Abstract
B-splines, Bezier, Ball curves and NURBS (non-uniform rational B-splines) are commonly used in CADand CAGD applications. Unfortunately their fairness is not guaranteed. Spiral segments help us in designingimproved form of curves called fair curves. Such fair curves are useful in sophisticated applications such asdesign of routes of high ways and railways and mobile robot trajectories. In this paper we have developed thepolynomial cubic Ball spiral segment with degree of freedom. The effect of shape parameters is also observed.In the end results are represented in graphical form.
Highlights
Curvature continuous curves with undesirable extrema are attributes to specific applications such as design of the trajectories of mobile robot and high ways or railway routes [1, 2]. These curves are called fair curves [3]. These curves are important in computer aided design CAD and computer aided geometric design CAGD applications such as [3, 4]
B-spline, Bezier, Ball curves and NURBS are used in CAD and CAGD applications
We study spiral in terms of a curved line segment with variation of signed curvature in a monotonic way
Summary
Curvature continuous curves with undesirable extrema are attributes to specific applications such as design of the trajectories of mobile robot and high ways or railway routes [1, 2]. These curves are called fair curves [3]. B-spline, Bezier, Ball curves and NURBS are used in CAD and CAGD applications. Where as cubic Spiral segments without any point of zero curvature exists [7] which is used for shape control [8].
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