A tetrahedron-based subdivision scheme for spatial G1 curves

In this paper, we propose a new “purely geometrical” interpolatory Hermite subdivision scheme for generating spatial subdivision curves which starts with a sequence of points and associated (unit) tangent vectors. The newly generated point lies inside a certain tetrahedron which is formed by the given Hermite data. The method is local and we prove that, by iterating this refinement procedure, the limit curve is G1 continuous. The additional property of the scheme is that planar data are preserved, i.e., planar subdivision curves are generated for planar initial Hermite data and, moreover, the scheme is circle-preserving.