自由曲面的平面映射原理及其算法

论述空间曲面的平面映射定义及其变形；分析了空间曲面的几种近似映射方法，并同时分析了各种映射方法的优缺点；针对在空间曲面应用最广泛的NURBS曲面，提出了NURBS曲面的混合映射算法；讨论了小曲率NURBS曲面平面映射的算法，并将该算法成功地应用于花纹鞋模的设计中。     

插值边界曲线的NURBS 近似极小曲面设计

探索性地设计了一个插值给定边界曲线的NURBS 近似极小曲面算法,弥补了当前NURBS 系统无法有效地设计工程所急需的一般NURBS 极小曲面的缺陷.运用NURBS 曲面的节点插入、Hybrid 多项式逼近等多种技术,将NURBS 曲面转化为相对简单的分片Bézier 曲面求解,并运用各子曲面片的控制顶点优化、整体曲面不断更新的迭代方法,成功地得到高精度的近似分片Bézier 极小曲面.最后,可以按用户的各种要求选择运用相应不同的迭代逼近算法,求取插值给定边界曲线的近似NURBS 极小曲面.     

NURBS曲面的可控修形及构造工程曲面的研究

本文研究了NURBS曲面的可控修形及其构造工程曲面，通过修改控制网格的顶点，反插节点，重新确定权因子，可快速得到所期望的NURBS曲面的状态，构造出复杂工程曲面的数学模型，此研究是用C语言实现其算法的。     

NURBS边界曲面直接生成法

由于非均匀有理B样条(NURBS)曲面的复杂性,传统NURBS边界曲面的生成是先构造孔斯曲面,再由孔斯曲面向NURBS曲面转换得到,其操作过程比较烦琐。针对此问题,提出了NURBS边界曲面直接生成算法,该算法根据给定的四条NURBS边界曲线,结合孔斯曲面生成方法直接插值生成NURBS曲面,从而避免了通过孔斯曲面向NURBS曲面转换所带来的计算代价,因此同传统方法相比,具有较低的计算代价。实验结果表明:该算法简化了曲面生成步骤,减少了曲面转换过程的计算量,生成的曲面边界信息明确,且连续性好。     

一种NURBS曲面拟合精度的量化评测算法

曲面重构是逆向工程中的核心技术之一,由于NURBS曲面在光顺性和局部可编辑等方面所具有的优点,使其成为点云数据自由曲面重构的常见形式。目前对NURBS曲面重构技术的研究上取得了一些成果,但各方法在拟合精度和效果上各有参差,因此有必要对NURBS曲面拟合精度评价算法进行研究。在采用NURBS实现曲面拟合的基础上,对拟合精度的量化指标进行研究,设计了一种基于区域划分的搜索迭代算法,可快速地计算得到原始点云与NURBS曲面的偏差。     

基于蚁群的数据点NURBS曲面快速拟合研究

研究数据点的NURBS曲面拟合问题,提高拟合速率。针对所要拟合的数据点分布散乱,传统的基于遗传算法多次迭代,造成曲面拟合速率不高的问题。为解决上述问题,提出一种基于蚁群的数据点NURBS曲面拟合算法。通过采用蚁群寻址算法搜索出控制顶点和边界数据点集,计算曲面的权因子后完成NURBS曲面的拟合,并使用蚁群算法对拟合曲面进行优化,避免了传统方法多代遗传迭代造成的拟合速率不高的问题。实验表明,这种方法能够快速完成散乱数据点的NURBS曲面拟合,并且具有一定的拟合效率,取得了满意的结果。     

等距曲面的NURBS放样插值方法

本文给出了等距曲面的一种NURBS放样插值生成方法，该方法主要是在原始NURBS曲面上取得一个能较好反映曲面特征的型值点阵，再交这个型值点阵按某种算法矢方向外推，从而得到原始曲面的等距曲面上的型值点阵，然后，再用NURBS放样插值曲面来逼近等距曲面，本文给出的算法几何意义明显，易于编程实现，且得到的等距曲面其u向和v向参数曲线仍是NURBS曲线，且具有C^2连续性，最后，给出了一个实例。     

NURBS曲面生成算法及仿真研究

讨论了一种生成NURBS曲面的算法,用C语言实现了该算法,并利用MATLAB进行仿真对该算法进行验证。在算法中讨论了曲面及其等距面生成方法以及曲面生成技术中相关的一些技术,如曲线段间参数过渡、曲面生成模式、曲面生成的实时性、改变曲面的形状等。仿真结果证明了算法的有效性。     

一种跟踪隐式曲面交线的算法*

传统的跟踪方法在求下一个跟踪点时一般是采用迭代法,而迭代法会出现初始值的选取和迭代收敛的问题。为此提出一种跟踪隐式曲面交线的算法。该方法最主要的优点是：在跟踪隐式曲面的交线时,在前一个跟踪交点已经求得的情况下,利用正方形与两个隐式曲面的交点,即可快速有效地求出下一个跟踪点,而不用涉及迭代收敛的判断。     

双三次NURBS曲面矩阵块表示及在曲面设计中的应用

研究了NURBS三次与二次曲面的矩阵块表示及在曲面设计中的应用。给出了NURBS三次与二次基函数系数矩阵表示和NURBS三次曲面矩阵块表示。从矩阵块表示中可很清楚地看出参数区间、曲面片与控制顶点对应关系,这点对NURBS曲面自由变形与求解都很重要。通过在Java2．0与Java3D环境下检验证明该算法高效可靠。     

隐式曲面／参数曲面的求交算法

本文介绍了一种实用有效的隐式曲面／参数曲面求交算法。算法主要分为两部分：特征初始点的求取和单调段的跟踪。解双变量多项式方程求解特征初始点。跟踪在三维空间进行，易于控制跟踪步长和离散交点对交线的逼近精度。算法不离散参数曲面，不漏交。     

一种改进的基于微分方程的曲面求交跟踪算法

参数曲面求交是计算机辅助几何设计领域中的关键技术之一。针对传统跟踪算法 中曲面求交的漏交和法向共线点处难于处理的问题,提出一种改进的基于微分方程的跟踪算法。 首先选择边界点和拐点作为跟踪的起点,解决了漏交问题。并采用基于交线微分形式的跟踪公 式计算后继交点,解决了法向共线点处难于处理的问题。最后利用牛顿迭代得到精确交点。该 算法不仅正确地跟踪到交线的每个分支,而且易于处理法向共线点处的跟踪,不遗漏关键点, 解决了传统跟踪法在法向共线点处交线不连续的问题。与传统跟踪法对比,其鲁棒性和稳定性 更强,精度更高且收敛略快,适用于求解任意参数曲面求交问题。     

直线与刀具扫描体求交算法及其应用研究

直线与刀具扫描体的交点问题是数控图形验证，加工过程仿真技术中的核心问题，本文根据五坐标联动机床的运动特点，把刀具扫描体表达成几组简单曲面的组合，利用直线与这几类曲交点来求解直线与刀具扫描体的交点。利用该算法，我们开发了一个用于检验五坐标铣削加工精度的计算机领导具软件。加工与仿真的实践证明，该算法计算正确正确，对进一步研制开发加工过程仿真系统有重要意义。     

Fast Ray Tracing NURBS Surfaces

In this paper,a new algorithm wit extrapolation process for computing the ray/surface intersection is presented.Also,a ray is defined to be the intersection of two planes,which are non-orthogonal in general,in such a way that the number of multiplication operations is reduced.In the preprocessing step,NURBS surfaces are subdivded adaptively into rational Bezier patches.Parallelepipeds are used to enclose the respective patches as tightly as possible Therefore,for each ray that hits the enclosure(i.e.,parallelepiped)of a patch the intersection points with the parallelepiped‘s faces can be used to yield a good starting point for the following iteration.The improved Newton iteration with extrapolation process saves CPU time by reducing the number of iteration steps.The intersection scheme is facter than previous methods for which published performance data allow reliable comparison.The method may also be used to speed up tracing the intersection of two parametric surfaces and oter operations that need Newton iteration.     

An intersection algorithm based on Delaunay triangulation

A robust method for finding points of intersection of line segments in a 2-D plane is presented. The plane is subdivided by Delaunay triangulation to localize areas where points of intersection exist and to guarantee the topological consistency of the resulting arrangement. The subdivision is refined by inserting midpoints recursively until the areas containing points of intersection are sufficiently localized. The method is robust in the sense that it does not miss points of intersection that are easily detectable when costly line-pair checking is performed. The algorithm is adaptive in the sense that most of the computational cost is incurred for the areas where finding points of intersection is difficult     

A Z-map update method for linearly moving tools

In numerically controlled (NC) machining simulation, a Z-map has been frequently used for representing the workpiece. Since the Z-map is usually represented by a set of z-axis aligned vectors, the machining process can be simulated through calculating the intersection points between the vectors and the surface swept by a machining tool. In this paper, we present an efficient method to calculate those intersection points when automatically programmed tool-type tools move along a linear tool path. Each of the intersection points can be expressed as the solution of a system of non-linear equations. We transform this system of equations into a single-variable equation, and calculate the candidate interval in which the unique solution exists. We prove the existence of a solution and its uniqueness in this candidate interval. Based on these properties, we can effectively apply numerical methods to finally calculate the solution of the non-linear equations within a given precision. The whole process of NC simulation is achieved by updating the Z-map properly. Our method can improve accuracy greatly while increasing processing time negligibly in comparison with previous Z-map update methods, making it possible to verify the tool path more accurately and reliably.     

A Tracing Algorithm for Surface-Surface Intersections on Surface Boundaries

In this paper we present an algorithm with a new trace-terminating condition for tracing along surface-surface intersection curves on surface boundaries,while several tracing methods and embedding methods that include tracing scheme may cause false termination with a traditional trace-terminating condition:tracing stops when the surface-domain‘s boundary is reached.And we also suggest another iterative method to calculate intersection points on surface boundaries with parallel surface normal.Some numerical examnples with these two ideas and comparisons to ‘DESIGNBASE‘,ACIS,and Parasolid are included to demonstrate the effectiveness of our algorithm.     

Theoretically-based algorithms for robustly tracking intersection curves of deforming surfaces

This paper applies singularity theory of mappings of surfaces to 3-space and the generic transitions occurring in their deformations to develop algorithms for continuously and robustly tracking the intersection curves of two deforming parametric spline surfaces, when the deformation is represented as a family of generalized offset surfaces. The set of intersection curves of two deforming surfaces over all time is formulated as an implicit 2-manifold I in an augmented (by time domain) parametric space R⁵. Hyperplanes corresponding to some fixed time instants may touchI at some isolated transition points, which delineate transition events, i.e. the topological changes to the intersection curves. These transition points are the 0-dimensional solution to a rational system of five constraints in five variables, and can be computed efficiently and robustly with a rational constraint solver using subdivision and hyper-tangent bounding cones. The actual transition events are computed by contouring the local osculating paraboloids. Away from any transition points, the intersection curves do not change topology and evolve according to a simple evolution vector field that is constructed in the Euclidean space in which the surfaces are embedded.     

DETECTING AND DETERMINING THE CHARACTERISTIC POINTS ON THE SURFACE／SURFACE INTERSECTIONS

ＤＥＴＥＣＴＩＮＧＡＮＤＤＥＴＥＲＭＩＮＩＮＧＴＨＥＣＨＡＲＡＣＴＥＲＩＳＴＩＣＰＯＩＮＴＳＯＮＴＨＥＳＵＲＦＡＣＥ／ＳＵＲＦＡＣＥＩＮＴＥＲＳＥＣＴＩＯＮＳＺｅｎｇＸｉａｎｇｌｉｎ；ＷａｎｇＱｉｆｕ；ＨｕａｎｇＺｈｅｎｇｄｏｎｇ；ＺｈｏｕＪｉＤＥＴ...     

基于活动仿射标架反求Nurbs曲线/曲面参数

Nurbs曲线/曲面在反求参数上的数值不稳定性,是Nurbs曲线/曲面的致命缺点.该文介绍了用于参数曲线/曲面求交的活动仿射标架(moving affine frame,简称MAF)方法.基于MAF方法的原理,提出了反求Nurbs曲线/曲面参数的一种新方法.该方法在数值稳定性和效率上均高于各种传统的迭代法,并已应用于商品化三维CAD系统GEMS 5.0.