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High Quality Content by WIKIPEDIA articles! In Euclidean geometry, the intersection of a line and a line can be the empty set, a point, or a line. Distinguishing these cases, and finding the intersection point have use, for example, in computer graphics, motion planning, and collision detection. The number and locations of possible intersections between two lines and the number of possible lines with no intersections (parallel) with a given line are the distinguishing features of Non-Euclidean geometry. The entry titled Parallel postulate provides additional background on this topic.