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.
- spatial curve