Visual Analysis of Billiard Dynamics Simulation Ensembles

Abstract. Mathematical billiards assume a table of a certain shape and dynamical rules for handling collisions. Some trajectories exhibit distinguished patterns. Detecting such trajectories manually for a given billiard is cumbersome, especially, when assuming an ensemble of billiards with different parameter settings. We propose a visual analysis approach for simulation ensembles of billiard dynamics based on phase-space visualizations and multi-dimensional scaling. We apply our methods to the well-studied approach of dynamical billiards for validation and to the novel approach of symplectic billiards for new observations.