抄録
This paper introduces new local minimum properties into the C2 interpolating curve, each span of which is determined by 6 or 8 neighboring given points. The marriage between the fairness based on variation problem and the local behavior obtained by degree-elevation or knot-insertion, the opposite-like concepts, of the curve is studied by various minimization conditions independent and dependent of the given set of interpolation points. The results are: (1) Every condition studied improves improper behavior in the previous curve. (2) One of the conditions may generate a curve with smaller value of "energy integral" and curvature plot consisting of fewer monotone pieces than the conventional cubic C2 interpolating curve. (3) Applying a minimization condition to the blending function leads to a new curve in simple yet fairly effective way.
