Abstract
AbstractThis paper focuses on the region constraint of the interpolating surface. The interpolating surface is constructed with a bivariate rational function which is based on the function values and the partial derivatives. If the spline surface protrudes irregularly in a patch, it can be modified by the interpolation parameters. But it is not easy to find the suitable modification parameters. Sometimes the protuberance surface is a big trouble for computer-aided geometric design. To overcome this problem, the sufficient conditions for surface control are derived. The interpolating surface will be above or below a given space plane in the interpolation subinterval by the constraint conditions. Some numerical examples are given to illustrate this method.
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