TY - JOUR
T1 - T-junctions in spline surfaces
AU - Karčiauskas, Kȩstutis
AU - Panozzo, Daniele
AU - Peters, Jörg
N1 - Funding Information:
Additional Key Words and Phrases: T-junctions, spline, surface, smoothness, highlight line distribution This work was supported in part by NSF grant CCF-1117695, NSF CAREER award 1652515, NIH grant R01 LM011300-01 and DARPA TRADES HR00111720031. Authors’ addresses: K. Karcˇiauskas, Vilnius University, LT-2006, Vilnius, Lithuania; New York University, NY, USA; email: Kestutis.Karciauskas@ mif.vu.lt; D. Panozzo, Courant Institute of Mathematical Sciences, New York University, 60 5th Ave, 5th floor, New York, NY 10011; email: [email protected]; J. Peters, University of Florida, Gainesville FL 32611-6120, USA; email: [email protected]. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or [email protected]. ©c 2017 ACM 0730-0301/2017/10-ART170 $15.00 DOI: http://dx.doi.org/10.1145/3136954
Publisher Copyright:
© 2017 ACM.
PY - 2017/10
Y1 - 2017/10
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
SN - 0730-0301
VL - 36
JO - ACM Transactions on Graphics
JF - ACM Transactions on Graphics
IS - 5
M1 - A170
ER -