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For each curve in the curve list determined by the corners on the pixel outline (see the previous section), Limn next removes knees---points on the inside of the outline that form a "right angle" with its predecessor and successor. That is, either (1) its predecessor differs only in x, and its successor only in y; or (2) its predecessor differs only in y, and its successor only in x.
It is hard to describe in words, but here is a picture:
** X* *
The point `X' is a knee, if we're moving in a clockwise direction.
Such a "right angle" point can be on either the inside or the outside of the outline. Points on the inside do nothing useful, they just slow things down and, more importantly, make the curve being fit less accurate. So we remove them. But points on the outside help to define the shape of the curve, so we keep those. (For example, if `X' was moved up one diagonally, we certainly want it as a part of the curve.)
Although we haven't found a case where removing knees produces an inferior result, there's no theory about it always helping. Also, you may just be curious what difference it makes (as we were when we programmed the operation). So Limn provides an option `-keep-knees'; if you specify it, Limn simply skips this step.
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