构造代数Blending曲面的Gr bner基方法

利用代数几何中关于理想的 Gr bner基的理论 ,结合 CAGD中的研究方法 ,对代数 Blending曲面做了较为细致的研究 ,给出了用 Gr bner基构造代数 Blending曲面的新方法 .该方法能够求出所有满足要求的代数Blending曲面 ,并能给出其中次数最低的曲面 .文中还讨论了如何利用代数曲面插值、最小平方逼近的方法来选取合适的自由参数 ,以达到对代数 Blending曲面进行形状控制的目的 .最后给出了一个茶壶表面造型示例 ,以说明方法的有效性     

Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis

In this paper, we propose an analysis methodology that is procedurally analogous to Constructive Solid Geometry (CSG) integrating design and analysis, and thereby enabling efficient optimal design. The procedure, due to its analogous nature to CSG, is termed Constructive Solid Analysis (CSA). The analysis methodology is partitioned, hierarchical and is based on constructing the boundary value problem for a compound geometry through operations on the field quantities defined on the primitives. Although the CSA procedure will allow any basis for approximating the fields, Non-Uniform Rational B-Splines (NURBS), currently popular in the geometric modeling literature, are used to represent the geometry of the primitives as well as the analysis fields. The use of the same basis to represent geometry and analysis fields enables ‘representational’ integration, and further, the developed methodology may be classified as a partition of unity meshless analysis scheme. A more general null-space solution scheme and a somewhat restrictive range-space solution scheme are outlined to solve the discretized equations resulting from the use of NURBS. Several representative problems from the field of linear elasticity are solved to demonstrate the validity of the procedure and to evaluate its computational cost relative to the finite element method. The optimal orientation of an elliptical hole to applied tractions is determined to demonstrate the power of the proposed methodology for shape optimal design.     

The Basic Constructive Logic for Negation-Consistency

In this paper, consistency is understood in the standard way, i.e. as the absence of a contradiction. The basic constructive logic B_Kc4, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending B_Kc4 up to minimal intuitionistic logic. All logics defined in this paper are paraconsistent logics.     

Constructive generation of the medial axis for solid models

The medial axis (MA) is a simplified representation of complicated models which is widely used in current research. However, the efficient generation of the MA for complicated solid models continues to pose a challenge. In this study, a constructive approach for the generation of the MA is proposed for solid models after they are voxelized. With this method, the MA of the model constructed from two operand models via a Boolean operation is efficiently generated by merging the MAs of the operand models in a certain way, instead of regenerating them from scratch. To support the proposed method, the affected region of the resultant model is computed first using a Boolean operation. Second, only the MA in the affected region is regenerated by distance dilation. Third, the complete MA of the resultant model is constructed by combining the newly generated MA with the unchanged MAs of the operand models. In this study, the accuracy and complexity are analyzed for the final MA and some examples are given to illustrate the performance of the proposed method.     

The Basic Constructive Logic for Absolute Consistency

In this paper, consistency is understood as absolute consistency (i.e. non-triviality). The basic constructive logic B_Kc6, which is adequate to this sense of consistency in the ternary relational semantics without a set of designated points, is defined. Then, it is shown how to define a series of logics by extending B_Kc6 up to contractionless intuitionistic logic. All logics defined in this paper are paraconsistent logics.     

多目标原油选择与混合优化方法

为保证原料的稳定供应,炼厂经常需要寻找相似原油替代库存量少的原油.以混合原油与目标原油质量偏差最小以及混合原料成本最低为目标,构建了一个多目标原油选择与混合优化模型.模型为混合整数非线性规划模型,可以将寻找替代原油转化为原油选择与混合优化问题.在原始多目标布谷鸟搜索(MOCS)算法基础上,对编码以及Lévy飞行进行了改进,结合非支配排序方法提出了一种改进的多目标布谷鸟搜索(IMOCS)算法.利用IMOCS算法求解模型,可同时确定原油的选择和混合比例,且一次计算可得到一组Pareto最优解.通过仿真,与非支配排序遗传算法(NSGA-Ⅱ)进行对比,验证算法的寻优效果.计算得到的混合方案可为炼厂寻找替代原油提供参考.     

基于几何解析的双雷达地面目标定位算法

传统的双雷达地面目标定位算法因测量数据本身固有的误差和量测噪声,使得基于非线性估计定位算法的定位精度不高。本文研究了一种新的双雷达地面目标定位算法,该算法将已知雷达探测数据以几何方式加以表示,通过几何解析对地面目标进行定位。此外,还详细分析了各种因素在不同情况下对定位精度的影响。所研究的算法具有计算量小、远距离定位精度高等优点。最后,通过仿真验证了该算法能够提高远距离定位的定位精度。     

面向球幕投影系统的几何校正方法

摘 要：用于飞行模拟的视景仿真系统，经常会以多台投影仪同步投影以得到较大范围的 视场角。当投影机斜对屏幕或者投影屏幕为曲面时，图像会发生几何失真。针对此问题，本文 提出了一种专门面向球幕投影系统的几何校正方法，并以一个三通道显示系统为实例，详述了 该方法的理论原理以及校正流程。实例结果表明，经几何校正后，各投影图像无几何畸变，通 道过渡处几何内容完全一致。该方法是一种纯软件方法，成本小而且操作简单，能够适应于不 同的投影场景。     

Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System

Automatic blending has characterized the major advantage of implicit surface modeling systems. Recently, the introduction of deformations based on space warping and Boolean operations between primitives has increased the usefulness of such systems. We propose a further enhancement which will extend the range of models that can be easily and intuitively defined with a skeletal implicit surface system. We describe a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and Boolean operations. We call this structure the BlobTree . Blending and space warping are treated in the same way as union, difference and intersection, i.e. as nodes in the BlobTree . The traversal of the BlobTree is described along with two rendering algorithms; a polygonizer and a ray tracer. We present some examples of interesting models which can be made easily using our approach that would be very difficult to represent with conventional systems.     

一种面向移动计算终端的几何压缩方法

鉴于移动计算终端具有显示屏幕小、对模型精度要求较低和处理能力相对较弱、处理高细节度的模型十分吃力,以及受带宽所限,需要对模型进行渐进传输等特点。而已有的几何压缩和简化方法又对移动计算终端的这些特点针对性不够,为此,围绕在移动计算终端上进行3维图形的显示,根据移动计算终端的特点,提出了一个实现过程简单、简化效率较高的几何压缩方法,同时提出了一个基于顶点相邻三角形单位法向量变化的边折叠几何压缩算法,并通过计算顶点相邻三角形单位法向量差值来识别出模型的特征点,提出了一个特征保留的策略。实践表明,完整的基于单位法向量变化和特征保留的边折叠几何压缩算法可以在保持模型外观的同时,有效地降低模型的规模。最后给出了该压缩方法在移动计算终端上的应用情况。通过用该压缩算法对模型进行预处理,实现了在移动计算终端上进行3维图形显示的这一目的。随着移动计算技术的发展,移动3维图形的应用将会越来越多,因此该压缩方法在移动3维图形计算方面具有较好的应用前景。     

一种利用几何约束求解图像隐藏元素的方法

对极几何是研究双目视觉的有力工具。利用对极点在成像对应关系上的特殊性,研究了求解空间交点和交线成像坐标的通用方法,并把它们应用于图像中简单凸多面体隐藏元素的求解思路之中。对多组双目图像中的隐藏元素确定其成像坐标,结果验证了方法的可行性和有效性。     

伪卫星在北斗导航系统中的布局研究

目前我国的北斗导航定位系统只能实现二维有源定位,这就大大限制了北斗导航系统的应用;采用伪卫星不但可以辅助增强北斗定位系统实现三维无源定位,提高定位精度,而且也可以单独组网并在区域范围内代替卫星导航系统进行独立定位;由于卫星定位系统的精度与卫星数目以及几何布局有着很大的关系,应用拉格朗日法,通过数学推导和仿真分析,研究了伪卫星数目以及布局对系统定位精度的影响,得出了伪卫星布局的相应结论。     

一种异类系统中多种故障检测与隔离的空间几何方法研究

针对量测干扰下一种异类过驱动系统中残差与干扰存在耦合关系的问题,提一种运用空间几何方法实现残差对干扰解耦的新算法.通过设计残差生成器并实 现残差对系统输入和量测干扰的解耦,由残差值反馈故障检测情况,根据不可观 测子空间中的空间分割建立结构化残差集,使得残差集与故障集满足完全对应关系,完成故障的隔离.最后通过提出对比仿真算例验证了我们所提算法的可行性和有效性.     

面向移动计算终端的渐进几何简化方法

在移动计算终端上进行移动三维图形计算是一个重要的课题.针对移动计算终端屏幕小、计算能力低、无线网络带宽受限等特点,研究如何进行移动三维图形的渐进显示具有十分重要的意义.提出了利用Kobbelt四边形细分算法的逆过程迭代地进行简化的方法,通过迭代地把模型分割为奇点和作为简化模型的偶点,实现了对四边形网格几何模型的渐进式简化;提出了渐进显示的模式,通过把每一层的奇点作为可添加的细节信息,可以支持在终端上渐进显示不同细节模型并实现原模型的无损还原.完整的简化方法简单快速,可以高效地实现移动三维图形的渐进简化显示.最后在型号为Mio 336的PDA上的实验结果表明,研究成果在移动计算终端上进行实时交互等方面具有很好的应用前景.     

直觉模糊熵的几何构造方法及其应用

针对直觉模糊集中模糊性和直觉性对不确定信息的综合影响以及直觉模糊熵连续变化等问题,提出2种直觉模糊熵的几何构造方法,完善传统直觉模糊熵的构造准则。利用几何方法,分别通过建立等熵平面和等熵圆弧,结合距离构造2种新的直觉模糊熵,并证明其相关性质。论述直觉模糊熵的一般构造方法,对算例与现存的一些熵公式进行比较分析。将直觉模糊熵应用到多属性决策中,验证该方法的正确性和合理性。     

一种遥感图像太阳—观测几何归一化方法

宽空间覆盖、高观测频率传感器往往具有较大的观测视场,大观测视场带来的问题是不同位置和不同时间的太阳—观测几何不同。因此,在半经验的核驱动BRDF模型基础上,提出一种新的模型用于遥感数据太阳—观测几何归一化,利用植被指数组成的二次多项式作为基于核驱动的半经验BRDF模型中体散射部分和几何光学散射部分的核系数,并使用目标在不同时间的多角度观测数据反推用于太阳—观测几何转换的模型系数。分别利用红色和近红外波段的模拟数据和真实观测数据对模型进行验证,结果表明新提出模型的模拟值与真实观测值具有较好的一致性,能够应用于遥感图像的太阳—观测几何转换。