Abstract: Based on the original geometrical definition of the convexity for planar parametric curve，the local and global convexity are discussed，and a few properties are obtained.In addition，the definition of inflection point is given，the relationship of local convexity and inflection points of planar parametric curve is discussed，a necessary and sufficient condition is presented for the distinguishable condition of inflection points.

Key words: local convexity, global convexity, inflection points, relative curvature

摘要： 依据参数曲线凸性的原始几何定义，讨论了参数曲线的局部凸和全局凸性，得到了参数曲线局部凸和全局凸的若干性质。给出了参数曲线的拐点定义，讨论了参数曲线的拐点与局部性之间的关系，导出了参数曲线拐点判别的充要条件及算法。

关键词: 局部凸性, 全局凸性, 拐点, 相对曲率