Given the enormous number of available methods for finding polygonal approximations to curves techniques are required to assess different algorithms. Some of the standard approaches are shown to be unsuitable if the approximations contain varying numbers of lines. Instead, we suggest assessing an algorithm's results relative to an optimal polygon, and describe a measure which combines the relative fidelity and efficiency of a curve segmentation. We use this measure to compare the application of fifteen algorithms to a curve first used by Teh and Chin [31]; their ISEs are assessed relative to the optimal ISE. In addition, using an example of pose estimation, it is shown how goal-directed evaluation can be used to select an appropriate assessment criterion.