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You cannot represent a section of an Euler spiral exactly with a polynomial or rational function. You can make a fine approximation if you either (a) increase
by jacobolus 8y ago
You cannot represent a section of an Euler spiral exactly with a polynomial or rational function.
You can make a fine approximation if you either (a) increase the degree of the polynomial or (b) increase the number of segments.
There is no particular advantage of NURBS for this vs. polynomials as far as I can tell.
- maire 8y agoYou are right. I just came across this article which talks about using rational cubic trigonometric Bézier curves. https://link.springer.com/article/10.1186/s40064-016-2544-3 https://link.springer.com/article/10.1186/s40064-016-2544-3
- jacobolus 8y agoI don’t really see the point of this paper. The reason to try to approximate Euler spirals by Bézier curves is that Bézier curves are ubiquitous in existing implementations. Trigonometric Bézier curves (https://ac.els-cdn.com/S0893965908001262/1-s2.0-S0893965908001262-main.pdf?_tid=8924d36c-e3b8-40a2-8e39-946f8ff09f00&acdnat=1544395363_14596f5d6adba170cd34f4745364919e https://ac.els-cdn.com/S0893965908001262/1-s2.0-S08939659080...) are not to my knowledge implemented anywhere.