摘要
计算机辅助教学(Computer Aided Instruction ,简称CAI)是在计算机的辅助下进行各种教学活动、开展教学训练的方法与技术。动态几何画板系统是众多CAI软件中的一种主要面向数学教学的软件系统。
本文首先介绍了动态几何画板系统的研究背景和国内外发展状况,提出了当前这类软件中存在的一些问题,然后介绍了《三维动态几何画板》的设计与实现。
使用《三维动态几何画板》,可以对三维几何模型进行编辑和修改,并提供视点变换、动画、文本等等功能更加清楚的展示动态几何问题,为数学课堂教学提供了更加丰富、生动的数形结合的教学情境。
这套系统由三个模块组成,它们分别为:数学库、几何模型库、场景管理。其中,数学库是系统实现的基础,系统的其它模块都是在数学库的基础上研究和开发的,数学库包括:数值计算、向量、矩阵、四元数。几何模型库是系统的核心,也是本文所要论述的重点。几何模型库包括几何模型和几何计算,几何模型包括点、线、面、平面图形、空间几何体等系列几何元素,几何计算包括几何元素之间进行相交、相切判断、几何造型、几何分析等等算法,本文对几何模型库要提供的几何模型和重要的几何算法进行了详细的介绍。场景管理对几何模型和它们之间的动态关系进行管理。
本文还对系统的几何模型、数学库、场景管理以及各个功能的实现进行了比较详细的介绍。
Computer aided Instruction is the method and technology of proceeding all kinds of teaching activities, developing teaching training in the assistance of computer. Dynamic Geometric Drawing Board system is the one of the main software system oriented at mathematical teaching.
The article firstly introduces the studying background of Dynamic Geometric Drawing Board system and the developmental situation in domestic and abroad, puts forwards the problems existed in the recent sort of the software, and then introduces the design and realization of the three-dimensional Dynamic Geometric Drawing Board.
People can edit and revise the three-dimensional Geometric models by using of the three-dimensional Dynamic Geometric Drawing Board, providing view transforming, cartoon, text and other functions in order to delay the problems of dynamic Geometric, and to provide more colorful and vivid teaching situation for the mathematical classroom.
The set of system is made up of three modules: mathematical library, Geometric modular library, the controlling of situation, among which the mathematical library is the basis of the realization of the system, and it is based on the mathematical library that other modules are analyzed and developed. The mathematical library concludes: numeral calculation, vector, matrix and the quaternion. Geometric modular library is the core of the system and is also the emphasis of the article. Geometric modular library concludes Geometric module and Geometric calculation; Geometric module concludes point, line, plane, plain figure, and spatial geometric body; Geometric calculation concludes the intersection, judgment among the Geometric elements, the Geometric modeling and the Geometric analyzes. The article mainly introduces the Geometric modules and Geometric calculation of the Geometric modular library. How the controlling situation controls the Geometric modules and the relationships among them.
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