Communications in Information and Systems

Volume 3 (2003)

Number 3

Computing Conformal Invariants: Period Matrices

Pages: 153 – 170



Xianfeng Gu

Yalin Wang

Shing-Tung Yau


This work introduces a system of algorithms to compute period matrices for general surfaces with arbitrary topologies. The algorithms are intrinsic to the geometry, and independent of surface representations. The computation is efficient, stable and practical for real applications. The algorithms are experimented on real surfaces including human faces and sculptures, and applied to surface identification problems. It is the first work that is both theoretically solid, and practically robust and accurate to handle real surfaces with arbitrary topologies.


Conformal Structure; Period Matrix; Conformal Geometry; Mesh

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