BSc. Thesis — Crowd Simulation

A mathematical model for terrain traversal built on differential geometry. The model evaluates paths on smooth height-map surfaces using cost functions derived from geometric properties — distance, surface normals, and heading directions. By varying the cost function, different traversal behaviors emerge: shortest path, easiest climb, or a weighted combination.

The continuous formulation is discretized into a weighted graph and solved with standard path-finding algorithms. Paths are then smoothed to produce natural-looking motion curves.

Implemented and evaluated in Houdini.