Research On The Positivity-preserving Interpolation Spline

In CAGD,a general problem is to construct the interpolant with a certain degree ofcontinuity.When there are some properties inherent in the data，like positivity, monotonicityand convexity,one wishes to preserve．In CAGD，the user may think it’s good that theinterpolant preserves some properties. In this paper, a class of positivity-preservinginterpolation spline is derived, and deprive a method of positivity preserving by adjusting thepartial derivative,and it is from a positivity preserving condition of a Bézīer surface.There are four chapters in this paper.The first chapter is the introduction, it introduce the development history andbackground of parameter curves and surfaces modeling with shape parameter in CAGD．ChapterⅡmainly summarizes a class of positivity-preserving interpolation spline ontangular grids and on rectangular grids.ChapterⅢare the researches of this paper. A positivity-preserving interpolation localscheme is developed.The surface for the data is arranged over a rectangular grids.Sufficientconditions are derived to ensure that the surfaces are always positive by modifying the Bezierordinates,and the surfaces areG~1continuious.ChapterⅣsummary the paper and give some future work prospects.