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2003

Global Conformal Parameterization

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Global Conformal Parameterization
We 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 modificati...
Xianfeng Gu, Shing-Tung Yau
Added 01 Nov 2010
Updated 01 Nov 2010
Type Conference
Year 2003
Where SGP
Authors Xianfeng Gu, Shing-Tung Yau
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