Energy-minimizing splines in manifolds

Michael Hofer, Helmut Pottmann

Research output: Contribution to journalConference articlepeer-review

79 Scopus citations

Abstract

Variational interpolation in curved geometries has many applications, so there has always been demand for geometrically meaningful and efficiently computable splines in manifolds. We extend the definition of the familiar cubic spline curves and splines in tension, and we show how to compute these on parametric surfaces, level sets, triangle meshes, and point samples of surfaces. This list is more comprehensive than it looks, because it includes variational motion design for animation, and allows the treatment of obstacles via barrier surfaces. All these instances of the general concept are handled by the same geometric optimization algorithm, which minimizes an energy of curves on surfaces of arbitrary dimension and codimension.

Original languageEnglish (US)
Pages (from-to)284-293
Number of pages10
JournalACM Transactions on Graphics
Volume23
Issue number3
DOIs
StatePublished - Dec 1 2004
EventACM Transactions on Graphics - Proceedings of ACM SIGGRAPH 2004 -
Duration: Aug 9 2004Aug 12 2004

Keywords

  • Geometric optimization
  • Motion design
  • Obstacle avoidance
  • Splines in manifolds
  • Variational curve design

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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