Shape control of Bézier surfaces with iso-parametric monotone curvature constraints Original Research Article

This paper describes a sufficient condition of Monotone Iso-parametric Curvature Variation (MICV) for tensor product Bézier surfaces. The condition is a set of inequalities of the control points of the Bézier surface. Based on the MICV condition, a shape control method is presented to generate a MICV Bézier surface. The method is implemented as a nonlinearly constrained optimization problem subject to the MICV constrains. The optimal MICV surface is closest to the initial one in terms of the least square of the control points. Cases studies verify the effectiveness of the proposed method of shape control.