Evading equilateral triangles without a map

Consider an arrangement of equilateral non-overlapping translated triangles in the plane and two points S and T so that the segment ST is parallel to a side of each of the triangles. Assume one needs to navigate from point S to point T by evading the triangular obstacles without any previous knowledge of the location of the obstacles. The navigator becomes aware of a triangle once it is contacted along the path. The given algorithm enables the navigator to reach the target point T by a path with length less than 3d(1 + 2 d2 ), where d is the length of ST.

• Type: Conference
• Year: 2010
• Where: CCCG
• Authors: Braxton Carrigan
• Keywords: CCCG 2010, Computational Geometry, Non-overlapping Translated Triangles, Segment St, Triangular Obstacles