工业几何： 在CAD的最近前进和应用

中文字数:3337,   英文字数:1987

工业几何： 在CAD的最近前进和应用
H. Pottmanna， *， S. Leopoldsedera， M. Hofera， T. Steinera， W. Wangb维也纳科技大学， Wiedner Hauptstr。 8-10/104， 1040年Wien，奥地利香港， Yei Ching Bldg， Pokfulam Rd，香港，中国大学 接受2004年8月11日

 摘要
工业几何为了统一各种各样的应用范围的现有的和开发的新的方法和算法与强几何组分。 这些包括CAD， CAM，几何模拟，电脑图形图像学，计算机视觉和图象处理，计算机图表形象化。 在这篇论文中，工业几何通过被表明区域的卓有成效的互相作用来说明以上 CAD的新颖的解决方法与上下文关连，涉及距离函数的几何优化问题：逼近与一般B样条曲线曲面或细分曲面，适用于建筑或制造的特别表面的近似值，从含蓄的近似转换为参数(NURBS)表示法和工业的注册问题检查和三维模型生成测量数据。 而且，我们描述一个“功能敏感”度量的表面，其定义依赖于图像流形的概念，由Kimmel，Malladi和Sochen引入计算机视觉和图像处理中。这个度量具有敏感的特点，如平滑的边缘，其特点是一个重大偏差的两个主曲率。我们在表面敏感曲线设计的一方面说明其应用，并且把当地社区的定义和区域增长作为一项援助分割进程逆向工程的几何对象。2004 Elsevier年有限公司。 版权所有。关键字 ： 几何优化; 距离函数; 曲线略计; 表面略计; 活跃等高; 注册; 特点敏感性;

Industrial geometry: recent advances and applications in CAD
     H. Pottmanna,*, S. Leopoldsedera, M. Hofera, T. Steinera, W. Wangb
a Vienna University of Technology, Wiedner Hauptstr. 8-10/104, 1040 Wien, Austria
b University of Hong Kong, 421 Chow Yei Ching Bldg, Pokfulam Rd, Hong Kong, China
Accepted 11 August 2004

Abstract
   Industrial Geometry aims at unifying existing and developing new methods and algorithms for a variety of application areas with a strong geometric component. These include CAD, CAM, Geometric Modelling, Robotics, Computer Vision and Image Processing, Computer Graphics and Scientific Visualization. In this paper, Industrial Geometry is illustrated via the fruitful interplay of the areas indicated above in the context of novel solutions of CAD related, geometric optimization problems involving distance functions: approximation with general B-spline curves and surfaces or with subdivision surfaces, approximation with special surfaces for applications in architecture or manufacturing, approximate conversion from implicit to parametric (NURBS) representation, and registration problems for industrial inspection and 3D model generation from measurement data. Moreover, we describe a ‘feature sensitive’ metric on surfaces, whose definition relies on the concept of an image manifold, introduced into Computer Vision and Image Processing by Kimmel, Malladi and Sochen. This metric is sensitive to features such as smoothed edges, which are characterized by a significant deviation of the two principal curvatures. We illustrate its applications at hand of feature sensitive curve design on surfaces and local neighborhood definition and region growing as an aid in the segmentation process for reverse engineering of geometric objects.  2004 Elsevier Ltd. All rights reserved.
Keywords: Geometric optimization; Distance function; Curve approximation; Surface approximation; Active contours; Registration; Feature sensitivity;
Mathematical morphology