Presenting a surface of revolution by using orthonormal projection with the TikZ package

Abstract

Orthonormal projections emerge from subjecting 3-dimensional vectors to orthogonal transformations and projecting them to 2 dimensions. They are not to be confused with the perspective projections, which are more realistic. Orthonormal projections may be thought of a limit of perspective projections at large distances, where large means that the distance of the observer is much larger than the dimensions of the objects that get depicted. The paper will calculate the critical points of light on revolution surfaces. After that, the TikZ library in the LaTeX compiler is used to represent cylinders, cones, and their curves accurately. Thereby, readers can draw most of the figures representing the revolutions in Mathematical subject, at the high school level.