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This is something related with Mathematics as well. But this is useful in computing as well.
Lets say you have 10 coordinates. (x1,y1)(x2,y2)….. in 2D Space. (i.e on a X-Y Plane). Can we find a single smooth curve going across the each coordinate.
While expanding the question, If the space is 3D, then can we find an equation of a smooth surface that going across a given set of spacial coordinates?
Are there any Libraries (Any language) \ tools to perform such calculations?
What you should be looking for is some library implementing NURBS (or Non Uniform Rational B-Splines). This will solve your problem in both 2d and 3d, since 2d is just a special case of the 3d.
Roughly speaking, you are not interested in the actual equation, you are only interested in getting the points approximated with smooth curves or surfaces. This is done by finding “control points” in 2d or 3d space, which are multiplied with B-spline base functions. A NURBS library will do this for you.
Cheers !
Edit:
Have a look at this one