@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 Kar{\v c}iauskas and Daniele Panozzo and J{\"o}rg Peters",
note = "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{\textquoteright} 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: panozzo@nyu.edu; J. Peters, University of Florida, Gainesville FL 32611-6120, USA; email: jorg@cise.ufl.edu. 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 permissions@acm.org. {\textcopyright}c 2017 ACM 0730-0301/2017/10-ART170 $15.00 DOI: http://dx.doi.org/10.1145/3136954 Publisher Copyright: {\textcopyright} 2017 ACM.",
year = "2017",
month = oct,
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",
}