2015/10/26 by Raimundas Vidūnas, Raimundas Vidunas, Vidunas, Raimundas
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #math.AG #math.DG #msc:57M20 #msc:58C25 #msc:65D07 #msc:65D17
paper · pdf · doi:10.48550/arxiv.1510.07475
46 pages; 12 figures
arxiv created 2015/10/26 · arxiv updated 2015/10/27
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined by G1 gluing data in terms of rational functions are analyzed further. A general structure for a spline basis is defined, and a dimension formula is proved for spline spaces of bounded degree on polygonal surfaces made up of rectangles and triangles. Lastly, a comprehensive example is presented, and practical perspectives of geometric continuity are discussed. The whole objective of the paper is to put forward a modernized, practicable framework of modeling with geometric continuity.