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提出了构造三角曲面片的一个新方法. 新方法通过基本逼近算子加上附加插值算子构造满足给定边界曲线和跨界切矢的三角曲面片. 基本逼近算子由逼近插值条件的 5 次多项式构成, 附加插值算子用边点法产生. 基本逼近算子和附加插值算子在构成三角曲面片中具有不同的作用, 前者使三角曲面片以五次多项式精度逼近插值条件, 而后者则使三角曲面片满足给定的插值条件. 所构造的三角曲面片可以重构五次多项式曲面. 给出了新方法和其他两种方法进行比较的结果.
A new method of constructing triangular surface patches is proposed.The new method constructs a triangular patch which satisfies the given boundary curve and the cross-cutting tangent vector through the basic approximation operator and the additional interpolation operator.The basic approximation operator is composed of approximation 5 Order polynomials and additional interpolation operators are generated by the edge point method.The basic approximation operator and the additional interpolation operator play different roles in the formation of the triangular surface patch. The former approximates the interpolation condition to the triangular patch by the fifth-order polynomial precision, while the latter The triangular patch can satisfy the given interpolation condition.The constructed triangular patch can reconstruct the quintic polynomial surface.The results of the new method and the other two methods are given.