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This paper presents a method to construct C1 polynomial surface with scattered data points. At first the given data points are divided into triangular networks, and then at the adjacent region of each point a C1 piecewise quadric interpolation patch is constructed. Objective function according to the stretching strain energy is constructed. Minimizing the objective function to determine the unknown...
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...
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