中文摘要：

作为平面曲线统一数学模型，从微分几何的角度在理论上详细讨论了缓和曲线的数学特征，推导出曲线上任意一点的曲率、切线方向和位置坐标的计算式，其结果与此前相关文献是一致的，但思路更清晰。作为特例，还讨论了直线、圆曲线和完整的缓和曲线的曲率特性，研究了数值积分的坐标计算方法，具有重要的理论研究和实用意义。

英文摘要：

Transition curve, as a general plane curve model, is discussed in detail from the aspect of differential geometry theory in this paper, and further the formulae of curvature, tangent azimuth and coordinates are deduced, which is in accord completely with previous related papers, but with more clear thoughts. To be contrasted, the property of curvature about straight-line, circular arc and special transition curve are also summarized. At the end of paper, power-series and numerical integration solutions are proposed, which is of great significance in theory research and practice.