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
The scipy documentation does not have anything to say about how one can take the coefficients and manually generate the spline curve. However, it is possible to figure out how to do this from the existing literature on B-splines. The following function bspleval shows how to construct the B-spline basis functions (the matrix B in … Read more
First of all, let me copy in the stable solution for linear interpolation proposed in my previous answer. ## given (x, y) data, find x where the linear interpolation crosses y = y0 ## the default value y0 = 0 implies root finding ## since linear interpolation is just a linear spline interpolation ## the … Read more
Cubic b-spline has been recently descried in a series of papers by Unser, Thévenaz et al., see among others M. Unser, A. Aldroubi, M. Eden, “Fast B-Spline Transforms for Continuous Image Representation and Interpolation”, IEEE Trans. Pattern Anal. Machine Intell., vol. 13, n. 3, pp. 277-285, Mar. 1991. M. Unser, “Splines, a Perfect Fit for … Read more
Recently I ran across the same question and wanted to implemented it on my own. This image from Wikipedia helped me: The following code is written in C++ and shows how to compute a quadratic bezier. int getPt( int n1 , int n2 , float perc ) { int diff = n2 – n1; return … Read more
For that type of graph, you want monotonic interpolation. The PchipInterpolator class (which you can refer to by its shorter alias pchip) in scipy.interpolate can be used: import numpy as np from scipy.interpolate import pchip import matplotlib.pyplot as plt # Data to be interpolated. x = np.arange(10.0) y = np.array([5.0, 10.0, 20.0, 15.0, 13.0, 22.0, … 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