T-junctions in spline surfaces

Kȩstutis Karčiauskas, Daniele Panozzo, Jörg Peters

Research output: Contribution to journalArticlepeer-review


T-junctions occurwhere surface strips start or terminate. This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces from quad-meshes that include T-junctions. All mesh nodes are interpreted as control points of GT-splines, that is, geometrically smoothly joined piecewise polynomials. GT-splines are akin to and compatible with B-splines and cover simple T-junctions by two polynomial pieces of degree bi-4 and more complex ones by four such patches. They complement multi-sided surface constructions in generating free-form surfaces with adaptive layout. Since GT-splines do not require a global coordination of knot intervals, GT-constructions are easy to deploy and can provide smooth surfaces with T-junctions where T-splines cannot have a smooth parameterization. GTconstructions display a uniform highlight linedistribution on input meshes where alternatives, such as Catmull-Clark subdivision, exhibit oscillations.

Original languageEnglish (US)
Article numberA170
JournalACM Transactions on Graphics
Issue number5
StatePublished - Oct 2017


  • Highlight line distribution
  • Smoothness
  • Spline
  • Surface
  • T-junctions

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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