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.