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I would have liked it to be more mathy, the "it seems complicated but it actually is" followed by an approximate explanation is confusing, and the math looks li

• TheRealPomax 10y ago
  For more detailed maths, wikipedia and actual B-spline articles are your content of choice. Doing a full analysis of B-splines is out of scope as a section in a Primer on Bezier curves (as noted in the text, I'd have to write a separate primer on B-splines instead), so the maths is not as detailed, and the implementation focuses on code in use by several libraries (like the JavaScript "bspline.js" or C "tinyspline" libraries). One note about it being an approximate explanation: it's not, B-Spline maths can analysed (like Bezier maths) either using calculus, using geometry, or using algorithm operations, all three being different ways to work out exactly the same thing. The explanation in this primer only covers the algorithmic approach of computing the B-spline function as iterative interpolation, but is functionally equivalent to a more "mathy" approach involving lots of calculus. Doing so does not give you the information you'd get from symbolic maths to aid in things like finding normals, tangents, extremities and inflection points, etc. etc. but for the scope of the section, and given the article it's part of, that's intentional.