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 de...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.展开更多
As a corner-cutting subdivision scheme,Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves:vertex splitting plus repeated midpoint averaging.In this paper,we modify t...As a corner-cutting subdivision scheme,Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves:vertex splitting plus repeated midpoint averaging.In this paper,we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting,and generalize the strategy to arbitrary topological surfaces of general degree.By adjusting the free parameter,the proposed method can generate subdivision surfaces with flexible shapes.Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.展开更多
基金This work was supported in part by NSF of China(No. 10201030)the TRAPOYT in Higher Education Institute of MOE of chinathe Doctoral Program of MOE of china(No. 20010358003)
文摘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.
文摘As a corner-cutting subdivision scheme,Lane-Riesefeld algorithm possesses the concise and unified form for generating uniform B-spline curves:vertex splitting plus repeated midpoint averaging.In this paper,we modify the second midpoint averaging step of the Lane-Riesefeld algorithm by introducing a parameter which controls the size of corner cutting,and generalize the strategy to arbitrary topological surfaces of general degree.By adjusting the free parameter,the proposed method can generate subdivision surfaces with flexible shapes.Experimental results demonstrate that our algorithm can produce subdivision surfaces with comparable or even better quality than the other state-of-the-art approaches by carefully choosing the free parameters.
