collisionswhere

Collisionswhere is a term used in discussions of collision analysis to denote the set of space-time points where collision events occur between moving objects. The concept emphasizes the geographic or spatial aspect of a collision, in contrast to temporal or kinetic descriptions. There is no universally standardized definition, and the term often appears in speculative, methodological, or glossary contexts to distinguish location-based hazard assessment from other perspectives.

Formally, in a simple kinematic model where each agent i has a trajectory r_i(t) and a footprint (such as a radius), a collision occurs when the distance between two agents falls below the sum of their footprints. Collisionswhere refers to the collection of space-time coordinates (x, t) that satisfy this collision condition for some pair of agents. In practice, many analyses discretize time and compute approximate collisionwhere sets, identifying hotspots rather than exact continuous solutions.

Applications for collisionswhere include traffic safety analysis, urban planning, robotics, and simulation visualization. By mapping where collisionsare likely to occur, researchers can target interventions, optimize routing, or plan safer trajectories. The concept helps separate analysis by location from other metrics such as time-to-collision or impact frequency, enabling distinct visualizations and decision frameworks.

Computationally, deriving collisionswhere requires high-quality trajectory data and careful treatment of uncertainty, sampling rates, and measurement error. It also faces challenges in distinguishing true collisions from near-misses and in extending from pairwise to multi-agent interactions. While related to collision detection and event-driven simulation, collisionswhere remains a less standardized term and may be used variably across disciplines.