A Ray Intersection Algorithm for Fast Growth Distance Computation Between Convex Sets

Researchers Akshay Thirugnanam and Koushil Sreenath have published a breakthrough algorithm for computing growth distance between convex sets, a critical problem in robotics and computational geometry. Unlike traditional minimum distance calculations, growth distance provides a unified measure for determining when two sets will intersect when scaled about center points. The algorithm reduces the problem to a ray intersection problem on the Minkowski difference set, then solves it through iterative construction of inner and outer polyhedral approximations.

The implementation demonstrates several key properties including primal and dual feasibility and monotone convergence, making it mathematically robust for real-world applications. Extensive benchmark results show the open-source implementation achieves state-of-the-art performance across various convex set types, significantly outperforming existing methods in both speed and accuracy. The algorithm's efficiency comes from its clever reduction of the growth distance problem to ray intersection, avoiding computationally expensive operations required by previous approaches.

Practical applications in robotics are already emerging, with the algorithm enabling faster motion planning and more efficient rigid-body simulation. By providing rapid growth distance computation, robots can make real-time decisions about collision avoidance and path planning, particularly important for autonomous systems operating in dynamic environments. The research represents a substantial advance in computational geometry with immediate implications for robotics development and simulation technology.