Generalized trigonometric curve and its spline

Abstract

On the extensions of the cubic Bézier curve with four control points, to connect multiple segments with required continuity has been strongly intended and for example, tangent and curvature continuity at the start and end points are guaranteed independently by adding extra shape parameters. Contrary to this research trend, κ-curves, which control one curvature extremum on each curve segment instead of the end points, are defined as a sequence of the quadratic Bézier curve with three control points. In this study, in order to extend κ-curves, we propose generalized trigonometric basis functions consisting of (sint,cost,1). Using these basis functions, we also define a new free-form curve named generalized trigonometric curve. We discuss its degree elevation, Miura’s triangle, Gobithaasan-Miura’s recursive algorithm, handwriting and spline.

Keywords

• generalized trigonometric spline
• κ-curves
• degree elevation
• miura’s triangle
• gobithaasan-miura’s recursive algorithm
• spline