ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB...ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.展开更多
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
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
基金the National Natural Science Foundation of China(61772164,61761136010)the Natural Science Foundation of Zhejiang Province(LY17F020025).
文摘ωB-splines have many optimal properties and can reproduce plentiful commonly-used analytical curves.In this paper,we further propose a non-stationary subdivision method of hierarchically and efficiently generatingωB-spline curves of arbitrary order ofωB-spline curves and prove its C^k?2-continuity by two kinds of methods.The first method directly prove that the sequence of control polygons of subdivision of order k converges to a C^k?2-continuousωB-spline curve of order k.The second one is based on the theories upon subdivision masks and asymptotic equivalence etc.,which is more convenient to be further extended to the case of surface subdivision.And the problem of approximation order of this non-stationary subdivision scheme is also discussed.Then a uniform ωB-spline curve has both perfect mathematical representation and efficient generation method,which will benefit the application ofωB-splines.
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.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
