We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^(2)-continuity.Instead of moving the control points,we minimize the distance between the original curves an...We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^(2)-continuity.Instead of moving the control points,we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve's discrete structure,where the approximation error is measured by L_(2)-norm.We use geometric information about the curves to generate the merged curve,and the approximation error is smaller.We can obtain control points of the merged curve regardless of the degrees of the two original curves.We also discuss the merged curve with point constraints.Numerical examples are provided to demonstrate the effectiveness of our algorithms.展开更多
Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curv...Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.展开更多
基金supported by the National Natural Science Foundation of China(No.60773179)the National Basic Research Program(973)of China(No.G2004CB318000)
文摘We present a novel approach for dealing with optimal approximate merging of two adjacent Bezier eurves with G^(2)-continuity.Instead of moving the control points,we minimize the distance between the original curves and the merged curve by taking advantage of matrix representation of Bezier curve's discrete structure,where the approximation error is measured by L_(2)-norm.We use geometric information about the curves to generate the merged curve,and the approximation error is smaller.We can obtain control points of the merged curve regardless of the degrees of the two original curves.We also discuss the merged curve with point constraints.Numerical examples are provided to demonstrate the effectiveness of our algorithms.
基金Supported by the National Natural Science Foundation of China (60873111, 60933007)
文摘Applying the distance function between two B-spline curves with respect to the L2 norm as the approximate error, we investigate the problem of approximate merging of two adjacent B-spline curves into one B-spline curve. Then this method can be easily extended to the approximate merging problem of multiple B-spline curves and of two adjacent surfaces. After minimizing the approximate error between curves or surfaces, the approximate merging problem can be transformed into equations solving. We express both the new control points and the precise error of approximation explicitly in matrix form. Based on homogeneous coordinates and quadratic programming, we also introduce a new framework for approximate merging of two adjacent NURBS curves. Finally, several numerical examples demonstrate the effectiveness and validity of the algorithm.
