Keenan Crane

CARNEGIE MELLON UNIVERSITY

Robust Fairing via Conformal Curvature Flow

SIGGRAPH 2013 / ACM Transactions on Graphics

We present a formulation of Willmore flow for triangulated surfaces that permits extraordinarily large time steps and naturally preserves the quality of the input mesh. The main insight is that Willmore flow becomes remarkably stable when expressed in curvature space—we develop the precise conditions under which curvature is allowed to evolve. The practical outcome is a highly efficient algorithm that naturally preserves texture and does not require remeshing during the flow. We apply this algorithm to surface fairing, geometric modeling, and construction of constant mean curvature (CMC) surfaces. We also present a new algorithm for length-preserving flow on planar curves, which provides a valuable analogy for the surface case.

Video

Topology Joke

Thanks to the hard work of Henry Segerman one of our flows has been realized in ceramic, and can be ordered from Shapeways. A nice writeup of this work was put together by Debra Thimmesch.

This research was supported by a Google PhD Fellowship, the Hausdorff Research Institute for Mathematics, BMBF Research Project GEOMEC, SFB / Transregio 109 "Discretization in Geometry and Dynamics," and the TU München Institute for Advanced Study, funded by the German Excellence Initiative. Meshes provided by the Stanford Computer Graphics Laboratory and the AIM@SHAPE Shape Repository.

@article{Crane:2013:RFC,
author = {Crane, Keenan and Pinkall, Ulrich and Schr\"{o}der, Peter},
title = {Robust Fairing via Conformal Curvature Flow},
journal = {ACM Trans. Graph.},
volume = {32},
issue = {4},
year = {2013},
publisher = {ACM},
address = {New York, NY, USA},
}

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