Boundary Conditions and Creases for Subdivision Curves of Arbitrary Degree

Boundary Conditions and Creases for Subdivision Curves of Arbitrary
Degree

No curve and surface subdivision scheme is complete without special
rules for boundary and crease points.
Crease rules are well understood for cubic and lower degree curves. We
compare three main approaches: knot insertion, ghost points, and
modifying subdivision rules. While knot insertion and ghost points
work for arbitrary degrees for B-splines, these methods introduce
unnecessary (ghost) control points.
The situation is not so simple in modifying subdivision rules.
Based on subdivision and subspace selection matrices, a novel approach
to finding boundary and sharp subdivision rules that generalises to
any degree will be presented.
Our approach leads to new higher-degree polynomial subdivision schemes
with crease control without introducing new control points.