Lecture Notes on Delaunay Mesh Generation.pdf

Lecture Notes on Delaunay Mesh Generation.pdf

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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

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