A research note on design of fair surfaces over irregular domains using data-dependent triangulation

Design of fair surfaces over irregular domain is a fundamental problem in computer aided geometric design (CAGD), and has applications in engineering sciences (i.e. aircraft science, automobile science and ship science etc.). In design of fair surfaces over irregular domain defined over scattered data it was widely accepted till recently that one should use Delaunay triangulation because of its global optimum property. However, in recent times it has been shown that for continuous piecewise polynomial parametric surfaces improvements in the quality of fit can be achieved if the triangulation pattern is made dependent upon some topological property of the data set or is simply data dependent. The smoothness and fairness of surface’s planar cuts is important because not only it ensures favorable hydrodynamic drag, but also helps in reducing manhours during the production of the surface. In this paper we discuss a method for construction of C1 piecewise polynomial parametric fair surfaces which interpolate prescribed R3R3 scattered data using spaces of parametric splines defined on R3R3 triangulation. We show that our method is more specific to the cases when the projection on 2-D plane may consist of triangles of zero area. The proposed method is fast, numerically stable and robust, and computationally inexpensive. In the present work numerical examples dealing with surfaces approximated on standard curved plates, and ship hull surface have been presented.