%0 Journal Article
%T A Class of Trigonometric Polynomial Curves on Four-Point Piecewise Scheme<br>基于四点分段的一类三角多项式曲线
%A HAN Xu-li
%A <br>韩旭里
%J 中国图象图形学报
%D 2002
%I 
%X A class of piecewise trigonometric polynomial curves of degree m(m=1,2,3) is presented in this paper. Weighted trigonometric polynomial curves are given by using a shape parameter. Analogous to the cubic B-spline curves, each trigonometric polynomial curve segment is generated by four consecutive control points. For equidistant knots, the given trigonometric polynomial curves of degree m are C 2m-1 continuous. The construction methods of an open and a closed trigonometric polynomial curves are described. The given curves can be used to generate ellipses conveniently. The comparisons between the trigonometric polynomial curves and the cubic B-spline curves are given. By choosing m or the shape parameter, the trigonometric polynomial curve can approach to the given control polygon in a different way. Therefore, the construction method of the trigonometric polynomial curves is simple and useful for curve design.
%K Curve design
%K Trigonometric polynomial
%K Spline curve<br>四点分段
%K 三角多项式曲线
%K 曲线设计
%K 样条曲线
%K 曲体设计
%K 曲线生成方法
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=D06194629680C940ACE75262F54B9D85&aid=C1BD104004837A5F&yid=C3ACC247184A22C1&vid=DF92D298D3FF1E6E&iid=F3090AE9B60B7ED1&sid=EE05CC1F800E4629&eid=63025EFC6CC49145&journal_id=1006-8961&journal_name=中国图象图形学报&referenced_num=10&reference_num=11