Flattenable mesh surface fitting on boundary curves

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This paper addresses the problem offittingflattenable mesh surfaces in R3 onto piecewise linear boundary curves, where a flattenable mesh surface inherits the isometric mapping to a planar region in R2, The developable surface in differential geometry shows the nice property. However it is dfficuIt to fit developable surfaces to a boundary with complex shape. The technique presented in this paper can model a piecewise linear flattenable surface that interpolates the given boundary curve and approximates the cross-tan gent normal vectors on the boundary. At first, an optimal planar polygonal region is computed from the given boundary curve B ε R 3, triangulated into a planar mesh surface, and warped into a mesh surface in R3 satisfying the continuities defined on B. Then, the fitted mesh surface is further optimized into a flattenable Laplacian (FL) mesh, which preserves the positional continuity and minimizes the variation of cross-tangential normals. Assembled set of such FL mesh patches can be employed to model complex products fabricated from sheets without stretching.

Original languageEnglish
Article number021006
Pages (from-to)210061-2100610
Number of pages1890550
JournalJournal of Computing and Information Science in Engineering
Issue number2
Publication statusE-pub ahead of print - 30 Apr 2008


  • Computational geometry
  • Curve fitting
  • Mesh generation


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