This work presents a method for drawing Virtual Reality panoramas by ruler and compass operations. VR panoramas are immersive anamorphoses rendered from equirectangular spherical perspective data. This data is usually photographic, but some artists are creating hand-drawn equirectangular perspectives to be visualized in VR. This practice, that lies interestingly at the interface between analog and digital drawing, is hindered by a lack of method, as these drawings are usually done by trial-and-error, with ad-hoc measurements and interpolation of pre-computed grids, a process with considerable artistic limitations. I develop here the analytic tools for plotting all great circles, line images and their vanishing points, and then show how to achieve these constructions through descriptive geometry diagrams that can be executed using only ruler, compass, and protractor. Approximations of line images by circular arcs and sinusoids are shown to have acceptable errors for low values of angular elevation. The symmetries of the perspective are studied and their uses for improving gridding methods are discussed.

中文翻译：

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使用标尺，指南针和量角器绘制等角VR全景图

这项工作提出了一种通过标尺和罗盘操作绘制虚拟现实全景图的方法。VR全景图是从等矩形球体透视数据渲染的沉浸变形。这些数据通常是摄影的，但是一些艺术家正在创建手绘的等角透视图，以便在VR中可视化。有趣的是，这种做法位于模拟和数字绘图之间的界面上，但由于缺乏方法而受到阻碍，因为这些绘图通常是通过反复试验，临时测量和预先计算的网格插值来完成的，具有相当大的艺术局限性的过程。我在这里开发了用于绘制所有大圆，直线图像及其消失点的分析工具，然后展示了如何通过只能使用标尺执行的描述性几何图形来实现这些构造，指南针和量角器。对于圆角仰角较小的值，圆弧和正弦曲线表示的线图像近似值具有可接受的误差。研究了透视图的对称性，并讨论了它们在改进网格化方法中的用途。