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1、LectureNotesonDelaunayMeshGenerationJonathanRichardShewchukFebruary5,2012DepartmentofElectricalEngineeringandComputerSciencesUniversityofCaliforniaatBerkeleyBerkeley,CA94720Copyright1997,2012JonathanRichardShewchukSupportedinpartbytheNationalScienceFoundationunderAwardsCMS-9318163,ACI-9875
2、170,CMS-9980063,CCR-0204377,CCF-0430065,CCF-0635381,andIIS-0915462,inpartbytheUniversityofCaliforniaLabFeesResearchProgram,inpartbytheAdvancedResearchProjectsAgencyandRomeLaboratory,AirForceMaterielCommand,USAFunderagreementnumberF30602-96-1-0287,inpartbytheNaturalSciencesandEngineeringRes
3、earchCouncilofCanadaundera1967ScienceandEngineeringScholarship,inpartbygiftsfromtheOkawaFoundationandtheIntelCorporation,andinpartbyanAlfredP.SloanResearchFellowship.Keywords:meshgeneration,Delaunayrefinement,Delaunaytriangulation,computationalgeometryContents1Introduction11.1MeshesandtheGo
4、alsofMeshGeneration...........................31.1.1DomainConformity..................................41.1.2ElementQuality....................................51.2ABriefHistoryofMeshGeneration..............................71.3Simplices,Complexes,andPolyhedra.............................121.
5、4MetricSpaceTopology.....................................151.5HowtoMeasureanElement..................................171.6MapsandHomeomorphisms..................................211.7Manifolds............................................222Two-DimensionalDelaunayTriangulations252.1Triangulat
6、ionsofaPlanarPointSet..............................262.2TheDelaunayTriangulation..................................262.3TheParabolicLiftingMap...................................282.4TheDelaunayLemma......................................302.5TheFlipAlgorithm..................................
7、.....322.6TheOptimalityoftheDelaunayTriangulation.........................342.7TheUniquenessoftheDelaunayTriangulation........................352.8ConstrainedDelaunayTriangulationsinthePlane.......................362.8.1PiecewiseLinearComplexesandtheirTriangul
