In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which impr...In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.展开更多
A surface interpolation algorithm is presented. By using a special kind of knot vector. a B-spline surface can be constructed to interpolate an array of m ×n positions, including parameter u and v tangent vectors...A surface interpolation algorithm is presented. By using a special kind of knot vector. a B-spline surface can be constructed to interpolate an array of m ×n positions, including parameter u and v tangent vectors and twist vector at each positions. Single surface interpolation approach is easier to ensure the smoothness of the interpolating surface than multi-patches method. This algorithm can be used to solve the approximating problem of B-spline approximation of general parametric surface.展开更多
An important class in the study of topology of 3-manifolds is the so-called 'sufficiently large 3-manifolds', i.e. those compact 3-manifolds which contain properly embedded, 2-sided incompressible surfaces. We...An important class in the study of topology of 3-manifolds is the so-called 'sufficiently large 3-manifolds', i.e. those compact 3-manifolds which contain properly embedded, 2-sided incompressible surfaces. We know that every sufficiently large 3-manifold can bc cut into some 3-cells along incompressible surfaces in a finite process. For a 3-manifold, it is interesting to know whether there exists an incompressible surface embedded in it and how the incompressible surface embeds.展开更多
基金The NSF (11071106) of Chinathe Program (LR2011031) for Liaoning Excellent Talents in University
文摘In this paper, by the twist-crossing number of knots, we give an upper bound on the Euler characteristic of a kind of essential surfaces in the complements of alternating knots and almost alternating knots, which improves the estimation of the Euler characteristic of the essential surfaces with boundaries under certain conditions. Furthermore, we give the genus of the essential surfaces.
文摘A surface interpolation algorithm is presented. By using a special kind of knot vector. a B-spline surface can be constructed to interpolate an array of m ×n positions, including parameter u and v tangent vectors and twist vector at each positions. Single surface interpolation approach is easier to ensure the smoothness of the interpolating surface than multi-patches method. This algorithm can be used to solve the approximating problem of B-spline approximation of general parametric surface.
文摘An important class in the study of topology of 3-manifolds is the so-called 'sufficiently large 3-manifolds', i.e. those compact 3-manifolds which contain properly embedded, 2-sided incompressible surfaces. We know that every sufficiently large 3-manifold can bc cut into some 3-cells along incompressible surfaces in a finite process. For a 3-manifold, it is interesting to know whether there exists an incompressible surface embedded in it and how the incompressible surface embeds.
