C-Bézier Curves and Surfaces

Abstract

Using the same technique as for the C-B-splines, two other forms of C-Bézier curves and a reformed formula for the subdivisions are proposed. With these new forms, C-Bézier curves can unify the processes for both the normal cases, and the limiting case (α→0) with precise results. Like the C-B-splines, a C-Bézier curve can be approximated by its cubic Bézier curve in high accuracy. For any tensor product C-Bézier patch, a pair of its opposite sides could have different parameters of α. All this will make the C-Bézier curves and surfaces more efficient in algorithms, more flexible in assembling and representing arcs, and will satisfy the demands of high precision in engineering and fast calculation in computer display.