Algorithms to support point-based cadcam

This paper presents a system that supports a point-based approach to CADCAM that was first suggested by McLaughlin. The core to the approach is the ability to interpolate a grid of points in a geometrically meaningful way that does not suffer from the disadvantages of the standard interpolation schemes based on NURBS. The essential features of the approach are based on recursive subdivision between existing points to generate intermediate points that are consistent with a smooth curvature profile. There are many advantages to this approach. Time-consuming surface fitting is not necessary; there are no problems with ensuring continuity between surfaces; data exchange can be carried out exactly. By chosing to work entirely with points, all of the standard interrogations available in CAE systems, including visualisations, FE analysis and NC machining, which are dependent on NURBS curves and surfaces have to be replicated. The feasibility of the point-based approach is illustrated by showing how geometric interrogations and machine tool paths can be accurately generated using just points.     

Semi‐Regular Triangle Remeshing: A Comprehensive Study

Semi‐regular triangle remeshing algorithms convert irregular surface meshes into semi‐regular ones. Especially in the field of computer graphics, semi‐regularity is an interesting property because it makes meshes highly suitable for multi‐resolution analysis. In this paper, we survey the numerous remeshing algorithms that have been developed over the past two decades. We propose different classifications to give new and comprehensible insights into both existing methods and issues. We describe how considerable obstacles have already been overcome, and discuss promising perspectives.     

基于球面三角剖分与"距离-星等"加权的导航星表构建方法

针对球矩形法剖分所得网格单元面积不均,且局部相邻网格所选导航星距离较近的问题,提出了一种基于球面三角剖分的导航星表构建方法.该方法采用三角网格代替赤经赤纬网格,使得网格单元面积近似相等,通过引入"距离-星等"加权,改善了局部相邻网格间导航星较近的问题.仿真结果表明:采用本方法所构建的导航星表在完备性没有降低的情况下,存储量小,均匀性好,体现了本方法的有效性.     

快速视差范围估计算法及其应用

视差范围估计在立体匹配中非常重要,准确的视差范围能提高立体匹配的精度和速度.为此提出一种基于匹配代价搜索和图像细分的快速视差范围估计算法.该算法将输入图像均匀分成多个图像块,采用匹配代价搜索计算每一图像块的视差,找到视差最大(最小)的图像块,并利用迭代细分规则将该图像块继续分成更小的子块,直至得到稳定的最大(最小)视差;利用匹配代价图对图像块进行可靠性检测,以解决弱纹理块容易误匹配的问题.实验结果表明,文中算法在保持97.3%的平均命中率的同时将立体匹配的平均搜索空间降低了27.7%,比采用传统算法可以得到更准确的视差范围;将该算法应用于立体匹配算法中降低了其平均误匹配率,并将计算时间缩短了20%~45%.     

基于插值细分的逼近细分法

通过在Hassan的四点三重插值细分法中引入一个偏移变量,推导出了一种逼近细分法,从而使三重逼近细分和插值细分统一到一个细分格式.该方法利用细分格式的生成多项式,在理论上分析了提出的细分格式的一致收敛性和Ck连续性;通过对细分格式中参数u取不同的值,可对生成的极限曲线形状进行控制.数值实验结果表明,文中方法是合理有效的.     

多边形三角剖分与三角细分的研究与实现

多边形是构成三维模型表面的基本元素,多边形的三角剖分及三角形的三角细分是计算机三维快速建模及纹理帖图的基本技术。本文在研究平面多边形的三角剖分及其三角网格化相关理论的基础上,利用面向对象技术及递归程序设计方法,实现多边形的三角剖分及其三角细分的算法设计,并对该算法的执行效率进行分析。实验结果表明,该算法具有较高的运算效率及实用价值,对实际应用有较好的参考作用。     

Point-augmented biquadratic C1 subdivision surfaces

Shape artifacts, especially for convex input polyhedra, make Doo and Sabin’s generalization of bi-quadratic (bi-2) subdivision surfaces unattractive for general design. Rather than tuning the eigenstructure of the subdivision matrix, we improve shape by adding a point and enriching the refinement rules. Adding a guiding point can also yield a polar bi-2 subdivision algorithm. Both the augmented and the polar bi-2 subdivision are complemented by a new Primal Bi-2 Subdivision scheme. All surfaces are $C^1$ and can be combined.     

改进三棱柱体剖分算法研究

针对现有矿山储量计算方法计算结果精度低以及边界条件适应能力差的问题,提出了改进三棱柱体剖分算法:结合改进三棱柱顶面、底面及三角形切割截面,按不同规则将三棱柱体剖分为不同的三角锥;根据边界控制条件得到储量范围,结合地质统计学,计算控制范围内所有改进三棱柱体的体积及储量。     

Generating planar spiral by geometry driven subdivision scheme

Spirals are curves with one-signed, monotone increasing or decreasing curvature. They are commonly useful in a variety of applications, either for aesthetic or for engineering requirements. In this paper we propose a new iterative subdivision scheme for generating planar spiral segments from two points and their tangent vectors. The subdivision process consists of two main steps, computing new points and adjusting tangent vectors adaptively for each iteration. We categorize this iterative scheme as geometry...