A Strange But Elegant Approach to a Surprisingly Hard Problem - GJK Algorithm

Explore the ingenious Gilbert Johnson Keerthi (GJK) algorithm for detecting collisions between complex objects in this 32-minute video. Delve into the fundamental concepts of convexity, Minkowski sums and differences, support functions, and simplexes. Follow the journey from problem introduction to full implementation of the 2D GJK algorithm, gaining valuable problem-solving techniques along the way. Discover how this clever solution has significantly impacted robotics, control, and computer graphics fields. Examine key questions, including point origin determination and line and triangle cases. Conclude with a recap and brief discussion of the original GJK paper, leaving with a deeper appreciation for the algorithm's elegant approach to a surprisingly challenging problem.

Introducing the Problem
Convexity
Infinite Point Perspective
Minkowski Sums and Differences
Triangles inside Minkowski Differences
Simplexes
Support Functions
Core GJK Algorithm: Broad Perspective
Remaining Key Questions
How to determine if a point passed the origin?
The line case
The triangle case
GJK Implementation
Recap and quick note about original GJK paper