A Geometric B-Spline Over the Triangular Domain

摘要: For modelling curves, B-splines [3] are among the most versatile control schemes. However, scaling this technique to surface patches has proven be a non-trivial endeavor. While suitable scheme exists for rectangular in form of tensor product B-splines, techniques involving triangular domain much less spectacular. The current cutting edge is DMS-spline [2]. resulting surfaces possess high degrees continuity, awkward and evaluation computationally expensive. A more fundamental problem construction bears little resemblance used B-Spline. This deficiency leads central idea thesis; what happens if simple blending functions found at heart B-Spline over higher dimension domains? In thesis I develop geometric generalization curves domain. mimics point that occurs with uniform B-Splines. preserves B-Splines, without immense computational requirements DMSsplines. result new patch scheme, G-Patch, possessing C continuity between adjacent patches.