中文摘要：

1引言随着现代工业生产的飞速发展,航空、气象、环境监测等领域需要研究解决限制在曲面上的四维数据插值问题,即由有限个位置处的信息推测其它若干位置点的信息.例如,地球上某个地区的温度分布、降雨量分布、大气层的"温室效应"等;飞行器(飞机、火箭、导弹等)表面压力分布规律、肿瘤的生长规律等.这些在数学上都可归结为限制在曲面上的曲面插值与逼近问题.这个问题自Barnhill提出以后,人们针对限制在球面上

英文摘要：

An approach for establishing surface interpolation on a sphere is presented by means of some base functions on the sphere.Firstly,we construct a triangulation of the sphere based on the distance of geodesic arics and give a closed three times Bezier curve around each interpolation point on the sphere.Secondly, we get a profile curve of interpolation base functions by projecting the curve on the sphere.Then we construct a base function with a local support around the neighborhood of the interpolation points ...