Multifunction interpolation is a classic but complex issue. Based on the previous binary graded interpolation research, we study the ternary graded interpolation further. Firstly, we give the definition of ternary graded space, then we explore the well-posedness of the ternary interpolation node group in the European space. We generalize the recursive structure principle to ternary space, and then construct new properly posed node group by adding bevel plane. Lastly, we research the problem of structuring the nodes group of ternary graded interpolation by adding plane and quadric surface, and show the calculation results of the practical examples by using MATLAB.
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