A strategy for B-spline curve data reduction based on non-uniform B-spline wavelet decomposition is presented. In existing methods of knot removal, ranking the removal knots depends on a procedure of assigning a weigh...A strategy for B-spline curve data reduction based on non-uniform B-spline wavelet decomposition is presented. In existing methods of knot removal, ranking the removal knots depends on a procedure of assigning a weight to each knot to indicate its significance. This is reasonable but not straightforward. Propose is a more straightforward and accurate method to calculate the weight. The wavelet coefficient is taken as a weight for the corresponding knot. The approximating curve and the error can be obtained directly from the wavelet decomposition. By using the hierarchical structure of the wavelet, the error can be computed efficiently in an accumulative manner.展开更多
Extension of a B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve...Extension of a B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC^2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC^2 parameter to be zero and determining the second GC^2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given.展开更多
基金Supported by the Natural Science Foundation of China (50075032) and State High-Technology Development Program of China (2001AA421150)
文摘A strategy for B-spline curve data reduction based on non-uniform B-spline wavelet decomposition is presented. In existing methods of knot removal, ranking the removal knots depends on a procedure of assigning a weight to each knot to indicate its significance. This is reasonable but not straightforward. Propose is a more straightforward and accurate method to calculate the weight. The wavelet coefficient is taken as a weight for the corresponding knot. The approximating curve and the error can be obtained directly from the wavelet decomposition. By using the hierarchical structure of the wavelet, the error can be computed efficiently in an accumulative manner.
文摘Extension of a B-spline curve or surface is a useful function in a CAD system. This paper presents an algorithm for extending cubic B-spline curves or surfaces to one or more target points. To keep the extension curve segment GC^2-continuous with the original one, a family of cubic polynomial interpolation curves can be constructed. One curve is chosen as the solution from a sub-class of such a family by setting one GC^2 parameter to be zero and determining the second GC^2 parameter by minimizing the strain energy. To simplify the final curve representation, the extension segment is reparameterized to achieve C-continuity with the given B-spline curve, and then knot removal from the curve is done. As a result, a sub-optimized solution subject to the given constraints and criteria is obtained. Additionally, new control points of the extension B-spline segment can be determined by solving lower triangular linear equations. Some computing examples for comparing our method and other methods are given.
