A discrete methodology for controlling the sign of curvature and torsion for NURBS

Ginnis, A.I. and Karousos, E.I. and Kaklis, Panagiotis (2009) A discrete methodology for controlling the sign of curvature and torsion for NURBS. Computing, 86 (2-3). 117–129. ISSN 0010-485X

[img]
Preview
PDF (A discrete methodology for controlling Computing 86)
A_discrete_methodology_for_controlling_Computing_86.pdf
Preprint

Download (392kB)| Preview

    Abstract

    This paper develops a discrete methodology for approximating the so-called convex domain of a NURBS curve, namely the domain in the ambient space, where a user-specified control point is free to move so that the curvature and torsion retains its sign along the NURBS parametric domain of definition. The methodology provides a monotonic sequence of convex polyhedra, converging from the interior to the convex domain. If the latter is non-empty, a simple algorithm is proposed, that yields a sequence of polytopes converging uniformly to the restriction of the convex domain to any user-specified bounding box. The algorithm is illustrated for a pair of planar and a spatial Bézier configuration.