Hierarchical Triangular Splines

Alex Yvart 1 Stefanie Hahmann 1, * Georges-Pierre Bonneau 2, *
* Corresponding author
2 EVASION - Virtual environments for animation and image synthesis of natural objects
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : Smooth parametric surfaces interpolating triangular meshes are very useful for modeling surfaces of arbitrary topology. Several interpolants based on this kind of surfaces have been developed over the last fifteen years. However, with current 3D acquisition equipments, models are becoming more and more complex. Since previous interpolating methods lack a local refinement property, there is no way to locally adapt the level of detail. In this paper, we introduce a hierarchical triangular surface model. The surface is overall tangent plane continuous and is defined parametrically as a piecewise quintic polynomial. It can be adaptively refined while preserving the overall tangent plane continuity. This model enables designers to create a complex smooth surface composed of a small number of patches, to which details can be added by locally refining the patches until an arbitrary small size is reached. It is implemented as a hierarchical data structure where the top layer describes a coarse, smooth base surface, and the lower levels encode the details in local frame coordinates.
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Alex Yvart, Stefanie Hahmann, Georges-Pierre Bonneau. Hierarchical Triangular Splines. ACM Transactions on Graphics, Association for Computing Machinery, 2005, 24 (4), pp.1374-1391. ⟨hal-00319643⟩

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