| 摘要 |
PURPOSE:To realize the division of a Gregory patch by converting a double 3-degree Gregory patch into a double 7-degree rational Bezier patch and dividing this rational Bezier patch formula. CONSTITUTION:A double 3-degree Gregory patch is converted into a double 7-degree rational Bezier patch. Then this rational Bezier patch formula is decomposed. In a tracing mode it is decided whether the Newton method is converged or not for the divided rational Bezier patches by means of the interval analysis. If not, the Bezier patches are further divided for reduction of the areas including the curved surfaces and the interval analysis is carried out again. Then the initial value is selected when the Newton method is converged and an intersecting point is calculated by the Newton method. Thus the same operations as those of the Bezier patches are possible and various algorithms requiring the division of the curved surface can be applied to the Gregory patch in addition to a tracing operation.
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