The Production of AVI Dynamic Images of Elliptic Cones and Elliptic Paraboloids

在常见二次曲面教学中，给定三元二次方程判断其曲面形状是一大难点，需要学生具备较强的空间想象能力，将方程与三维图形建立联系。传统的“板书 + 粉笔”教学方式存在局限，所绘静态图耗时且抽象，不利于学生理解。MATLAB凭借强大的绘图功能与程序设计技巧，可制作AVI格式动态图并直接插入PPT用于课堂教学。本文借助MATLAB编程，针对椭圆锥面和椭圆抛物面这两种常见且难区分的二次曲面展开教学探讨。从截痕法、伸缩变形法这两个维度实现AVI动态图制作，辅助课堂教学。让教学内容更生动形象，增强直观性，激发学生的积极性，有效提升学生的空间想象、分析及解决问题的能力，助力学生扎实掌握知识。In the teaching of common quadratic surfaces, determining the shape of a surface given a ternary quadratic equation is a major difficulty, which requires students to have strong spatial imagination and establish a connection between the equation and the three-dimensional graph. The traditional “blackboard + chalk” teaching method has limitations. The static graphs drawn are time-consuming and abstract, which is not conducive to students’ understanding. MATLAB, with its powerful drawing capabilities and programming skills, can create dynamic AVI format images and directly insert them into PPT for classroom teaching. This paper uses MATLAB programming to conduct teaching discussions on two common and difficult-to-distinguish quadratic surfaces: elliptic cones and elliptic paraboloids. The AVI dynamic images are created from two dimensions: the section method and the stretching and deformation method to assist classroom teaching. This makes the teaching content more vivid and intuitive, enhances the directness, stimulates students’ enthusiasm, effectively improves students’ spatial imagination, analysis and problem-solving abilities, and helps students master the knowledge solidly.