Mathematics

Elliptical Orbit Geometry and Mechanics

This post explains the mathematical principles and dynamics of elliptical orbits in celestial mechanics. To fully grasp how planets move and where they are at any given time, it begins by introducing the concept of planetary orbits as ellipses, following Johannes Kepler’s first law of planetar...

Spherical Harmonics Visualizer

This article introduces Spherical Harmonics (SH) and explains their mathematical foundation and applications. It covers how SH functions are used to represent data on spherical surfaces, particularly in computer graphics, including 3D Gaussian Splatting field. The interactive demo allows users...

A Derivation of Depth Filter

The depth filter is a useful component in monocular camera visual odometry systems, such as SVO (Semi-Direct Visual Odometry) 1 2. It is designed to estimate depth values from a sequence of images captured by a single camera. The filter operates under the assumption of Gaussian measurement noi...