Surface skinning using periodic TT-spline in semi-NURBS form

NURBS skinning is a powerful and effective process in Computer Aided Geometric Design (CAGD). It constructs a surface by interpolating a set of cross sectional NURBS curves. These curves however may not be compatible, i.e., they have different knot vectors. This incompatibility is conventionally solved by knot refinement bringing all curves to share the same knot vector, which leads to an explosion in the number of control points defining the skinned surface. Another disadvantage of NURBS skinning is the difficulty of local modification: adjusting one cross section may result in a global change of the surface. In this paper, periodic TT-spline in semi-NURBS form is discussed. Surface skinning using such TT-splines is able to handle closed cross sections, to support local modifications and to control smoothness along the cross sectional curves. We provide explicit formulae for constructing such TT-spline skinned surfaces, which avoid solving a large system of equations. Experimental results and theoretical analysis confirm that our approach is better than NURBS skinning as it generates surfaces with fewer control points.