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This paper examines the relation between the observation of cartographic lines and locations distinguished by critical points. It specifically assesses the results of an experiment designed for this purpose. The method applied in order to measure the subjects' performance is the eye movement analysis. The application of eye tracking methodology provides the opportunity to inspect the human gaze. In this experiment, three lines studied in Marino's research, Thapa's test line and the coastline of Peristera Island compose the visual scenes observed. Subjects are asked to scan these lines for a predefined duration. The regions of the visual scenes where subjects fixate, are revealed through data analysis and visualizations, composed of fixations' locations and heatmaps respectively. The results deriving from eye movement analysis are tested in locations distinguished by critical points. The results of the study reveal the existence of relation between fixation points and locations of critical points.