Spline surfaces with T-junctions

T-junctions support merging or spreading out feature lines. This paper develops a new way to create smooth piecewise polynomial free-form spline surfaces that include T-junctions. The construction is based on varying the parameterization and therefore does not require the non-local coordination of knot intervals. Conversely, a simple example shows that some T-junctions do not admit C 1 hierarchical splines and T-splines in particular. Our recommended G 1 cap of the T-junction consists of two pieces of degree bi-4 framed by bi-cubic splines. Numerous experiments show good highlight line distribution where alternatives, such as Catmull-Clark subdivision, fail and hierarchical splines do not apply.