Minimum Energy Curve in Polynomial Interpolation

Construction of smooth or more technically fair interpolating curve has been of great interest among researchers. The concept of smoothness involves more than tangent and curvature continuity. One plausible suggestion for smoothness is that the strain energy should attain minimum value. In this paper, planar minimum energy curve is constructed using numerical optimization technique. Magnitude of tangent and second derivatives vector are varied to find the curve that minimizes the curvature functional measuring the strain energy. The resulting curve is free of undesirable shape and exhibited local control.