T-junctions in spline surfaces

Kȩstutis Karčiauskas, Daniele Panozzo, Jörg Peters

Research output: Contribution to journalArticle

Abstract

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
Volume36
Issue number5
DOIs
StatePublished - Oct 1 2017

Fingerprint

Splines
Polynomials
Parameterization

Keywords

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

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

Cite this

T-junctions in spline surfaces. / Karčiauskas, Kȩstutis; Panozzo, Daniele; Peters, Jörg.

In: ACM Transactions on Graphics, Vol. 36, No. 5, A170, 01.10.2017.

Research output: Contribution to journalArticle

Karčiauskas, Kȩstutis ; Panozzo, Daniele ; Peters, Jörg. / T-junctions in spline surfaces. In: ACM Transactions on Graphics. 2017 ; Vol. 36, No. 5.
@article{cfd5706be13545778115e25438d5ad1f,
title = "T-junctions in spline surfaces",
abstract = "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.",
keywords = "Highlight line distribution, Smoothness, Spline, Surface, T-junctions",
author = "Kȩstutis Karčiauskas and Daniele Panozzo and J{\"o}rg Peters",
year = "2017",
month = "10",
day = "1",
doi = "10.1145/3136954",
language = "English (US)",
volume = "36",
journal = "ACM Transactions on Graphics",
issn = "0730-0301",
publisher = "Association for Computing Machinery (ACM)",
number = "5",

}

TY - JOUR

T1 - T-junctions in spline surfaces

AU - Karčiauskas, Kȩstutis

AU - Panozzo, Daniele

AU - Peters, Jörg

PY - 2017/10/1

Y1 - 2017/10/1

N2 - 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.

AB - 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.

KW - Highlight line distribution

KW - Smoothness

KW - Spline

KW - Surface

KW - T-junctions

UR - http://www.scopus.com/inward/record.url?scp=85032929468&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85032929468&partnerID=8YFLogxK

U2 - 10.1145/3136954

DO - 10.1145/3136954

M3 - Article

VL - 36

JO - ACM Transactions on Graphics

JF - ACM Transactions on Graphics

SN - 0730-0301

IS - 5

M1 - A170

ER -