Controlling torsion sign

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Karousos, E.I. and Ginnis, A.I. and Kaklis, Panagiotis (2009) Controlling torsion sign. Computer Aided Geometric Design, 26 (4). pp. 396-411. ISSN 0167-8396 (https://doi.org/10.1016/j.cagd.2008.12.003)

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Abstract

For all curve representations that adopt the control-point paradigm, we present a method for computing the domain, where a user-specified control point is free to move so that the corresponding spatial curve is regular and of constant sign of torsion along a subinterval of its parametric domain of definition. The method is illustrated for a Bézier and a B-spline curve. Furthermore, its utility for fairing curves under torsion-sign constraints in quadratic-programming context, is illustrated for a pair of Bézier curves. Finally, it is shown that the obtained results remain useful if, besides the user-selected free control point, neighboring ones are permitted to vary within convex polyhedra.

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