Abstract: Automatic differentiation is a technique to evaluate the derivatives of a function defined by a computer program.This paper combines automatic differentiation technique with Taylor method and applies them into the subdivision based implicit curve plotting algorithm.A comparison of this new method with other two traditional methods is conducted which shows that the new method is more accurate.

Key words: automatic differentiation, implicit curve, Taylor method

摘要： 自动微分是用于计算多变量函数的导数和偏导数的一种微分技术，在给定一个多变量光滑函数值的程序代码后，可以很容易地利用自动微分来实现有关导数和偏导数的精确计算。将自动微分技术与泰勒方法相结合应用到计算机图形学领域隐式函数曲线绘制的细分算法中，并与未使用自动微分技术前的隐式曲线绘制方法作比较和分析，展示了自动微分方法在绘制隐式曲线方面的优势。

关键词: 自动微分, 隐式曲线, 泰勒方法