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Simplify, Object > Path > Smooth, the Smooth tool and freehand strokes turned every refitted curve whose handles lay near its chord into a straight line. A short curve whose end directions were off the chord passed that test, and the anchor between it and the next curve became a corner the path did not have: a Smooth tool drag along a line jagged by up to 6 pt left corners of 7.7 to 40.6 degrees. A curve now becomes a line only when the line runs within 0.5 degrees of the directions the path arrives and leaves along. A nearly straight piece that would turn more stays a flat curve. Convert to Straight Lines is unchanged.