Curve Shape Modification and Fairness Evaluation for Computer Aided Aesthetic Design

A method to modify curve shape according to the specified radius of curvature distribution is described. The difference between the radius of curvature of the curve and the specified radius of curvature is minimized by introducing the least-squares method. Evaluation of whether the designed curve is fair or not is accomplished by a comparison of the designed curve to a curve whose radius of curvature is monotone. The radius of curvature is specified by linear, quadratic, and cubic function. A curve whose radius of curvature is reshaped by one of these algebraic functions is considered as a fair curve. A comparison of curvature vectors is used to evaluate the similarity of the curve. If the directional similarity of the designed curve is close to the fair curve, and also the similarity of the curvature is close to the fair curve, the designed curve can be judged as a fair curve.