15th International Meshing Roundtable
Birmingham, Alabama, U.S.A.
September 17-20, 2006
Per-Olof Persson and Robert Haimes
Massachusetts Institute of Technology
Michael J. Aftosmis
NASA Ames Research Center
This work examines the use of Loop subdivision surfaces as a surrogate
for CAD or analytic-based geometry. The modeler begins by constructing a subdivision surface from a full-resolution imported surface triangulation, and then queries this surface to return information about the model. Evaluations on the surface are performed using a simplified implementation of Stamís exact evaluation procedure for Loop subdivision surfaces. The paper presents details of this simplified approach and shows how it can be used to provide surface coordinates, derivatives, and curvatures for evaluations at arbitrary parameter values. The implementation also provides the ability to tag hard-edges (and implicitly hard-vertices) in the imported geometry to preserve creases and points using a one-dimensional cubic-spline scheme which preserves C2 continuity along hard-edges. Away from hard-edges and vertices, the Loop surface is C2 continuous everywhere except in the immediate vicinity of irregular vertices in the control-net where it still retains C1 continuity. Examples are presented using control-nets built from a variety of legacy triangulations with widely varying complexity. To demonstrate the modeler, we use a simplified meshing application which queries arbitrary locations on the surface to support either uniform or curvature-adaptive triangle refinement. The simple evaluation rules for surface coordinates and derivatives make the scheme extremely fast and robust. Since the input triangulation becomes the control-net of the subdivision surface, it is not necessarily an interpolant for the input data. Various approaches for making the surface interpolating are discussed, and this area remains one of active research.
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