Bezier三角曲面的分割及求交计算

本文通过对Ｂｅｚｉｅｒ三角曲面分割算法的分析研究，较系统地讨论了Ｂｅｚｉｅｒ三角曲面在分割和平面三角法近似过程中的不连续问题。提出了判别断层不协调点的相关角准则和相应处理方法。根据Ｂｅｚｉｅｒ三角曲面的良好分割性质，本文还讨论了Ｂｅｚｉｅｒ三角曲面的几何求交、裁剪等问题。     

散乱数据曲面造型的凸组合Bezier三角曲面片插值方法

本文讨论了在计算机辅助设计和计算机图形学的散乱数据曲面造型中一种有效的凸组合Ｂｅｚｉｅｒ三角曲面片插值方法。构造曲面的方法是对三角剖分的每一条边,得到一个插值已知条件的５次Ｂｅｚｉｅｒ三角曲面片,它与共此边的相邻５次Ｂｅｚｉｅｒ三角曲面片满足Ｃ＾２连续条件,然后对三角剖分的每一个三角形,将三边对应的Ｂｅｚｉｅｒ三角曲面片作凸组合,使之仍然插值已知条件并满足Ｃ＾２连续条件,从数值例子看,效果是不错的     

Bezier曲面的函数复合及其应用

目前有两种常用的Ｂｅｚｉｅｒ曲面片,分别称为三角和四边Ｂｅｚｉｅｒ曲面片,它们分别用不同的基函数表示,本通过移位算子和函数复合的方法,得到了两个关于这两种Ｂｅｚｉｅｒ曲面片的结果,一个是四边Ｂｅｚｉｅｒ曲面片与一次三角Ｂｅｚｉｅｒ函数的复合,另一个是三角Ｂｅｚｉｅｒ曲面片与双线性四边Ｂｅｚｉｅｒ函数的复合,在第一种情况中,复合所得到的Ｂｅｚｉｅｒ曲面片的控制顶点ｅｚｉｅｒ曲面片的控制顶点拇性组合     

NURBS曲面的有限元网格三角划分

主要介绍一种ＮＵＲＢＳ曲面的有限元网格三角剖分算法，首先讨论ＮＵＲＢＳ曲面的离散算法，接着在此基础上，提出了利用网格前沿技术剖分ＮＵＲＢＳ曲面的算法，并且网格单元和结点同时生成。     

NURBS曲面的有限元网格三角剖分

主要介绍一种ＮＵＲＢＳ曲面的有限元网格三角剖分算法。首先讨论ＮＵＲＢＳ曲面的离散算法，接着在此基础上，提出了利用网格前沿技术剖分ＮＵＲＢＳ曲面的算法，并且网格单元和结点同时生成     

实现3D离散点优化三角划分的三维算法

本文系统研究了３Ｄ离散数据的直接三角划分，并解决了与多值曲面相对应离散数据的分片三角划分问题。实现这一算法的关键是将这些与多值曲面相对应的离散数据按有关的特征线分解，慢之转化成较简单的问题分别进行处理。目前，这种分片三角划分算法已在Ｂｅｚｉｅｒ三角曲面插值中取得了良好的效果。     

二元三方向样条曲面的快速显示算法与实现

本文应用Ｂ网分裂加密的思想，讨论在计算机上快速实现二元三方向网格上三角域样条曲面的显示。该算法具有快速、稳定和高效率等优点，可用于相应的曲面设计与曲面求交。     

可展Bézier参数曲面

给出B啨ｚｉｅｒ参数曲面可展的特征 这里的B啨ｚｉｅｒ参数曲面包括三角域上的Ｂ B参数曲面和矩形域上的张量积B啨ｚｉｅｒ参数曲面 特别地 ,给出了三角域上可展二次B B参数曲面的具体形式及其构造方法 ,以及三角域上可展三次B B参数曲面为切线面的一种特例     

关于空间三角网格上G1插值的阶数

本文给出在空间三角网格上用三角Ｂｅ’ｚｉｅｒ曲面构造Ｇ１插值所需的最低次数，并给出五次Ｇ１插值的具体构造方法．     

NURBS曲线和曲面的递推矩阵及其应用

本文运用Ｔｏｅｐｌｉｔｚ矩阵，导出了任意非均匀Ｂ样条的递推矩阵公式；提出了一个计算非均匀Ｂ样条基矩阵的新方法，该递推矩阵公式即可以用于ＮＵＲＢＳ曲线和曲面的分析计算，也可以用于Ｂｅｚｉｅｒ，均匀和非均匀Ｂ样条曲线及曲面的分析计算。     

Progressive surface modelling scheme from unorganised curves

This paper presents a novel surface modelling scheme to construct a freeform surface progressively from unorganised curves representing the boundary and interior characteristic curves. The approach can construct a base surface model from four ordinary or composite boundary curves and support incremental surface updating from interior characteristic curves, some of which may not be on the final surface. The base surface is first constructed as a regular Coons surface and upon receiving an interior curve sketch, it is updated. With this progressive modelling scheme, a final surface with multiple sub-surfaces can be obtained from a set of unorganised curves and transferred to commercial surface modelling software for detailed modification. The approach has been tested with examples based on 3D motion sketches; it is capable of dealing with unorganised design curves for surface modelling in conceptual design. Its limitations have been discussed.     

一类三次隐式代数曲面参数化研究

在CAGD中隐式曲面和参数曲面作为曲面的两种表示形式各有其内在的优点 ,多年来如何有效地实现二者的相互转换一直是CAGD的一个热点问题 对一类GC1拼接两个二次曲面的三次混合代数曲面进行了研究 ,提出一种基于同轴平面束与代数曲面相交的几何化参数化方法 与传统参数化方法相比 ,该方法结构直观且具有可使三次代数曲面位于 [0 ,1]× [0 ,1]参数区间内 ,以及曲面的边界位于等参数线上等特点 ,利用这种参数曲面可以方便地实现机器作图和各种操作 实验结果验证了方法的有效性     

一类极小曲面的几何设计

极小曲面是变分学意义下具有极小面积的曲面。它能量最小、结构稳定的优点。形如马鞍的负高斯曲率的极小曲面可作为房顶曲面的设计模型。由负高斯曲率的极小曲面设计得到房顶曲面不但外形美观,而且牢固经济。该文提出一种几何构造法,得到了一类三次多项式形式的负高斯曲率极小曲面,将其表示为三次Ｂ－Ｂ曲面,进而高次Ｂ－Ｂ曲面表示出负高斯曲率极小曲面的裁剪曲面以增加设计的灵活性。算法给出一个可变参数,通过调整该参数可改     

Intersecting a freeform surface with a general swept surface

We present efficient and robust algorithms for intersecting a rational parametric freeform surface with a general swept surface. A swept surface is given as a one-parameter family of cross-sectional curves. By computing the intersection between a freeform surface and each cross-sectional curve in the family, we can solve the intersection problem. We propose two approaches, which are closely related to each other. The first approach detects certain critical points on the intersection curve, and then connects them in a correct topology. The second approach converts the intersection problem to that of finding the zero-set of polynomial equations in the parameter space. We first present these algorithms for the special case of intersecting a freeform surface with a ruled surface or a ringed surface. We then consider the intersection with a general swept surface, where each cross-sectional curve may be defined as a rational parametric curve or as an implicit algebraic curve.     

基于轮廓数据的B样条曲面重建

针对B样条曲面拟合中出现的问题和困难,提出了一种基于行组织的轮廓数据（截面数据）的曲面重建方法。该方法避免了数据点的参数化问题,使得逼近曲面拥有较好的形状和合理的控制顶点数量。该方法的基本思想是：首先构造易于控制的低阶曲面拟合数据点,此曲面称控制曲面,然后利用高次曲面逼近该曲面,此高次曲面称为逼近曲面,为所需要的重建曲面。在曲面重建中利用最佳平方逼近和光顺函数,减少了逼近曲面的控制顶点冗余,较有效地防止了逼近曲面的形状突变和曲面的扭曲,很大程度地提高了曲面的质量。     

切片级管线表面三维重建

在比较表面重建中的面绘制法和体绘制法以及面绘制中的切片级和体素级两种表面重建方法、分析表面重建流程的基础上,提出了一种计算型值点集的方法,它在计算弯道部分的管线时较为简便。该方法通过二次曲面求管线表面轮廓方程进而求得管线的型值点集。之后用三角网格对型值点集进行拼接来获得管线的表面模型,最后利用图形学的方法对管线表面模型进行绘制,达到管线表面三维重建的目的。文末利用Java3D给出了一个具体的实现。     

The effect of surface waviness on friction between Neolite and quarry tiles

Friction is widely used as an indicator of surface slipperiness in preventing accidents in slips and falls. Surface texture affects friction, but it is not clear which surface characteristics are better correlated with friction. Highly correlated surface characteristics could be used as potential interventions to prevent slip and fall accidents. The dynamic friction between quarry tiles and a commonly used sole testing material, Neolite, using three different mixtures of glycerol and water as contaminants at the interface was correlated with the surface parameters of the tile surfaces. The surface texture was quantified with various surface roughness and surface waviness parameters using three different cut-off lengths to filter the measured profiles for obtaining the profiles of either surface roughness or surface waviness. The correlation coefficients between the surface parameters and the measured friction were affected by the glycerol contents and cut-off lengths. Surface waviness parameters could potentially be better indicators of friction than commonly used surface roughness parameters, especially when they were measured with commonly used cut-off lengths or when the viscosity of the liquid contaminant was high.     

基于高斯映射下自由曲面的形状分析及边界计算

测定单一类型（凸或马鞍）区域和计算其边界是进行自由曲面的形状分析与控制研究的基本内容之一．目前这方面的研究局限于一些特殊曲面，如可展曲面，对自由曲面则无来境的理论和方法．本文提出了一些对复杂自由曲面进行形状分析的几何结论．通过计算高斯抛物线，划分了曲面的单类型区域．设计了算法判断单类型区域、分离单类型区域，并计算其边界，对自由曲面整体的形状有了较好的把握．最后蛤出了算法对两个例子的计算结果．     

成都市地表温度对不透水面的响应研究

根据成都三环路内的Landsat 7/ETM+影像,利用单窗算法和不透水面与植被覆盖度在城市建成区呈负相关关系两种反演方法,通过空间建模建立反演模型,获取地表温度与不透水面信息。通过随机样点分析、相关性分析以及等温线与等透水面线叠加分析等方法,研究了城市地表温度对不透水面的响应效果。结果表明:地表温度随距市中心区距离增大而降低,同时不透水能力也降低;成都市地表温度与不透水面之间存在着正相关关系,相关度为0.7253;等透水面线的空间分布对等温线具有显著的响应规律。研究成果对于改善城市生态环境、提升土地利用水平和加强科学规划等都具有参考价值。     

A two-level approach to implicit surface modeling with compactly supported radial basis functions

We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear combination of compactly supported radial basis functions (CSRBFs). The method preserves the simplicity and efficiency of implicit surface interpolation with CSRBFs and the reconstructed implicit surface owns the attributes, which are previously only associated with globally supported or globally regularized radial basis functions, such as exhibiting less extra zero-level sets, suitable for inside and outside tests. First, in the coarse scale approximation, we choose basis function centers on a grid that covers the enlarged bounding box of the given point set and compute their signed distances to the underlying surface using local quadratic approximations of the nearest surface points. Then a fitting to the residual errors on the surface points and additional off-surface points is performed with fine scale basis functions. The final function is the sum of the two intermediate functions and is a good approximation of the signed distance field to the surface in the bounding box. Examples of surface reconstruction and set operations between shapes are provided.