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Parametrising Flat-foldable surfaces with incomplete data

Project Description:
We propose a novel way of computing surface folding maps via solving a linear PDE.This framework is a generalization to the existing quasiconformal methods and allows manipulationof the geometry of folding. Moreover, the crucial quantity that characterizes the geometry occurs asthe coe cient of the equation, namely the Beltrami coe cient. This allows us to solve an inverseproblem of parametrizing the folded surface given only partial data but with known folding topology.Various interesting applications such as fold sculpting on 3D models and self-occlusion reasoning aredemonstrated to show the e ectiveness of our method.


  • D. Syl, K.C. Lam, L.M. Lui, Parametrising Flat-foldable surfaces with incomplete data, to be submitted (2018)