Large multi-agent systems such as crowds involve inter-agent interactions that are typically anticipatory in nature, depending strongly on both the positions and the velocities of agents. We show how the nonlinear, anticipatory forces seen in multi-agent systems can be made compatible with recent work on energy-based formulations in physics-based animation, and propose a simple and effective optimization-based integration scheme for implicit integration of such systems. We apply this approach to crowd simulation by using a state-of-the-art model derived from a recent analysis of human crowd data, and adapting it to our framework. Our approach provides, for the first time, guaranteed collision-free motion while simultaneously maintaining high-quality collective behavior in a way that is insensitive to simulation parameters such as time step size and crowd density. These benefits are demonstrated through simulation results on various challenging scenarios and validation against real-world crowd data.

Background: Clinical rating tools such as the electronic, clinician-graded facial function (eFACE) scale provide detailed information about aspects of facial functioning relevant to the assessment and treatment of facial paralysis. Past research has established that eFACE scores significantly relate to expert ratings of facial disfigurement. However, no studies have examined the extent to which eFACE scores relate to casual observers’ perceptions of disfigurement in facial paralysis. Methods: Casual observers (n = 539) were recruited at the 2016 Minnesota State Fair, and were shown short videos of facial expressions made by patients (n = 61) with unilateral facial paralysis. Observer ratings of disfigurement were recorded and related to eFACE scores (total and subscores) using mixed-effect regression models. Results: Patients’ eFACE scores were significantly related to observers’ disfigurement ratings, such that improved function (as indicated by a higher eFACE score) corresponded to a decreased perception of disfigurement. The resting face of patients, their total movement capability, and their involuntary movement through synkinesis all played a significant role in predicting the casual observers’ ratings. Conclusions: The results establish a clear connection between clinician eFACE ratings of facial function and casual observer judgments of disfigurement. In addition, the findings provide insight into which clinical aspects of facial dysfunction are most salient for casual observers’ perceptions of disfigurement. Such insights can help both patients and clinicians better understand the expected social implications of different clinical aspects of facial dysfunction.