论文标题
行人运动的时空度量
Spacetime metric for pedestrian movement
论文作者
论文摘要
本文将通过定义时空度量来展示行人运动的模型。该模型考虑了通过定义适当的度量标准的行人运动（例如障碍，墙壁和其他行人）的有效因素。实际上，影响行人运动的周围环境会改变平坦（欧几里得）的时空度量，因此是通往其目的地的最短路径。这种变化就是这样，行人在环境中的任何时刻和时刻都有不同的时间感觉。基于这种感觉，他们调整了通往目的地的路线，以便在弯曲的时空中行驶的最短路线，该路线跟随了大地测量。贡献是：1。定义行人运动的时空度量。2。可视化几个时间段的时空几何形状3。在行人的时间感觉方面引入一个称为时间因素及其物理含义的参数。根据本文的表述，行人在每个位置和时刻的时间都有不同的时间，而时间因素则衡量了这种时间的感觉。 4。提出一个具有适用于数据同化方法的微分方程的简单模型，同时保留碰撞避免行为的基本特征。
This paper will present a model for pedestrian motion by defining a spacetime metric. This model considers the factors that are effective in the movement of pedestrians (such as obstacles, walls and other pedestrians) by defining a proper metric. In fact, the surrounding environment that affects the motion of pedestrians changes the flat(Euclidean) spacetime metric and, therefore, the shortest possible path to their destination. This change is such that pedestrians have a different feeling of time at any point and moment in the environment. Based on this feeling, they adjust their route to the destination so that they travel the shortest possible route in curved spacetime, which follows a geodesic. The contributions are :1. Defining spacetime metric for pedestrian movement.2. Visualizing the spacetime geometry for several timesteps.3. Introducing a parameter called the time factor and its physical meaning in terms of the pedestrian feeling of time. According to this paper formulation, pedestrians feel time differently at each position and moment, and the time factor measures this feeling of time. 4. Proposing a simple model with differential equations suitable for data assimilation methods while preserving the essential feature of collision avoidance behaviour.
