Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a suff...Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.展开更多
In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved ...In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.展开更多
We estimate the kinematic measure of one convex domain moving to another under the group G of rigid motions in IR~n.We first estimate the kinematic formula for the total scalar curvature ∫Rdv of the n-2 dimensional i...We estimate the kinematic measure of one convex domain moving to another under the group G of rigid motions in IR~n.We first estimate the kinematic formula for the total scalar curvature ∫Rdv of the n-2 dimensional intersection submanifold D∩g D.Then we use Chern and Yen’s kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in IR~n(≥4).For n=4,we directly obtain another sufficient condition in IR~4.展开更多
文摘Surface convexity is a key issue in computer aided geometric design, which is widely applied in geometric modeling field, such as physical models, industrial design, automatic manufacturing, etc. In this paper, a sufficient convexity condition of the parametric Bézier surface over rectangles is proposed, which is firstly considered as a sufficient convexity condition for the Bézier control grid. The condition is proved by De Casteljau surface subdivision arithmetic, in which the recursive expressions elaborate that the control grid eventually converges to the surface. At last, two examples for the modeling of interpolation-type surface are discussed, one of which is a general surface and the other is a degenerate surface.
基金National Natural Science Foundation of China(1 9971 0 72 )
文摘In this paper,the optional and predictable projections of set-valued measurable processes are studied.The existence and uniqueness of optional and predictable projections of set-valued measurable processes are proved under proper circumstances.
文摘We estimate the kinematic measure of one convex domain moving to another under the group G of rigid motions in IR~n.We first estimate the kinematic formula for the total scalar curvature ∫Rdv of the n-2 dimensional intersection submanifold D∩g D.Then we use Chern and Yen’s kinematic fundamental formula and our integral inequality to obtain a sufficient condition for one convex domain to contain another in IR~n(≥4).For n=4,we directly obtain another sufficient condition in IR~4.
