Designing fair curves using monotone curvature pieces Original Research Article

Sufficient Monotone Curvature Variation (MCV) conditions for planar Bézier and B-spline curves are described in this paper. Based on the MCV conditions which are presented, a shape control method for Bézier and B-spline curves is proposed. This method is described as finding a solution of an optimization problem subject to the MCV constraints. Since the shape control method for curves retains the desirable MCV pieces and eliminates all unwanted curvature waves, designers could easily modify curves to meet their design intentions. Practical curve examples for automobile body design verify the proposed method and demonstrate its applicable potentials.