自由曲线曲面造型理论发展综述

摘要

自由曲线曲面造型是研究在计算机中表达物体模型形状的技术.基于其理论的实用化系统在航空航天、汽车、造船、机械、建筑和电子等行业建模中得到了广泛的应用.自上世纪60年代Bezier曲线曲面面世至今,其领域发展了逼近、插值、空间分解、细分技术、多分辨率分析等理论及应用.文中论述了曲线曲面建模理论的产生、发展和应用过程,以及当前的研究状况和发展趋势.%The technology of free curves and surfaces design refers to how to construct and represent the shapes of models. Some modeling software developed with this technology have been used in modeling products of many industries, such as airplanes, automobiles, ships, architecture, and so on. Since 1960s when the well-known Bezier curves and surfaces was developed, this research filed has encapsulated and developed many theories and the application of these theories, such as approximation theory, interpolation theory, space splitting, subdivision, and multi-resolution analysis. This paper discusses on the development of the modeling theory of free curves and surfaces and points out the problems and challenges encountered now and future.