Rational ruled surfaces and their offsets

Helmut Pottmann*, Wei Lü, Bahram Ravani

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Scopus citations


In this paper, geometric design problems for rational ruled surfaces are studied. We investigate a line geometric control structure and its connection to the standard tensor product B-spline representation, the use of the Klein model of line space, and algorithms for geometry processing. The main part of the paper is devoted to both classical and "circular" offsets of rational ruled surfaces. These surfaces arise in NC milling. Excluding developable surfaces and, for circular offsets, certain conoidal ruled surfaces, we show that both offset types of rational ruled surfaces are rational. In particular, we describe simple tool paths which are rational quartics.

Original languageEnglish (US)
Pages (from-to)544-552
Number of pages9
JournalGraphical Models and Image Processing
Issue number6
StatePublished - Nov 1996
Externally publishedYes

Bibliographical note

Funding Information:
This work has been supported in part by the Austrian Science Foundation through Project P09790-MAT. The second author is grateful for a research fellowship by the Austrian Academic Exchange Service and acknowledges support from the Doctoral Science Foundation and National Defense Science Foundation of China.

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design


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