最优组合重新参数化

提出了一种最优的曲线重新参数化方法.该方法采用分段有理线性函数作为重新参数化函数来增加自由度.其中一个自由度用于保证连续性条件的满足,其余的自由度用于达到L2范数下的最优参数化.在不改变参数区问和参数域的情况下,得到在任意参数节点集上的C1连续有理参数化的显式表示形式.相对于新的参数,目标函数是线性的,最优值能够通过求解一个二次方程得到.最后用实例验证了新方法的有效性.

Optimal Composite Re-parameterization

An optimal composition algorithm was proposed to re-parameterize the polynomial or rational curve. The algorithm uses the class of piecewise rational linear function as re-parameterization function, which increases degrees of freedom. Certain degree of freedom is spent on guaranteeing continuity conditions, and the others are used to obtain the optimal parameterization under L2 norm but with less segmentation. A closed-form derivation for the optimal C 1continuous rational parameterization on a free set of nodes that does not alter the curve parameter domain and degree is obtained. With respect to the new parameter, the objective function is linear, and can be easily identified by solving a quadratic equation. Illustrative examples were given to assess the performance of the new method.