Study On The Problem Of Shape Preserving Spline With Shape Parameters

The construction of spline curves with shape parameters is one of the most important topics in the study of Computer Aided Geometric Design and Computer Graphics.This paper first introduces the development of Computer Aided Geometric Design and the research of spline curve with shape parameters.Then aG~1cubic shape preserving polynomial spline function based on function value is constructed according to the basis function with shape parameters.Finally,spline curves with shape parameters are constructed for a class of non-uniform knots.The main research work and achievements are as follows:1.Based on cubic basis functions with two shape parameters,aG~1 cubic shape preserving spline is constructed.The spline is only based on function values and is non-rational.And the shape preserving conditions are derived on shape parameters to demonstrate positive,constrained and monotone shapes of the data.Finally,some numerical examples are presented to show the performance of the method.2.The basis function of quadratic non-uniform trigonometric B-spline with shape parameters is constructed.The curve possesses properties similar to those of quadratic non-uniform B-spline.By changing values of the shape parameters,the shape of curve can be adjusted.By applying multiple knots open curves or closed curves can be constructed.Furthermore,the circle and ellipse can be represented with basis functions accurately.The examples show that the given curve has the advantages of simple structure and flexible use,and provides an effective method to design curves and surfaces.