随着数字技术的飞速发展，口腔正畸的方式越来越现代化，利用计算机构建牙齿的3D模型进行牙齿矫正的技术也在不断提高，开发3D牙齿模型的有关算法具有重要的实用价值。本文主要研究基于STL文件的3D牙齿模型的数学建模，给出了一种牙龈轮廓线的自动识别算法，对算法和数据结构进行了优化、并通过实例验证了算法的可行性和有效性。

With the rapid development of digital technology, orthodontic technique are increasingly modern, the technology of constructing 3D models of teeth by computer is constantly improving. Developing algorithms for 3D models of teeth is of great value. This paper mainly carries on the mathematical modeling of 3D models of teeth based on STL file. It presents an automatic recognition algorithm of gingival contour line, optimizes the algorithm and the data structures and verifies the feasibility and effectiveness of the algorithm by an example.