Approximation with active B-spline curves and surfaces

Helmut Pottmann, Stefan Leopoldseder, Michael Hofer

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

101 Scopus citations


An active contour model for parametric curve and surface approximation is presented. The active curve or surface adapts to the model shape to be approximated in an optimization algorithm. The quasi-Newton optimization procedure in each iteration step minimizes a quadratic function which is built up with the help of local quadratic approximants of the squared distance function of the model shape and an internal energy which has a smoothing and regularization effect. The approach completely avoids the parametrization problem. We also show how to use a similar strategy for the solution of variational problems for curves on surfaces. Examples are the geodesic path connecting two points on a surface and interpolating or approximating spline curves on surfaces. Finally we indicate how the latter topic leads to the variational design of smooth motions which interpolate or approximate given positions.

Original languageEnglish (US)
Title of host publicationProceedings - 10th Pacific Conference on Computer Graphics and Applications, PG 2002
EditorsShi-Min Hu, Heung-Yeung Shum, Sabine Coquillart
PublisherIEEE Computer Society
Number of pages18
ISBN (Electronic)0769517846
StatePublished - 2002
Externally publishedYes
Event10th Pacific Conference on Computer Graphics and Applications, PG 2002 - Beijing, China
Duration: Oct 9 2002Oct 11 2002

Publication series

NameProceedings - Pacific Conference on Computer Graphics and Applications
ISSN (Print)1550-4085


Other10th Pacific Conference on Computer Graphics and Applications, PG 2002

Bibliographical note

Publisher Copyright:
© 2002 IEEE.


  • Active contours
  • Application software
  • Character generation
  • Computer vision
  • Geometry
  • Least squares approximation
  • Parameter estimation
  • Polynomials
  • Smoothing methods
  • Spline

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design
  • Modeling and Simulation


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