Approximation of NURBS Curves and Surfaces Using Adaptive Equidistant Parameterlzatlons

Non-uniform rational B-spline (NURBS) curves and surfaces are very important tools for modelling curves and surfaces. Several important details, such as the choice of the sample points, of the parameterization, and of the termination condition, are however not well described. These details have a great influence on the performance of the approximation algorithm, both in terms of quality as well as time and space usage. This paper described how to sample points, examining two standard parameterizations: equidistant and chordal. A new and local parameterization, namely an adaptive equidistant model, was proposed, which enhances the equidistant model, Localization can also be used to enhance the chordal parameterizatfon, For NURBS surfaces, one must choose which direction will be approximated first and must pay special attention to surfaces of degree 1 which have to be handled as a special case.     

An approach to 3D NURBS modeling of complex fault network considering its historic tectonics

Fault disposal is a research area that presents difficulties in 3D geological modeling and visualization. In this paper, we propose an integrated approach to reconstructing a complex fault network (CFN). Based on the non-uniform rational B-spline (NURBS) techniques, fault surface was constructed, reflecting the regulation of its spatial tendency, and correlative surfaces were enclosed to form a fault body model. Based on these models and considering their historic tectonics, a method was put forward to settle the 3D modeling problem when the intersection of two faults in CFN induced the change of their relative positions. First, according to the relationships of intersection obtained from geological interpretation, we introduced the topological sort to determine the order of fault body construction and rebuilt fault bodies in terms of the order; then, with the disposal method of two intersectant faults in 3D modeling and applying the Boolean operation, we investigated the characteristic of faults at the intersectant part. An example of its application in hydropower engineering project was proposed. Its results show that this modeling approach can increase the computing efficiency while less computer memory is required, and it can also factually and objectively reproduce the CFN in the engineering region, which establishes a theoretical basis for 3D modeling and analysis of complex engineering geology.     

基于三次NURBS的椭圆弧的实用方法

圆弧的表示一直是计算机辅助几何设计关心的问题,而圆弧仅是椭圆的特例。现有的方法对于椭圆弧的表示并未进行深入的研究。本文给出的三次NURBS表示大于180度椭圆弧的实用方法,克服了三次有理Bezier曲线只能表示不超过240度的椭圆弧的条件。该方法给出的控制顶点和权因子的计算结果。符合对椭圆弧NURBS表示的要求,为工程应用NURBS表示椭圆弧曲线提供了方便。     

虚拟技术在立体构成中的应用

计算机虚拟技术帮助艺术家，设计家实现多年的夙愿－模拟任何构成物体和场景，臆造所有造型细节，作为设计基础之一的立体构成，在虚拟环境下进行训练与制作，可以全真地再现各种形态的视觉效果，改变了传统方法，节省了材料和时间，从虚拟造型等三个方面阐述了应用的手段和步骤，得出了突破局限，开创新纪元的结论。     

五轴联动刀具路径NURBS插补技术

针对复杂曲面五轴加工直线圆弧插补的不足,对五轴加工NURBS插补算法进行相关研究,同时对NURBS插补过程中插补点的曲率分析计算,推导出插补误差与进给速度的关系,实现用进给速度对插补误差自适应地调整。最后,针对双转台五轴数控机床,基于IMSPOST开发了具有NURBS插补的专用后置处理器,实现了NC 程序的输出。实验结果表明：该技术方法提高了刀具运动平稳性和加工精度,优化了加工精度与加工效率,为五轴NURBS插补加工提供了理论指导。     

曲面造型的动态设计研究

研究了曲面造型技术及基于物理定律的动态造型方法.     

Rhino中NURBS曲线的探讨

NURBS曲线在CAD软件开发中被广泛应用。Rhino软件中的NURBS曲线,涉及到NURBS曲线的构成元素、属性、关键定义项目、缺陷和用NURBS曲线构建曲面,对于进行工业产品造型设计有着较强的现实意义。     

STL切片数据的NURBS曲线拟合算法

在快速成形加工过程中，由于对STL文件切片所得数据是由极不均匀的细微离散线段序列组成，为提高制件加工速度和精度，必须对切片数据进行重新拟合处理，为简化后续插补处理，不适宜采用抛物线、双曲线、B样条等标准圆锥曲线及不规则参数等多种类型组合曲线拟合，基于此，提出了一种合适于STL文件切片数据的二次NURBS曲线拟合算法，以便对于标准曲线和自由曲线提供统一的表达式。     

用二次NURBS作曲线插值

对于给定的曲线型值点及端点切向量，本文利用二次ＮＵＲＢＳ曲线的矩阵表达式，给出了一个反求二次ＮＵＲＢＳ曲线控制顶点的算法，并且证明了所求控制顶点的存在唯一性。     

非均匀B样条曲线的快速显示算法与实现

本文应用数据结构的思想,讨论在计算机上快速实现非均匀Ｂ样条曲线的显示及节点插入,该算法具有快速,稳定和高效率等优点。