The topic of the paper is the problem of marine traffic control. A model of a relative motion of two vessels is considered. Marine traffic control is an exceptionally large scientific and technical challenge. In practice, such control is implemented by the onshore vessel traffic systems (VTSs), i.e., by specialized companies, whose main task is to prevent dangerous situations, such as ship collisions. Estimation of the parameters of the path of the motion of each vessel (coordinates, velocity, etc.) and their extrapolation are the methodological basis for recognition of the dangerously close approach of vessels. If the vessels are identified to be approaching each other dangerously, the traffic control system generates an alarm and recommendations to modify their motion paths. The control decision, which ensures the traffic safety, depends on a number of factors: the velocity of the vessels, the distance between them, their size, maneuverability, and the characteristics of their paths. The prediction of the shipping traffic always has an element of uncertainty, which requires a formalization of the verbal concept of a "dangerous situation" with the identification of different danger levels such as "very dangerous," "dangerous," and "safe." The danger levels are determined on the basis of the experience and navigation practice. This approach allows the ship driver and the coastal VTS operator to control their actions: to make different types of decisions in the situations with different danger levels and, thereby, to reduce the degree of uncertainty in making specific decisions. This paper is devoted to the study of a collision avoidance system for ships, which makes it possible to detect dangerous situations and estimate the danger level by a continuous value using the ideas of the fuzzy logic systems. The paper introduces a new approach to displaying information on targets. The proposed display visualizes three types of information: targets' motion parameters (typical for target tracking), combinations of the own course and speed, of colliding with those targets (typical for Collision Threat Parameters Area display by Mitrofanov and Degree, Lefevre model) and combinations of the own course and speed, which in this case are not compliant with the fuzzy logic risk assessment systems (based on the ships' motion parameters). A superposition of the last two types of data enables a navigator to quickly choose a collision avoidance maneuver, which would be sufficient. Additionally, the displayed data may be filtered on the basis of the remaining Time To Collision (TTC), so that the navigators can concentrate on the direct threats. The paper includes a description of the proposed visualization technique, as well as examples of the visualized data for some encounter situations in Nakhodka Bay.