Equivalence constants for some norms on the space of N-piece cubic Bézier curves
Abstract
This paper is concerned with norms of N -piece cubic Bézier curves and the equivalence relations between some norms on the space B N , 3 of N -piece cubic Bézier curves. We introduce a norm ∥ · ∥ Bp 3 on the space B 3 of cubic Bézier curves and a norm ∥·∥ Bp N , 3 on the space B N , 3 of N -piece cubic Bézier curves. This article we deal with the equivalence constants for the norm ∥ · ∥ Bp N , 3 and the L p norm on the space B N , 3 of N -piece cubic Bézier curves. An N -piece Bézier curve of degree m can be considered as an N -piece Bézier curve of degree m + 1 . We also study the equivalence constants for the norm ∥ · ∥ Bp N , m and the norm ∥ · ∥ Bp N , m + 1 on the space B N , m of N -piece Bézier curves of degree m .