Written in Python, Manim is an animation engine for creating beautiful explanatory math videos. It was originally created by Grant Sanderson of 3Blue1Brown. Today, Manim has a community version called ManimCE. Articles posted in here are more of the community version of Manim.
In this post, we extend the idea of cycloidal curves to a more complex path: the parabola. Using the tangent angle, arc length, and no-slip condition, we derive the parametric description of the tracing point and show how these formulas can be translated into Python code for accurate Manim visualization.
The purpose of this post is to systematically derive the corresponding parametric equations and implement them in Python for visualization using Manim. The goal is not only to understand these curves analytically but also to see them come alive through animation.
The sphere is of radius 4 units, it is hardcoded to the parametric equations. The parametric equations are as follows:
If you check the code, you can see that the latitude and longitude of the sphere are reoriented. The reason is for the sphere to fit the Manim's camera settings.
The orientation of the camera was done by trial and error until I found a view that I wanted.
A cylindrical surface of radius radius 4 and axis on the xz-plane and at a distance of 1.5 units from the xy-plane. The thickness of the cylinder is 4 units and the curvilinear length is half the circle.
Below is the Python code for the logo. The image generated by Manim is transparent PNG file and the colors are suitable for dark background.
