Your data look like a two-dimensional parametric plot of (x,y) as a function of some underlying parameter t. As such, it may be possible to do a least-squares fit of x(t) and y(t) if you can come up with a reasonable model for them. Your data appear to describe a limacon.
You can reduce the number of points using the Ramer–Douglas–Peucker algorithm there is a C# implementation here. I gave this a try using WPFs PolyQuadraticBezierSegment and it showed a small amount of improvement depending on the tolerance. After a bit of searching sources (1,2) seem to indicate that using the curve fitting algorithm from Graphic … Read more
Short answer: from scipy import interpolate def f(x): x_points = [ 0, 1, 2, 3, 4, 5] y_points = [12,14,22,39,58,77] tck = interpolate.splrep(x_points, y_points) return interpolate.splev(x, tck) print(f(1.25)) Long answer: scipy separates the steps involved in spline interpolation into two operations, most likely for computational efficiency. The coefficients describing the spline curve are computed, using … Read more
After hours of investigation, I did not find any pip installable packages which could fit a natural cubic spline with user-controllable smoothness. However, after deciding to write one myself, while reading about the topic I stumbled upon a blog post by github user madrury. He has written python code capable of producing natural cubic spline … Read more
I’ve written some quick-and-dirty code that estimates this for Bézier curves of any degree. (Note: this is pseudo-brute force, not a closed-form solution.) Demo: http://phrogz.net/svg/closest-point-on-bezier.html /** Find the ~closest point on a Bézier curve to a point you supply. * out : A vector to modify to be the point on the curve * curve … Read more
The problem with joining subsequent sample points together with disjoint “curveTo” type functions, is that where the curves meet is not smooth. This is because the two curves share an end point but are influenced by completely disjoint control points. One solution is to “curve to” the midpoints between the next 2 subsequent sample points. … Read more