%0 Journal Article
%T Interpolation and Blending on Parametric Surfaces<br>参数曲面上的插值与混合
%A WANG Xiao-Ping
%A ZHOU Ru-Rong
%A YU Zhan-Yue
%A YE Zheng-Lin
%A <br>王小平
%A 周儒荣
%A 余湛悦
%A 叶正麟
%J 软件学报
%D 2004
%I 
%X Representing a curve contained in a surface is very important in dealing with path generation in computer numerical control (CNC) machining and the trimming issues that frequently occur in the field of CAD/CAM. This paper develops methods for tangent direction continuous (G1) and both tangent direction and curvature continuous (G2) interpolation of a range of points on surface with specified tangent and either a curvature vector or a geodesic curvature at every point. As a special case of the interpolation, the blending problems of curves on surface are also discussed. The basic idea is as follows: with the help of the related results of differential geometry, the problem of interpolating curve on a parametric surface is converted to a similar one on its parametric plane. The methods can express the G1 and G2 interpolation curve of an arbitrary sequence of points on a parametric surface in a 2D implicit form, which transforms the geometric problem of surface intersection, usually a troublesome issue, into the algebraic problem of computing an implicit curve in displaying such an interpolation curve. Experimental results show the presented methods are feasible and applicable to CAD/CAM and Computer Graphics.
%K interpolation
%K blending
%K GG1 continuity
%K GG2 continuity
%K tangent mapping<br>插值
%K 混合
%K G1连续
%K G2连续
%K 切映射
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=5B3AB970F71A803DEACDC0559115BFCF0A068CD97DD29835&cid=8240383F08CE46C8B05036380D75B607&jid=7735F413D429542E610B3D6AC0D5EC59&aid=D5DF653FEA9B6E16&yid=D0E58B75BFD8E51C&vid=23CCDDCD68FFCC2F&iid=38B194292C032A66&sid=9B95A71E6639C039&eid=E0172F1A638CE984&journal_id=1000-9825&journal_name=软件学报&referenced_num=10&reference_num=20