Spline surfaces with T-junctions

TL;DR

This paper introduces GT-splines, a novel class of smooth, piecewise polynomial spline surfaces from quad-meshes with T-junctions, enabling flexible, smooth free-form surface modeling without global knot coordination.

Contribution

The paper presents GT-splines, a new method for creating smooth T-junction surfaces that are easy to deploy and improve upon existing T-spline techniques in handling T-junctions.

Findings

GT-splines produce smooth, visually appealing surfaces with uniform highlight lines.

GT-splines can handle T-junctions better than T-splines, avoiding oscillations.

GT-splines are adaptable and do not require global knot interval coordination.

Abstract

This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces from quad- meshes that include T-junctions, where surface strips start or terminate. All mesh nodes can be interpreted as control points of geometrically-smooth, piecewise polynomials that we call GT-splines. GT-splines are B-spline-like and cover T-junctions by two or four patches of degree bi-4. 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 can not have a smooth parameterization. GT-constructions display a uniform highlight line distribution on input meshes where alternatives, such as Catmull-Clark subdivision, exhibit oscillations.