detail techniques for those processes using triangle meshes. A supplemental website contains downloads and additional information.

Preface Surface RepresentationsSurface Definition and PropertiesApproximation PowerParametric Surface RepresentationsImplicit Surface RepresentationsConversion MethodsSummary and Further Reading Mesh Data StructuresFace-Based Data StructuresEdge-Based Data StructuresHalfedge-Based Data StructureDirected-Edge Data StructureSummary and Further Reading Differential GeometryCurvesSurfacesDiscrete Differential OperatorsSummary and Further Reading SmoothingFourier Transform and Manifold HarmonicsDiffusion FlowFairingSummary and Further Reading ParameterizationGeneral GoalsParameterization of a Triangulated SurfaceBarycentric MappingConformal MappingMethods Based on Distortion AnalysisSummary and Further Reading RemeshingLocal StructureGlobal StructureCorrespondencesVoronoi Diagrams and Delaunay TriangulationsTriangle-Based RemeshingQuad-dominant RemeshingSummary and Further Reading Simplification & ApproximationVertex ClusteringIncremental DecimationShape ApproximationOut-of-Core MethodsSummary and Further Reading Model RepairTypes of Artifacts: The "Freak Show"Types of Repair AlgorithmsTypes of InputSurface-Oriented AlgorithmsVolumetric Repair AlgorithmsSummary and Further Reading DeformationTransformation PropagationShell-Based DeformationMulti-Scale DeformationDifferential CoordinatesFreeform DeformationRadial Basis FunctionsLimitations of Linear MethodsSummary and Further Reading A. NumericsDiscretizing Poisson and Laplace EquationsData Structures for Sparse MatricesIterative SolversSparse Direct Cholesky SolverNon-Symmetric Indefinite SystemsComparisonBibliographyIndex

Leif Kobbelt is a professor of Computer Graphics & Multimedia at RWTH Aachen University in Germany. Mario Botsch is a professor of Computer Science at Bielefeld University and leads the Computer Graphics & Geometry Processing Group. Mark Pauly is an assistant professor in the computer science department of ETH Zurich, Switzerland. Pierre Alliez is a researcher in Computer Science at INRIA Sophia-Antipolis, in the GEOMETRICA group. Bruno Lvy is a senior researcher in INRIA-NGE, and a member of the LORIA lab. He is the scientific head of the ALICE project team.