Abstract: The magnitudes of the endpoint tangent vectors are optimized in the process of Hermite interpolation so that the curvature variation of the optimized geometric Hermite curve is a minimum.The tangent angle constraints guaranteeing an optimized geometric Hermite curve geometrically smooth is got and proved.For the cases in which the given tangent vectors do not satisfy the constraints,new methods for constructing 2-segment and 3-segment composite optimized geometric Hermite curves are presented.Examples have been presented to shown that combination of these new methods and those based on strain energy minimization can get satisfying results in all the tangent angle regions.