实现3个二次曲面GC1拼接的一种具体算法

研究拼接3个二次代数曲面所形成的混合代数曲面的整体参数化问题,提出相应的参数化方法,给出了具体算法.利用拼接曲面在仿射坐标系下的简单表达式,不分块直接对混合拼接曲面进行参数化.     

中国剩余定理在曲面拼接中的应用

用计算机代数方法,研究了两个二次曲面的光滑拼接,给出了应用中国剩余定理得到的在两个截面平行的条件下的三次拼接曲面,并且由此得到的拼接曲面还满足超限插值问题.     

两个二次代数曲面的3次GC~1阶拼接研究及应用

利用代数方法,探索了两个二次代数曲面的3次GC1阶拼接条件,得出一个充要条件的结论,并利用结论给出了实例,结合MATLAB软件工具给出了球面和圆柱体沿截平面光滑拼接图形.     

曲面造型的方法与实现

对非均匀有理B样条(NURBS)参数化特征设计和隐式代数曲面的原理实现曲面造型进行了介绍。在仿真的过程中运用CAD/CAM技术软件实现了凉亭顶部的设计,证实了在软件中运用非均匀有理B样条(NURBS)参数化特征设计在曲面造型方面是可行的,不仅拟合度好而且可以提高设计效率,并且可以使得图形更严密。     

用二次曲面光滑拼接多个圆柱面的研究

在用二次曲面光滑拼接多个圆柱面方面,球面和单叶双曲面是较好的选择．以曲面光滑拼接、微分几何、空间解析几何的理论和Maple等数学软件为工具,采用适当的过渡曲面,分别实现圆柱面与半球面的光滑拼接,单叶双曲面与一个球面、半球面的光滑拼接,进而给出用二次曲面对多个圆柱面进行光滑拼接的方法,并得到了光滑拼接的充分必要条件,构造...     

基于Sylvester结式消元低次拼接条件的研究

根据拼接中的主曲面和辅助曲面方程,利用同伦映射方法构造出含有单位区间变元的代数方程,应用Sylvester结式方法消去变元得到拼接曲面表达式.然后,假设该曲面表达式能够进行因式分解,分析G0和G1次光滑拼接中拼接曲面的次数最低时辅助曲面S（hi）应满足的条件.最后,运用Grobner基理论判断分解因式后各因式是否在主曲面和辅助曲面生成的理想中,从而得出符合条件的低次拼接曲面.     

C2连续奇异混合插值曲面

利用奇异混合函数将双三次B样条曲面与虚拟曲面片作混合,构造一类可插值给定数据点的插值曲面,该类曲面在边界处可达到C~2连续,参数α可对曲面片整体形状进行调控。进一步,构造了可局部调控形状的带形状参数的插值曲面。     

基于逆向工程的玩偶三维曲面模型重构技术

本文研究了应用UG软件对"点云"数据进行曲面重构的过程:扫描线的生成、扫描线的排序、曲面裁剪和曲面的拼接直至曲面的构成,提出了一种先平面裁剪后拼接融合的多个小平面拼接方法,可使多个曲面光滑地连接成为一体。     

TC-B样条曲线与λ-B样条曲线的光滑拼接

在CAGD中,人们对曲线曲面的拼接做了大量的研究与分析.本文研究了三次TC-B样条曲线与带参数λ的三次B样条曲线的光滑拼接问题,并讨论了三次TC-B样条曲线与λ-B样条曲线的G0、G1和G2光滑拼接问题.     

基于Geomagic Design X的弧面分度凸轮逆向建模

以弧面分度凸轮为例,利用激光扫描仪测量了弧面分度凸轮的三维几何数据,阐述了弧面分度凸轮点云的拼接方法,使用曲面拟合、曲线混合和曲面放样等功能分段创建了弧面分度凸轮的工作廓面,在通过曲面剪切和曲面缝合功能最终创建了弧面分度凸轮的三维实体模型。该方法对创建弧面分度凸轮的三维实体模型提供了一种切实可行的方案,具有较好的应用价值。     

NURBS curve blending using extension

Curve and surface blending is an important operation in CAD systems, in which a non-uniform rational B-spline （NURBS） has been used as the de facto standard. In local comer blending, two curves intersecting at that comer are first made disjoint, and then the third blending curve is added-in to smoothly join the two curves with G^1- or G^2-continuity. In this paper we present a study to solve the joint problem based on curve extension. The following nice properties of this extension algorithm are exploited in depth： （1） The parameterization of the original shapes does not change; （2） No additional fragments are created. Various examples are presented to demonstrate that our solution is simple and efficient.     

A spherical parameterization approach based on symmetry analysis of triangular meshes

We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle distortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.     

论校报思想政治教育功能与“三个统一”的关系

本从舆论宣传与信息传播职能、导向性与可读性、言论的思想性和艺术性的有机统一等三方面，论述了校报如何更好地、更有效地发挥其思想政治教育功能。     

用割补的方法平滑曲面间的奇异交线

为了平滑曲面拼接中出现的奇点（或奇线），章提供一种割补法，即在奇线附近割去一小块曲面，同时补充一过渡曲面片，使曲面整体具有GC^1连续，并给出过渡曲面和原曲面接触程度和割补面积的计算方法。     

Easy cross parameterization for articulated shapes

This paper presents a novel interactive system for establishing compatible meshes for articulated shapes. Given two mesh surfaces, our system automatically generates both the global level component correspondence and the local level feature correspondence. Users can use some sketch-based tools to specify the correspondence in an intuitive and easy way. Then all the other vertex correspondences could be generated automatically. The cross parameterization preserves both high level and low level features of the shapes. The technique showed in the system benefits various applications in graphics including mesh inter- polation, deformation transfer, and texture transfer.     

Mesh parameterization based on edge collapse

Parameterizations that use mesh simplification to build the base domain always adopt the vertex removal scheme. This paper applies edge collapse to constructing the base domain instead. After inducing the parameterization of the original mesh over the base domain, new algorithms map the new vertices in the simplified mesh back to the original one according to the edge transition sequence to integrate the parameterization. We present a direct way, namely edge classification, to deduce the sequence. Experimental results show that the new parameterization features considerable saving in computing complexity and maintains smoothness.     

关于单形中线Veljan-Korchmaros型不等式稳定性版本的推广

本文利用单形的几何不等式理论和偏正度量,研究En中n维单形的稳定性,获得单形中线Veljan-Korch-maros型不等式稳定性版本的推广.