C1 spline implicitization of planar curves

Mohamed Shalaby, Bert Jüttler, Josef Schicho

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

4 Scopus citations


We present a new method for constructing a low degree C1 implicit spline representation of a given parametric planar curve. To ensure the low degree condition, quadratic B-splines are used to approximate the given curve via orthogonal projection in Sobolev spaces. Adaptive knot removal, which is based on spline wavelets, is used to reduce the number of segments. The spline segments are implicitized. After multiplying the implicit spline segments by suitable polynomial factors the resulting bivariate functions are joined along suitable transversal lines. This yields a globally C1 bivariate function.

Original languageEnglish (US)
Title of host publicationAutomated Deduction in Geometry
EditorsFranz Winkler
PublisherSpringer Verlag
Number of pages17
ISBN (Print)3540209271, 9783540209270
StatePublished - 2004
Externally publishedYes
Event4th International Workshop on Automated Deduction in Geometry, ADG 2002 - Hagenberg Castle, Austria
Duration: Sep 4 2002Sep 6 2002

Publication series

NameLecture Notes in Artificial Intelligence (Subseries of Lecture Notes in Computer Science)
ISSN (Print)0302-9743


Other4th International Workshop on Automated Deduction in Geometry, ADG 2002
CityHagenberg Castle

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2004.


  • Approximation
  • B-spline
  • Implicitization
  • Knot removal

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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