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
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