An algorithm to build convex hulls for 3‐D objects

Abstract

In this paper, a new algorithm based on the Quickhull algorithm is proposed to find convex hulls for 3‐D objects using neighbor trees. The neighbor tree is the data structure by which all visible facets to the selected furthest outer point can be found. The neighboring sequence of ridges on the outer boundary of all visible facets also can be found directly from the neighbor tree. This new algorithm is twice as efficient as Barber's algorithm.     

Searching for empty convex polygons

A key problem in computational geometry is the identification of subsets of a point set having particular properties. We study this problem for the properties of convexity and emptiness. We show that finding empty triangles is related to the problem of determining pairs of vertices that see each other in a star-shaped polygon. A linear-time algorithm for this problem which is of independent interest yields an optimal algorithm for finding all empty triangles. This result is then extended to an algorithm for finding empty convex r-gons (r> 3) and for determining a largest empty convex subset. Finally, extensions to higher dimensions are mentioned.The first author is pleased to acknowledge support by the National Science Foundation under Grant CCR-8700917. The research of the second author was supported by Amoco Foundation Faculty Development Grant CS 1-6-44862 and by the National Science Foundation under Grant CCR-8714565.     

基于半定规划的阵列天线方向图旁瓣抑制

基于半定规划理论提出了一种新的阵列天线方向图旁瓣抑制算法。与传统旁瓣抑制方法不同,该方法通过合理设计优化准则,避免了在凸优化问题建模过程中引入近似,保证了波束形成器的最优性;并且使得在压低旁瓣的同时,可准确控制信噪比增益和主瓣宽度到期望的范围之内。该方法对阵列流形没有限制,计算机仿真结果验证了其有效性。     

复一致凸和复一致平滑Banach空间的几点注记

Ｖ．Ｉ．Ｉｓｔｒａｔｅｓｃｕ引入了复一致凸性和复一致平滑性的概念．本文证明了它们分别等价于一致凸性和一致平滑性．     

铝合金铸件机箱四孔定位加工工艺方法研究

铸造铝合金材料因其良好的抗腐蚀性、流动性和切削加工性能,适合铸造薄壁、形状复杂和强度高的机箱等各类零件。根据实际生产过程中某薄壁类铸件机箱加工中易变形的问题,进行工艺流程改进,总结出铸件机箱的典型加工工艺方法,提高了产品质量和生产效率。     

翼子板轮弧圆角不顺解决对策

根据汽车翼子板结构特点及成形机理,分析了翼子板轮弧位置翻边圆角不顺的原因及解决对策,为汽车翼子板的工艺设计提供思路、积累经验。     

Stochastic iteration for a constrained optimization problem

A primal dual method of Kushner and Sanvicente for a constrained optimization problem with convex regression functions is investigated without a priori bounds. For the stochastic approximation sequence almost sure convergence to a random optimal solution and a random Kuhn-Tucker vector is shown, and for the uniqueness case, a functional central limit theorem is given.     

凸度量空间内广义渐近拟非扩张映射不动点的迭代

在凸度量空间中，引入一类比渐近拟非扩张映射更加广泛的广义渐近拟非扩张型映射，并在完备凸度量空间给出修改的Ishikawa迭代序列收敛于广义渐近拟非扩张型映射不动点的充要条件。     

Equidistant Smoothing of Polyhedra with Arbitrary Topologies

Smoothing of polyhedron with arbitrary topology is an important issue in CAGD and CAD/CAM, but so far it is deemed to be difficult to smooth the complex corners of a polyhedron. In this paper, the concept of distance surfaces of a surface and a solid is introduced, and the incisive properties of such surfaces are addressed which provide a theoretical foundation for modifying a general corner. The method is based on making constricted volume and the maximum distance the volume can be constricted is given too. It is shown that by the proposed method in this paper any polyhedron can be G¹ smoothed with quadraic and, sometimes toroidal surfaces. The new approach is suitable for engineering design and NC machining. The associated algorithm based on the classification theorem of corners is simple, fast and robust.     

变信赖域序列凸规划RLV再入轨迹在线重构

针对可重复使用运载器（RLV）的再入轨迹重构问题,提出一种基于变信赖域序列凸规划的RLV再入轨迹快速求解方法. 首先,通过离散化及对非凸约束的线性化处理,将RLV的非凸轨迹优化问题转换为凸优化问题,然后通过序列凸规划方法对凸优化问题进行求解. 在序列凸规划求解过程的初始迭代中,采用预测校正算法对初值猜测轨迹进行设计,确定轨迹求解的终端时间;在后续迭代过程中,设计基于优化性能指标的信赖域更新策略,提升算法的收敛性能. 在轨迹快速求解方法的基础上,考虑RLV再入过程中可能发生的突发事件,如实际轨迹大幅度偏离参考轨迹或目标点变更,基于变化的初值约束及终端约束在线重构轨迹,并结合重构轨迹和LQR（Linear quadratic regulator）方法设计再入制导律实现对重构轨迹的有效跟踪. 最后,将此设计方法与Gauss伪谱法及传统序列凸规划算法进行仿真对比验证. 仿真结果表明:变信赖域序列凸规划方法相较于伪谱法和传统的序列凸规划方法在轨迹求解实时性及收敛性方面有较大的提升,具备应用于轨迹在线重构的能力,此外,所提出的轨迹在线重构方法具备良好的鲁棒性以及抗扰性.