Optimized Geometric Hermite Curve Based on Curve Length Minimization

The magnitudes of the endpoint tangent vectors are optimized in the Hermite interpolation process so that the curve length of the optimized geometric Hermite curve is a minimum. The tangent angle constraints ensuring an optimized geometric Hermite curve geometrically smooth are discussed. For the cases in which the given tangent vectors do not satisfy the constraints, new methods for constructing 3-segment composite optimized geometric Hermite curves are presented. Examples have been presented to show that combination of these new methods with those based on strain energy minimization and curve variation minimization can get pleasant results in all tangent angle regions.