Industrial geometry: Recent advances and applications in CAD

Helmut Pottmann*, S. Leopoldseder, M. Hofer, T. Steiner, W. Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)751-766
Number of pages16
JournalCAD Computer Aided Design
Volume37
Issue number7
DOIs
StatePublished - Jun 1 2005

Keywords

  • Active contours
  • Curve approximation
  • Distance function
  • Feature sensitivity
  • Geometric optimization
  • Mathematical morphology
  • Registration
  • Surface approximation

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

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