A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this met...A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.展开更多
Incremental algorithm is one of the most popular procedures for constructing Delaunay triangulations （DTs）. However, the point insertion sequence has a great impact on the amount of work needed for the construction ...Incremental algorithm is one of the most popular procedures for constructing Delaunay triangulations （DTs）. However, the point insertion sequence has a great impact on the amount of work needed for the construction of DTs. It affects the time for both point location and structure update, and hence the overall computational time of the triangulation algorithm. In this paper, a simple deterministic insertion sequence is proposed based on the breadth-first-search on a Kd-tree with some minor modifications for better performance. Using parent nodes as search-hints, the proposed insertion sequence proves to be faster and more stable than the Hilbert curve order and biased randomized insertion order （BRIO）, especially for non-uniform point distributions over a wide range of benchmark examples.展开更多
Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference...Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.展开更多
文摘A smooth interpolatory subdivision algorithm for the generation of surfaces over arbi-trary triangulations is introduced and its convergence properties over nonuniform triangulationsstudied. For uniform data, this method is a generalization of the analysis for univariatesubdivision algorithms and for nonuniform data, an extraordinary point analysis is introducedand the local subdivision matrix anaiysis presented. It is proved that the algorithm producessmooth surfaces over arbitrary triangular networks provided the shape parameters are kept with-in an appropriate range. Finally, two graphical examples of surface interpolation overnonuniform data are given to show the smoothing process of the algorithm.AMS (MOS): 65D05, 65D15,65D17.
基金supported by the National Natural Science Foundation of China (10972006 and 11172005)the National Basic Research Program of China (2010CB832701)
文摘Incremental algorithm is one of the most popular procedures for constructing Delaunay triangulations （DTs）. However, the point insertion sequence has a great impact on the amount of work needed for the construction of DTs. It affects the time for both point location and structure update, and hence the overall computational time of the triangulation algorithm. In this paper, a simple deterministic insertion sequence is proposed based on the breadth-first-search on a Kd-tree with some minor modifications for better performance. Using parent nodes as search-hints, the proposed insertion sequence proves to be faster and more stable than the Hilbert curve order and biased randomized insertion order （BRIO）, especially for non-uniform point distributions over a wide range of benchmark examples.
文摘Interpolatory subdivision algorithms for the generation of curves and surfaces play a veryimportant rule in shape design and modelling in CAD/CAM systems. In this paper, by using the dif-ference and divided difference analysis, a systematic method to construct Cn (n≥ 0) interpolatorycurves by subdivision from given data is described and the mask (filter) of the algorithm is presentedexplicitly. This algorithm generates a Cn smooth curve which interpolates the initial control points.Control parameters are also provided so that the shape of the final curve can be adjusted according torequirements. An immediate generalisation of the method is the construction of smooth interpolatorysubdivision algorithms over uniform triangular networks (tensor product type data) in Rm. The mainresults of this algorithm for smooth interpolatory surface subdivision algorrthm are also included.AMS(MOS) : 65D05 , 65D15 , 65D17.
