de Boor-fix functionals and polar forms

The relationship between the polar form perspective of spline curves [Ramshaw '87a, '87b, '89; de Casteljau '85, '86] and the dual functional viewpoint [de Boor & Fix '73, de Boor & Höllig '87] is explored. An explicit connection between these two formulations is derived, and this link is elaborated further through some examples of spline properties provable by both techniques. The relationship of these techniques to knot insertion is also briefly discussed.