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I was really hyped up by the beginning of the article, but it seems really miss the points with the conclusion. I don't think it is easier to manipulate with the last two examples, and I am guessing no actual graphic artist has read this or play with this before you publish it. To think of ways to improve bezier curves for vector graphics, you need to fully contextualize your thinking about the use case; this is not an academic mathematical discussion after all. Based on my understanding, your finding has no mathematical value as Pomax pointed it out, it is not new, it is an old math with a few constraints that is pre-defined, based on your assumption of what graphic artist wanted most of the time, which I agree is a good direction. I strongly suggest for anyone to try to make a better vector graphics tool, try to draw a letter S with the new approach as a test case, you can choose an existing font to match. And know existing vector graphics rules, here is a couple as example: - add anchor points at the horizontal and vertical extrema of your paths - control points should not cross path with one another Curves that doesn't follow these rules are valid, fine mathematical curves, but graphic artists has practices this for years to rule out them as bad for the purpose of graphic design. Again, the goal is to find the more much smaller set of suitable curves from the infinite realm of mathematical possibilities, for the context of graphic design |