Those working in interface capturing techniques such as level set. Examples include stretched membranes, drops deforming under shear flows etc.
You may try this. The set of points, whether in 2D or 3D, if ordered, may be considered as a set of points represented as a function of a single parametric t. For example, if you have them in the order (x(1),y(1),z(1)),....,(x(n), y(n), z(n)), then x,y and z may be parametrized as x(t), y(t) and z(t). Thus you have functional relationships between t and x(t), t and y(t), and t and z(t). Using cubic spline or other piecewise interpolation methods, you may compute the coordinates of the intermediate points lying on the curve. Then making use of the formula for the curvature of a parametric curve (you have to use finite difference for the derivatives appearing here), you should be able to compute the curvature easily. Hope this helps.
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