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pythonmatplotlibinterpolationsmoothing

Smoothing a 2-D figure

I have a number of vaguely rectangular 2D figures that need to be smoothed. A simplified example:

fig, ax1 = plt.subplots(1,1, figsize=(3,3))
xs1 = [-0.25,  -0.625, -0.125, -1.25, -1.125, -1.25, 0.875, 1.0, 1.0, 0.5, 1.0, 0.625, -0.25]
ys1 = [1.25, 1.375, 1.5, 1.625, 1.75, 1.875, 1.875, 1.75, 1.625, 1.5, 1.375, 1.25, 1.25]

ax1.plot(xs1, ys1)
ax1.set_ylim(0.5,2.5)
ax1.set_xlim(-2,2) ;

enter image description here enter image description here

I have tried scipy.interpolate.RectBivariateSpline but that apparently wants data at all the points (e.g. for a heat map), and scipy.interpolate.interp1d but that, reasonably enough, wants to generate a 1d smoothed version.

What is an appropriate method to smooth this?

Edit to revise/explain my goal a little better. I don't need the lines to go through all the points; in fact I'd prefer that they not go through all the points, because there are clear outlier points that "should" be averaged with neighbors, or some similar approach. I've included a crude manual sketch of the start of what I have in mind above.

Solution

  • Chaikin's corner cutting algorithm might be the ideal approach for you. For a given polygon with vertices as P0, P1, ...P(N-1), the corner cutting algorithm will generate 2 new vertices for each line segment defined by P(i) and P(i+1) as

    Q(i) = (3/4)P(i) + (1/4)P(i+1)
    R(i) = (1/4)P(i) + (3/4)P(i+1)

    So, your new polygon will have 2N vertices. You can then apply the corner cutting on the new polygon again and repeatedly until the desired resolution is reached. The result will be a polygon with many vertices but they will look smooth when displayed. It can be proved that the resulting curve produced from this corner cutting approach will converge into a quadratic B-spline curve. The advantage of this approach is that the resulting curve will never over-shoot. The following pictures will give you a better idea about this algorithm (pictures taken from this link)

    Original Polygon
    Original Polygon

    Apply corner cutting once
    Apply corner cutting once

    Apply corner cutting one more time
    enter image description here

    See this link for more details for Chaikin's corner cutting algorithm.