Constructing collision-free paths in Euclidean space is a well-known problem in computational geometry having applications in many fields that include robotics, VLSI, and covert surveillance. In this thesis, we investigate the development of efficient algorithms for constructing a collision-free path that satisfies directional and visibility constraints. We present algorithms for constructing monotone collision-free paths that tend to maximize the visibility of the boundary of obstacles. We also present implementation of some monotone path planning algorithms in Java Programming Language.
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