“Developability of triangle meshes” by Stein, Grinspun and Crane

  • ©Oded Stein, Eitan Grinspun, and Keenan Crane



Entry Number: 77


    Developability of triangle meshes

Session/Category Title: Cutting, Zipping and Folding Surfaces




    Developable surfaces are those that can be made by smoothly bending flat pieces without stretching or shearing. We introduce a definition of developability for triangle meshes which exactly captures two key properties of smooth developable surfaces, namely flattenability and presence of straight ruling lines. This definition provides a starting point for algorithms in developable surface modeling—we consider a variational approach that drives a given mesh toward developable pieces separated by regular seam curves. Computation amounts to gradient descent on an energy with support in the vertex star, without the need to explicitly cluster patches or identify seams. We briefly explore applications to developable design and manufacturing.


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