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
Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme ...Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.展开更多
In this work, a novel morphing machining strategy （MMS） is proposed. In the method, the workpiece is progressively carved out from the stock. Pitfalls in conventional iso-height strategy, such as sharp edges and une...In this work, a novel morphing machining strategy （MMS） is proposed. In the method, the workpiece is progressively carved out from the stock. Pitfalls in conventional iso-height strategy, such as sharp edges and unevenly distributed left-over materials, are overcome. Moreover, to calculate different levels in the MMS, an energy-based morphing algorithm is proposed. Finally, the proposed strategy is employed in the machining of artificial bone represented by a T-spline surface. The excellent properties of T-spline, such as expressing complex shapes with a single surface, have been well adopted to artificial bone fabri- cation. Computer simulation and the actual machining of the middle finger bone show the feasibility of the proposed strategy.展开更多
Trajectory optimization and simulation is performed for Venus round trip (VeRT) mission using solar sail propulsion. Solar gravity is included but atmospheric drag and shadowing effects are neglected in the planet-cen...Trajectory optimization and simulation is performed for Venus round trip (VeRT) mission using solar sail propulsion. Solar gravity is included but atmospheric drag and shadowing effects are neglected in the planet-centered escape and capture stages. The spacecraft starts from the Geostationary orbit (GEt) at a predetermined time to prepare a good initial condition for the Earth-Venus transfer, although the launch window is not an issue for spacecraft with solar sails. The Earth-Venus phase and the return trip are divided into three segments. Two methods are adopted to maintain the mission trajectory for the VeRT mis- sion and then compared through a numerical simulation. According to the first approach, Planet-centered and heliocentric ma- neuvers are modeled using a set of blended analytical control laws instead of the optimal control techniques. The second pro- cedure is the Direct Attitude Angle Optimization in which the attitude angles of the solar sail are adopted as the optimization variables during the heliocentric transfer. Although neither of the two methods guarantees a globally optimal trajectory, they are more efficient and will produce a near-optimal solution if employed properly. The second method has produced a better result for the minimum-time transfer of the VeRT mission demonstrating the effectiveness of the methods in the preliminary design of the complex optimal interplanetary orbit transfers.展开更多
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.
文摘Suppose {Xi, i≥1} and {Yi, i≥1} are two independent sequences with distribution functions FX(x) and FY(x), respectively. Zi is the combination of Xi and Yi with a probability pn for each i with 1≤i≤n. The extreme value distribution ,n GZ(x) of this particular triangular array of the i.i.d. random variables Z1, , Z2, ,…, Zn n n ,nis discussed. We found a new form of the extreme value distribution ΛA(ρx)Λ(x)(0<ρ <1), which is not max-stable. It occurs if FX(x) and FY(x) belong to the same MDA(Λ). GZ(x) does not exist as mixture forms of the different types of extreme value distributions.
基金Project supported by the Science Fund for Creative Research Groups of National Natural Science Foundation of China （No. 51221004）, and the National Natural Science Foundation of Chi：na （Nos. 51175461 and 51105335）
文摘In this work, a novel morphing machining strategy （MMS） is proposed. In the method, the workpiece is progressively carved out from the stock. Pitfalls in conventional iso-height strategy, such as sharp edges and unevenly distributed left-over materials, are overcome. Moreover, to calculate different levels in the MMS, an energy-based morphing algorithm is proposed. Finally, the proposed strategy is employed in the machining of artificial bone represented by a T-spline surface. The excellent properties of T-spline, such as expressing complex shapes with a single surface, have been well adopted to artificial bone fabri- cation. Computer simulation and the actual machining of the middle finger bone show the feasibility of the proposed strategy.
基金supported by the National Postdoctoral Science Foundation of China (Grants No. 20110491873)the Foundation of State Key Laboratory of Astronautic Dynamics (Grants No. 2011ADL-DW0201)
文摘Trajectory optimization and simulation is performed for Venus round trip (VeRT) mission using solar sail propulsion. Solar gravity is included but atmospheric drag and shadowing effects are neglected in the planet-centered escape and capture stages. The spacecraft starts from the Geostationary orbit (GEt) at a predetermined time to prepare a good initial condition for the Earth-Venus transfer, although the launch window is not an issue for spacecraft with solar sails. The Earth-Venus phase and the return trip are divided into three segments. Two methods are adopted to maintain the mission trajectory for the VeRT mis- sion and then compared through a numerical simulation. According to the first approach, Planet-centered and heliocentric ma- neuvers are modeled using a set of blended analytical control laws instead of the optimal control techniques. The second pro- cedure is the Direct Attitude Angle Optimization in which the attitude angles of the solar sail are adopted as the optimization variables during the heliocentric transfer. Although neither of the two methods guarantees a globally optimal trajectory, they are more efficient and will produce a near-optimal solution if employed properly. The second method has produced a better result for the minimum-time transfer of the VeRT mission demonstrating the effectiveness of the methods in the preliminary design of the complex optimal interplanetary orbit transfers.
