I've seen many people ask for a way to find the closest point on a curve from some given point in space. If the curve is a piecewise linear one, this is not too difficult, since this reduces to finding the closest point on a line segment, and then testing each line segment. (With care, you need not test EVERY line segment.)
For a cubic spline however, this becomes more difficult, but still doable in a mathematical sense without an explicit optimization. Not too much more than roots is necessary.
Distance2curve allows you to specify a set of general points in an n-dimensional space as a connected space curve. A spline (or pchip) is then fit in terms of arc length along the curve, and the closest point identified.
John D'Errico (2022). distance2curve (https://www.mathworks.com/matlabcentral/fileexchange/34869-distance2curve), MATLAB Central File Exchange. Retrieved .
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