Instead of measuring only distance from the curve itself for the error metric, how about adding in deviation of the derivatives of the curve and its approximation?
Yes, this is the idea behind the proposed error metrics in my thesis, particularly the "hybrid error metric" in 9.6.1 and then implemented in the Python code (see curves/to_cubic.py in the spiro-0.01 release). But it needs refinement, specifically calibration against perceptual data as measured by experiment.
