Smooth parametric surfaces interpolating triangular meshes are very useful for modeling a surface of arbitrary topological type. Several interpolants based on this kind of surfaces have been develloped these last fifteen years. However, with current 3D acquisition equipments, models are 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 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 refining locally 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 where lower levels encode details in local frame coordinates.

@article{YHB05,
author = {Alex Yvart and Stefanie Hahmann and Georges-Pierre Bonneau},
title = {Hierarchical Triangular Splines},
journal = {ACM Trans. Graph.},
volume = 24,
number = {4},
pages = {1374--1391},
keywords = {hierarchical surface modelling},
month = oct,
year = 2005
}