Motivated by questions on orthogonality of isometries, we present a new construction of the conformal model of the 3D space using just elementary linear algebra. In addition to pictures that can help the readers to understand the conformal model, our approach allows to obtain matrix representation of isometries that can be useful, for example, in applications of computational geometry, including computer graphics, robotics, and molecular geometry.

中文翻译：

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3D空间共形模型中等轴测图的正交性

受关于等距性正交性问题的启发，我们提出了仅使用基本线性代数的3D空间共形模型的新构造。除了可以帮助读者理解共形模型的图片外，我们的方法还可以获取等距的矩阵表示形式，这些形式在例如计算机图形学，机器人技术和分子几何学等计算几何学的应用中很有用。