KamiWaAi-基于欧氏空间Cl（4，1）共形模型的Java交互式三维草图
KamiWaAi - Interactive 3D Sketching with Java Based on Cl(4,1) Conformal Model of Euclidean Space
摘要：
本文介绍了新的交互式Java素描软件KamiWaAi，最近开发的福井大学。它的图形用户界面使用户没有任何数学或计算机科学的知识，做完整的三维"图纸"在屏幕上。可以通过在屏幕上拖动其点来交互地重塑所得到的构造。编程方法是新的。KamiWaAi将点、线、圆、球体等几何对象直接实现为同名的软件对象（Java类）。这些软件对象是在保形几何代数中数学定义和操作的几何实体，结合了原点、三维空间和无穷大的五个维度。简单的几何产品在这个代数表示几何工会，交叉，任意旋转和平移，投影，距离等，以减轻坐标自由和矩阵自由实现这一基本的几何产品，一个新的代数三个层次的方法。最后给出了新的GeometricAlgebra软件包的Java类及其相关方法。KamiWaAi可供免费互联网下载。关键词：几何代数，共形几何代数，几何演算软件，几何代数，Java软件包，交互式3D软件，几何对象
英文摘要：
This paper introduces the new interactive Java sketching software KamiWaAi, recently developed at the University of Fukui. Its graphical user interface enables the user without any knowledge of both mathematics or computer science, to do full three dimensional "drawings" on the screen. The resulting constructions can be reshaped interactively by dragging its points over the screen. The programming approach is new. KamiWaAi implements geometric objects like points, lines, circles, spheres, etc. directly as software objects (Java classes) of the same name. These software objects are geometric entities mathematically defined and manipulated in a conformal geometric algebra, combining the five dimensions of origin, three space and infinity. Simple geometric products in this algebra represent geometric unions, intersections, arbitrary rotations and translations, projections, distance, etc. To ease the coordinate free and matrix free implementation of this fundamental geometric product, a new algebraic three level approach is presented. Finally details about the Java classes of the new GeometricAlgebra software package and their associated methods are given. KamiWaAi is available for free internet download. Key Words: Geometric Algebra, Conformal Geometric Algebra, Geometric Calculus Software, GeometricAlgebra, Java Package, Interactive 3D Software, Geometric Objects
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
