Real-Time Local Unfolding for Agents Navigation on Arbitrary Surfaces

Agents path planning is an essential part of games and crowd simulations. In those contexts they are usually restricted to planar surfaces due to the huge computational cost of mapping arbitrary surfaces to a plane without distortions. Mapping is required to benefit from the lower computational cost of distance calculations on a plane (Euclidean distance) when compared to distances on arbitrary surfaces (Geodesic distance). Although solutions have been presented, none have properly handled non-planar surfaces around the agent. In this paper we present mesh parametrization techniques to unfold the region around the agent allowing to extend to arbitrary surfaces the use of existing path planning algorithms initially designed only for planar surfaces. To mitigate the high computational cost of unfolding the entire surface dynamically, we propose pre-processing stages and massive parallelization, resulting in performances similar to that of using a planar surface. We also present a GPU implementation schema that permits a solution to be computed in real-time allowing agents to navigate on deformable surfaces that require dynamic unfolding of the surface. We present results with over 100k agents to prove the approach practicality.