插值特殊曲线的可展曲面造型研究进展  

Researches on developable surface modeling by interpolating special curves

作　　者：李彩云[1] 朱春钢[2] 王仁宏[2] 

机构地区：[1]大连理工大学盘锦校区基础教学部,盘锦124221 [2]大连理工大学数学科学学院,大连116024

出　　处：《中国科学：数学》2015年第9期1441-1456,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11290143;11401077和11271060);民用飞机专项(批准号:MJ-F-2012-04);中央基本科研业务费(批准号:DUT14YQ111);辽宁省高等学校优秀人才支持计划(批准号:LJQ2014010)资助项目

摘　　要：可展曲面一直是计算机辅助几何设计领域中的热点问题,其在曲线曲面造型中有着很好的应用前景.另外,它与逼近论、最优化、微分几何、线几何等领域密切相关,并产生了一些很好的数学结果.本文主要综述可展曲面的一些基本结果及作者近年来在该方向的一些研究工作,并对未来工作进行展望,主要包括具有一定几何约束的可展曲面的构造和拼接等.The developable surface is always a hot issue in computer aided geometric design. It has very nice application prospect in curves and surfaces modeling. Moreover, it is closely related with approximation theory, optimization, differential geometry and line geometry. Therefore, it produces many beautiful mathematical results. This article mainly sums up some basic results of developable surfaces and the researches which the authors have done in recent years. At the same time, we describe the prospect for the future. The main work mainly includes the construction and blending of the developable surface owning certain geometric constraints.

关 键 词：可展曲面 测地线 曲率线 

分 类 号：O186.11[理学—数学]