几何造型中不同目标函数特点研究

曲线的长度最短、能量最小和曲率变化最小等目标函数被广泛应用在曲线曲面造型中。以插值三次样条为例，讨论了这些目标函数产生的曲线的形状、与型值多边形的逼近程度、拐点个数等方面的特点，还对这几种目标函数与它们的近似函数进行了比较。最后讨论了这些目标函数在导矢估计中的应用，通过实例说明曲率变化最小曲线及其近似曲线用于局部估计型值点切线方向时逼近较好。

Study of Characteristics of Different Objective Functions in Geometric Modeling

In geometric modeling, curves and surfaces are often generated by minimizing objective functions such as length, energy and curvature variety. It is discussed the impact of the functions and their approximate functions on the interpolating cubic spline condition, including the shape, the distances from data polygon and numbers of inflexion of the objective curves. Applications to locally estimating tangent of data points are discussed, and instances show that minimum curvature variety curve generally gets better result than other methods.