Construction of robust geometric computation algorithms for time-varying spaces

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Robust geometric algorithms were constructed in three examples of time-varying spaces. First, algorithms for computing shortest paths for a boat in a time-varying flow field was constructed, and were applied to rescue-boat path planning and computation of rescue-boat Voronoi diagrams. Second, mathematical models of subjective depth perception was constructed and was applied to the design of new illusions named impossible motions. Third, a robust method was constructed to find a cutter path that can avoid vibration due to the change of the material shape.