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Computational Conformal Geometry: Theories and Applications

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GeometryGeometryGeometry MatchingMatchingMatching-brain--brainbrain mappingmappingmapping ConformalConformalConformal brainbrainbrain mappingmappingmapping demo GeometricGeometricGeometric MatchingMatchingMatching-brain--brainbrain mappingmappingmapping MinimizeMinimizeMinimize L2L2L2 normnormnorm underunderunder MobiusMobiusMobius transformationtransformationtransformation LeastLeastLeast squaresquaresquare problemproblemproblem demo GeometryGeometryGeometry CompressionCompressionCompression SphericalSphericalSpherical harmonicharmonicharmonic functionsfunctionsfunctions SpectrumSpectrumSpectrum compressioncompressioncompression SolutionSolutionSolution OutlineOutlineOutline TheoreticTheoreticTheoretic backgroundbackgroundbackground GenusGenusGenus zerozerozero closedclosedclosed surfacessurfacessurfaces NonzeroNonzeroNonzero genusgenusgenus closedclosedclosed surfacessurfacessurfaces SurfacesSurfacesSurfaces withwithwith boundariesboundariesboundaries SummarySummarySummary TheoreticTheoreticTheoretic backgroundbackgroundbackground –––RiemannRiemann Riemann surfacesurfacesurface ForForFor genusgenusgenus zerozerozero closedclosedclosed surfaces,surfaces,surfaces, aaa mappingmappingmapping isisis conformalconformalconformal ififif andandand onlyonlyonly ififif ititit isisis harmonic.harmonic.harmonic. 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