Collision response

In the context of classical mechanics simulations and physics engines employed within video games, collision response deals with models and algorithms for simulating the changes in the motion of two solid bodies following collision and other forms of contact. t ^ = { v r − ( v r ⋅ n ^ ) n ^ | v r − ( v r ⋅ n ^ ) n ^ | v r ⋅ n ^ ≠ 0 f e − ( f e ⋅ n ^ ) n ^ | f e − ( f e ⋅ n ^ ) n ^ | v r ⋅ n ^ = 0 f e ⋅ n ^ ≠ 0 0 v r ⋅ n ^ = 0 f e ⋅ n ^ = 0 {displaystyle mathbf {hat {t}} =left{{egin{matrix}{frac {mathbf {v} _{r}-(mathbf {v} _{r}cdot mathbf {hat {n}} )mathbf {hat {n}} }{|mathbf {v} _{r}-(mathbf {v} _{r}cdot mathbf {hat {n}} )mathbf {hat {n}} |}}&mathbf {v} _{r}cdot mathbf {hat {n}} eq 0&\{frac {mathbf {f} _{e}-(mathbf {f} _{e}cdot mathbf {hat {n}} )mathbf {hat {n}} }{|mathbf {f} _{e}-(mathbf {f} _{e}cdot mathbf {hat {n}} )mathbf {hat {n}} |}}&mathbf {v} _{r}cdot mathbf {hat {n}} =0&mathbf {f} _{e}cdot mathbf {hat {n}} eq 0\mathbf {0} &mathbf {v} _{r}cdot mathbf {hat {n}} =0&mathbf {f} _{e}cdot mathbf {hat {n}} =0\end{matrix}} ight.} f f = { − ( f e ⋅ t ^ ) t ^ v r ⋅ t ^ = 0 f e ⋅ t ^ ≤ f s − f d t ^ (otherwise) {displaystyle mathbf {f} _{f}=left{{egin{matrix}-(mathbf {f} _{e}cdot mathbf {hat {t}} )mathbf {hat {t}} &mathbf {v} _{r}cdot mathbf {hat {t}} =0&mathbf {f} _{e}cdot mathbf {hat {t}} leq f_{s}\-f_{d}mathbf {hat {t}} &{ ext{(otherwise)}}\end{matrix}} ight.} j f = { − ( m v r ⋅ t ^ ) t ^ v r ⋅ t ^ = 0 m v r ⋅ t ^ ≤ j s − j d t ^ (otherwise) {displaystyle mathbf {j} _{f}=left{{egin{matrix}-(mmathbf {v} _{r}cdot mathbf {hat {t}} )mathbf {hat {t}} &mathbf {v} _{r}cdot mathbf {hat {t}} =0&mmathbf {v} _{r}cdot mathbf {hat {t}} leq j_{s}\-j_{d}mathbf {hat {t}} &{ ext{(otherwise)}}\end{matrix}} ight.} In the context of classical mechanics simulations and physics engines employed within video games, collision response deals with models and algorithms for simulating the changes in the motion of two solid bodies following collision and other forms of contact. Two rigid bodies in unconstrained motion, potentially under the action of forces, may be modelled by solving their equations of motion using numerical integration techniques. On collision, the kinetic properties of two such bodies seem to undergo an instantaneous change, typically resulting in the bodies rebounding away from each other, sliding, or settling into relative static contact, depending on the elasticity of the materials and the configuration of the collision. The origin of the rebound phenomenon, or reaction, may be traced to the behaviour of real bodies that, unlike their perfectly rigid idealised counterparts, do undergo minor compression on collision, followed by expansion, prior to separation. The compression phase converts the kinetic energy of the bodies into potential energy and to an extent, heat. The expansion phase converts the potential energy back to kinetic energy.