The problem of constructing curve on parametric surface (or surface that canbe parameterized) such that it interpolates a sequence of points with prescribed tangent directionand curvature vector (or geodesic curvature...The problem of constructing curve on parametric surface (or surface that canbe parameterized) such that it interpolates a sequence of points with prescribed tangent directionand curvature vector (or geodesic curvature) at every point and the issue of curve blending on thiskind of surface are researched. The mapping and tangent mapping from the surface to its parametricplane are introduced and thus several conclusions with differential geometry are deduced. Based onthose conclusions, the problem of interpolating (or blending) curve on a parametric surface isconverted to a similar one on its parametric plane. The final solution curve of either interpolationor blending issue is explicit and can still be expressed by parametric form. And so, unlikeexisting methods, the presented method needs not to use any surface/ surface intersectionalgorithms, usually a troublesome process, for displaying such interpolation curve. Experimentresults show the presented methods are feasible and applicable to CAD/CAM and computer graphics展开更多
基金This project is supported by National Natural Science Foundation of China(No.50475041)Huo Ying-Dong Education Foundation, China (No.03-91053).
文摘The problem of constructing curve on parametric surface (or surface that canbe parameterized) such that it interpolates a sequence of points with prescribed tangent directionand curvature vector (or geodesic curvature) at every point and the issue of curve blending on thiskind of surface are researched. The mapping and tangent mapping from the surface to its parametricplane are introduced and thus several conclusions with differential geometry are deduced. Based onthose conclusions, the problem of interpolating (or blending) curve on a parametric surface isconverted to a similar one on its parametric plane. The final solution curve of either interpolationor blending issue is explicit and can still be expressed by parametric form. And so, unlikeexisting methods, the presented method needs not to use any surface/ surface intersectionalgorithms, usually a troublesome process, for displaying such interpolation curve. Experimentresults show the presented methods are feasible and applicable to CAD/CAM and computer graphics
