ESTIMATING ERROR BOUNDS FOR TERNARY SUBDIVISION CURVES/SURFACES  

作　　者：Ghulam Mustafa Jiansong Deng 

机构地区：[1]Department of Mathematics, Islamia University, Bahawalpur, Pakistan Department of Mathematics, University of Science and Technology of China, Hefei 230026, China [2]Department of Mathematics, University of Science and Technology of China, Hefei 230026, China

出　　处：《Journal of Computational Mathematics》2007年第4期473-484,共12页计算数学（英文）

基　　金：This work was supported in part by NSF of China(No. 10201030);the TRAPOYT in Higher Education Institute of MOE of china;the Doctoral Program of MOE of china(No. 20010358003)

摘　　要：We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametrization therefore it can be easily and efficiently implemented. This is useful and important for pre-computing the error bounds of subdivision curves/surfaces in advance in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and so on.We estimate error bounds between ternary subdivision curves/surfaces and their control polygons after k-fold subdivision in terms of the maximal differences of the initial control point sequences and constants that depend on the subdivision mask. The bound is independent of the process of subdivision and can be evaluated without recursive subdivision. Our technique is independent of parametrization therefore it can be easily and efficiently implemented. This is useful and important for pre-computing the error bounds of subdivision curves/surfaces in advance in many engineering applications such as surface/surface intersection, mesh generation, NC machining, surface rendering and so on.

关 键 词：Subdivision curve Subdivision surface Subdivision depth Error bound. 

分 类 号：O187.1[理学—数学]