  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.
