Abstract: Lots of CAD software has no function of extension for non-circular curves. Intelligent extension-technology for non-circular curves is studied based on the principles of trend extrapolation. Four kinds of intelligent extension-models, including quadratic extension-model, cubic extension-model, exponential extension-model and Gompertz extension-model, are built. Moreover, the methods of identifying and choosing extension-models are discussed separately. Several applications of intelligent extension for non-circular curves are offered, which shows us that the extension-models can be available for approximate extension for a short distance if the shapes of non-circular curves are arbitrary. The theories in this paper, a kind of core technologies and generic key problems, can be used for upgrading or secondary development of existing CAD software.

Key words: non-circular curves, trend extrapolation, intelligent extension, mathematical models

摘要： 为解决众多CAD软件不具备非圆曲线延伸功能，引入趋势外推原理，研究非圆曲线智能延伸技术。建立了二次和三次多项式曲线延伸、指数曲线延伸、戈珀兹曲线延伸三类智能延伸模型，分别给出趋势外推模型的识别与选择方法，可据曲线特征点合理选用。提供了智能延伸实例，阐述了智能延伸的步骤及方法，分析了它们的延伸精度，指出模型使用范围。解决了CAD软件共性核心难题，可应用于现有CAD软件的核心升级或二次开发，以增加或完善非圆曲线延伸功能。

关键词: 非圆曲线, 趋势外推法, 智能延伸, 数学模型