Piecewise polynomial spaces and geometric continuity of curves (Q1099576)

We say that a curve has geometric continuity if its Frenet frame is continuous. The curve has arc-length continuity of order k if it is k time continuously differentiable in the arc-length parametrization. In this paper we introduce spaces of piecewise polynomials which can be used to model space curves with geometric on arc-length continuity. We show that the basic theoretical properties of ordinary spline functions also hold for these spaces. These results extend and unify recent work on Beta-splines and Nu-splines, which are used as a design tool in computer- aided geometric design of free form curves and surfaces.