产品设计中用户感知意象的思维结构

为获取产品总意象、子意象和产品构成元素之间的关系,分析了产品设计中用户感知意象的生成机制,并提出了感知意象思维结构的模型。以太阳镜外形为研究案例,采用多元自适应回归样条技术构建产品总意象与造型、色彩、材质和光影子意象的关系模型,据此应用子意象最低规则和意象值近似规则,在Matlab软件中求解四个子意象的最优组合。采用回归树技术得到各子意象与产品构成元素的关系模型,进一步地以感知意象区间为基础,求解对应于四个最优子意象的最优产品构成元素,据此得到对应于用户感知意象的最优产品构成元素组合。研究表明:在感知意象的思维结构中,产品子意象与构成元素的关系可用树结构表征,而与产品总意象之间存在复杂的映射关系。     

波形内插语音编码中特征波形表达和对齐快速算法

针对波形内插编码模型中特征波形的表达和对齐算法计算复杂度较高的问题,应用快速傅里叶变换、3 次B样条插值和周期延拓等技术对特征波形表示和对齐2个模块作了相应的改进．改进后的算法是相对独立的,2个模块的复杂度从43．252×106次／s操作降到9．178×106次／s操作．实验结果表明,改进后算法复杂度大幅下降,大大减少了编码器的计算负载,并保持了原有编码器的合成语音质量．     

关于Lagrange插值导数的误差估计

关于Ｌａｇｒａｎｇｅ插值导数的误差估计曾提出过以下猜想：对任意ｎ＋１次连续可微的函数ｆ和任意ｎ＋１个连续点，ｎ次ｌａｇｒａｎｇｅ插值多项式Ｌ满足：‖ｆ（ｊ）－Ｌ（ｊ）‖≤‖ｗ（ｊ）‖‖ｆ（ｎ＋１）‖（ｎ＋１）！，其中ｊ是所有的整数，‖·‖表示上确界范数．ＧａｒｙＷＨｏｗｅｌ在文献［１］中证明了ｊ＝ｎ时猜想成立，ｊ＝１，２，…，ｎ－１猜想没被解决，而仅得到了‖ｆ（ｊ）－Ｌ（ｊ）‖≤‖ｗ（ｊ）‖‖ｆ（ｎ＋１）‖ｊ！（ｎ＋１－ｊ）！这样的估计式，本文主要研究ｊ＝ｎ－１时，可以得到了较好的估计式     

再生核空间算子样条插值函数

在具体的再生核空间Ｈ￣１中，解出了再生核的解析表达式，并建立了空间Ｈ；中的微分算子样条插值函数与再生核的联系，丰富了再生核空间微分算子样条函数的一系列重要性质。     

A New Approach for Direct Manipulation of Free-Form Curve

There is an increasing demand for more intuitive methods for creating and modifying free-form curves and surfaces in CAD modeling systems. The methods should be based not only on the change of the mathematical parameters, such as control points, knots, and weights, but also on the user's specified constraints and shapes. This paper presents a new approach for directly manipulating the shape of a free-form curve, leading to a better control of the curve deformation and a more intuitive CAD modeling interface. The user's intended deformation of a curve is automatically converted into the modification of the corresponding NURBS control points and knot sequence of the curve. The algorithm for this approach includes curve elevation, knot refinement, control point repositioning, and knot removal. Several examples shown in this paper demonstrate that the proposed method can be used to deform a NURBS curve into the desired shape. Currently, the algorithm concentrates on the purely geometric consideration. Further work will include the effect of material properties.     

一种用于飞机几何造型的局部曲线、曲面方法

本文描述了一种用于 CAD/CAM 系统中的称之为多结点 Hermite 样条的曲线、曲面方法。基于[1][4]的研究,本文得到了关于多结点 Hermite 样条曲线、曲面的一些定量结果。结果表明,多结点 Hermite 样条具有局部修改、节省计算机内存容量以及计算量小等特点。     

Surface reconstruction using bivariate simplex splines on Delaunay configurations

Recently, a new bivariate simplex spline scheme based on Delaunay configuration has been introduced into the geometric computing community, and it defines a complete spline space that retains many attractive theoretic and computational properties. In this paper, we develop a novel shape modeling framework to reconstruct a closed surface of arbitrary topology based on this new spline scheme. Our framework takes a triangulated set of points, and by solving a linear least-square problem and iteratively refining parameter domains with newly added knots, we can finally obtain a continuous spline surface satisfying the requirement of a user-specified error tolerance. Unlike existing surface reconstruction methods based on triangular B-splines (or DMS splines), in which auxiliary knots must be explicitly added in advance to form a knot sequence for construction of each basis function, our new algorithm completely avoids this less-intuitive and labor-intensive knot generating procedure. We demonstrate the efficacy and effectiveness of our algorithm on real-world, scattered datasets for shape representation and computing.     

有理三次均匀B样条曲线的形状控制

采用建立局部仿射价值系的方法,研究了有理三次均匀Ｂ样条的几何结构及端点性质。给出了有理三次均匀Ｂ样条曲线的几何形状修改法,使对该样条曲线的修改更加灵活、方便。     

水银封闭间隙对毛管压力测试的影响及应用

在测定不规则样品以及小样品(如岩屑)的毛管压力时,水银封闭间隙现象对测量精度有着重要的影响.在研究水银封闭间隙现象的基础上,提出了用三次样条插值函数计算水银封闭间隙的新方法.应用此法很方便地取得了川东北部罗家寨气田飞仙关组鲕滩储层各类碳酸盐岩的水银封闭间隙数值范围,分析了其对毛管压力曲线的影响,并依此对毛管压力进行了修正,以提高毛管压力资料质量,方便了应用.     

Manifold splines with a single extraordinary point

This paper develops a novel computational technique to define and construct manifold splines with only one singular point by employing the rigorous mathematical theory of Ricci flow. The central idea and new computational paradigm of manifold splines are to systematically extend the algorithmic pipeline of spline surface construction from any planar domain to an arbitrary topology. As a result, manifold splines can unify planar spline representations as their special cases. Despite its earlier success, the existing manifold spline framework is plagued by the topology-dependent, large number of singular points (i.e., |2g−2| for any genus-g surface), where the analysis of surface behaviors such as continuity remains extremely difficult. The unique theoretical contribution of this paper is that we devise new mathematical tools so that manifold splines can now be constructed with only one singular point, reaching their theoretic lower bound of singularity for real-world applications. Our new algorithm is founded upon the concept of discrete Ricci flow and associated techniques. First, Ricci flow is employed to compute a special metric of any manifold domain (serving as a parametric domain for manifold splines), such that the metric becomes flat everywhere except at one point. Then, the metric naturally induces an affine atlas covering the entire manifold except this singular point. Finally, manifold splines are defined over this affine atlas. The Ricci flow method is theoretically sound, and practically simple and efficient. We conduct various shape experiments and our new theoretical and algorithmic results alleviate the modeling difficulty of manifold splines, and hence, promote the widespread use of manifold splines in surface and solid modeling, geometric design, and reverse engineering.