Geodesic
A Study of Paths Formed by Directed Arcs and Line Segments
Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 207-218.

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We study paths formed by directed arcs and line segments in the real plane R2. The central angle and radius of the arc that we consider are π/4 and 1, respectively, and the length of the line segments is 1. We are interested in the properties of the paths that are formed by these elements. We derive the conditions that determine which locations can be reached with these paths, and a method for constructing a path to an arbitrary location within a specified distance tolerance. We also show that the number of elements in a closed path is even. Further, we show that any open path can be closed by connecting eight or fewer identical paths.
Classification : 51M04, 68U05
Mots-clés : Path, arc, line segment 
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     title = {A {Study} of {Paths} {Formed} by {Directed} {Arcs} and {Line} {Segments}},
     journal = {Journal for geometry and graphics},
     pages = {207--218},
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     number = {2},
     year = {2018},
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J. Mitani . A Study of Paths Formed by Directed Arcs and Line Segments. Journal for geometry and graphics, Tome 22 (2018) no. 2, pp. 207-218. http://geodesic.mathdoc.fr/item/JGG_2018_22_2_JGG_2018_22_2_a4/