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Proceedings of CAD'15, 2015, 23-26
On the Interpolation of Non-Iso-Parametric Curves
Abstract. The particular choice of the title of the paper is motivated by the problem of modifying an initial B-spline surface to interpolate a non-constant-parameter B-spline curve; a problem that is still defying an exact solution, even after a few decade of research. Moreover, the approximate solutions that have so far been developed for that problem are not sufficiently efficient for practical purposes. Furthermore, the particular wording of the above title is also decided in the spirit of the title of the above reference. In this context, it may be argued that the main difficulty standing in the way of an exact and practical solution of the problem is the inability to incorporate the given curve as an integral part of the surface without destroying the regular B-spline nature of the surface, and therefore threatening the starting premise of the problem itself. This may also be taken as the source of the high degree of the curve-on-surface emanating from the original curve, and therefore resulting in the inability of exactly matching the original curve with the corresponding curve-on-surface, and consequently resulting in the inability of obtaining an exact solution of the problem.
Keywords. Non-iso-parametric curves, Curve interpolation, Catmull-Clark subdivision surfaces, Polygonal complexes, X-Configurations