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 language | English (US) |
|---|---|
| Article number | A170 |
| Journal | ACM Transactions on Graphics |
| Volume | 36 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 1 2017 |
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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 journal › Article
}
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
AN - SCOPUS:85032929468
VL - 36
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
SN - 0730-0301
IS - 5
M1 - A170
ER -