Constructive algorithms for forming compound cubic Bezier curves in space and on plane

Abstract

The article considers two graph-analytical algorithms. The first algorithm makes it possible to form a spatial curve passing through given nodal points with direction vectors specified at these points. The second algorithm allows you to generate a flat compound curve passing through the given nodal points with direction vectors and curvature radii specified at these points. The constructed curves are formed by cubic Bezier segments. Direction vectors are treated as a control for the shape of the curve being constructed. At the nodal points, second-order geometric smoothness is ensured, due to the continuity of the slope and curvature. A distinctive feature of the proposed algorithms is the significant use of constructive means of computer graphics.

Keywords

• cubic segment
• direction vector
• curvature
• torsion
• geometric smoothness