文献类型：期刊文献

英文题名：Constructing up to G ² continuous curve on freeform surface

作者：Wang, Xiaoping[1];Meng, Yaqin[2];Wang, Zhiguo[1];Zhang, Liyan[1]

机构：[1]Nanjing Univ Aeronaut & Astronaut, Res Ctr CAD CAM Engn, Nanjing 210016, Peoples R China;[2]E China Univ Sci & Technol, Coll Sci, Shanghai 200237, Peoples R China

年份：2010

卷号：26

期号：6-8

起止页码：813

外文期刊名：VISUAL COMPUTER

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000278135800041)】；

基金：The authors would like to thank the anonymous reviewers for valuable comments. The work reported in this paper was supported by National Natural Science Foundation of China under grant (Nos. 60673026, 50875130, 50805075 and 50875126).

语种：英文

外文关键词：Hermite interpolation; Curve projection; Freeform surface; G(2) continuity; Ordinary differential equation

摘要：This paper presents new methods for G (1) and G (2) continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with prescribed tangent direction and both tangent direction and curvature vector, respectively, at every point. We design a G (1) or G (2) continuous curve in three-dimensional space, construct a so-called directrix vector field using the space curve and then project a special straight line segment onto the given surface along the directrix vector field. With the techniques in classical differential geometry, we derive a system of differential equations for the projection curve. The desired interpolation curve is just the projection curve, which can be obtained by numerically solving the initial-value problems for a system of first-order ordinary differential equations in the parametric domain associated to the surface representation for the parametric case or in three-dimensional space for the implicit case. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification such that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface, and numerical experiments demonstrate that it is effective and potentially useful in patterns design on surface.