Global Conformal Surface Parameterization

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dc.contributor.authorGu, Xianfengen_US
dc.contributor.authorYau, Shing-Tungen_US
dc.contributor.editorLeif Kobbelt and Peter Schroeder and Hugues Hoppeen_US
dc.date.accessioned2014-01-29T08:19:42Z
dc.date.available2014-01-29T08:19:42Z
dc.date.issued2003en_US
dc.description.abstractWe solve the problem of computing global conformal parameterizations for surfaces with nontrivial topologies. The parameterization is global in the sense that it preserves the conformality everywhere except for a few points, and has no boundary of discontinuity. We analyze the structure of the space of all global conformal parameterizations of a given surface and find all possible solutions by constructing a basis of the underlying linear solution space. This space has a natural structure solely determined by the surface geometry, so our computing result is independent of connectivity, insensitive to resolution, and independent of the algorithms to discover it. Our algorithm is based on the properties of gradient fields of conformal maps, which are closedness, harmonity, conjugacy, duality and symmetry. These properties can be formulated by sparse linear systems, so the method is easy to implement and the entire process is automatic. We also introduce a novel topological modification method to improve the uniformity of the parameterization. Based on the global conformal parameterization of a surface, we can construct a conformal atlas and use it to build conformal geometry images which have very accurate reconstructed normals.en_US
dc.description.seriesinformationEurographics Symposium on Geometry Processingen_US
dc.identifier.isbn3-905673-06-1en_US
dc.identifier.issn1727-8384en_US
dc.identifier.urihttps://doi.org/10.2312/SGP/SGP03/127-137en_US
dc.publisherThe Eurographics Associationen_US
dc.subjectCategories and Subject Descriptors (according to ACM CCS): I.3.5 [Computer Graphics]: Surface parameterization, global conformal parameterizationen_US
dc.titleGlobal Conformal Surface Parameterizationen_US
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SGP03: Eurographics Symposium on Geometry Processing