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Generally speaking, trying to fish around for practical applications of a specific mathematical theorem or theory --- such as Alexander's Theorem from knots and braid theory, or surgery theory from your previous question --- does not usually work out well. It's sort of like asking which diseases can be cured using a hammer. That's not to say that ...


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Douglas-Peucker does its best to find the corners, but it can't as they are rounded. Anyway, you now have a very good approximation of the quadrilateral. What you can do is start from the corners that DP found, and on the original outline skip the segments that form the circular arc (you can simply skip on a certain length or detect curvature). Only ...


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As @lhf suggested in the comments I tried Hough transform on the actual contour. This gave me a number of lines per side. Altough I tried a wide range of parameters, Hough transform was not able to fill the gaps: I solved this by dividing the lines into groups of similar lines. The weighted average of each group gave me a pretty accurate side of the ...


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I'm not sure I understand the problem 100%, but here are some suggestions, anyway. If you want an explicit NURBS representation of a curve that lies exactly on your surface of revolution, then the only option is a surface parameter space curve of the type mentioned by Fang. So, take the data you want to fit, and map it back into a two-dimensional $uv$ ...



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