Smooth Adaptive Fitting of 3D models using hierarchical triangular splines

The recent ability to measure quickly and inexpensively dense sets of points on physical objects has deeply influenced the way engineers used to represent shapes in CAD systems, animation software or in the game industry. Many researchers advocated to completely bypass smooth surface representations, and to stick to a dense mesh model throughout the design process. Yet smooth analytic representations are still required in standard CAD systems and animation software, for reasons of compactness, control, appearance and manufacturability. In this paper we present a method for fitting a smooth adaptively refinable triangular spline surface of arbitrary topology to an arbitrary dense triangular mesh. The final surface is composed of low-degree polynomial patches that join with G1-continuity. The ability to adaptively refine the model allows to achieve a given approximation error with a minimal number of patches.

@InProceedings\{YHB05a,
  author       = "Yvart, Alex and Hahmann, Stefanie and Bonneau, Georges-Pierre",
  title        = "Smooth Adaptive Fitting of 3D models using hierarchical triangular splines",
  booktitle    = "Shape Modeling International",
  month        = "june",
  year         = "2005",
  url          = "http://www-evasion.imag.fr/Publications/2005/YHB05a"
}