Visualizing and gauging collision risk

Abstract

We propose a new definition of collision risk that we call projective risk that is based on human perception.We showhowvarious collision scenarios can be modelled in a unified manner on the Riemann Sphere using projective and hyperbolic geometry. From this we show how a practical gauge for risk can be developed that we call the Risk Watch. Lastly, we show how the general problem of ship collision risk can be modelled using projective geometry and the cross ratio.