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Dynamic Path Planning with Regular Triangulations

Brož P., Zemek M., Kolingerová I., Szkandera J.

Machine Graphics and Vision

2014

Vol. 23, No. 3/4

119--142

Path planning is a well known problem that has been extensively studied in many scientific disciplines. In general, it defines a task of finding a path between two given spots in an abstract environment so that the path satisfies certain criterion of optimality. Although there are many methods solving this objective, they usually assume the examined space does not change in runtime. Modern applications, however, do not have to meet these requirements, especially in case of virtual reality or computer games. Therefore, we propose a general model for real-time path planning in dynamic environment where the obstacles can nondeterministically appear, disappear, change the position, orientation or even shape. The model uses a triangulation for dynamic space subdivision among bounding spheres of the obstacles and a heuristic algorithm to repair an already found path after any change of the scene. The presented solution is the first one using regular triangulation. At the price of the suboptimal result, it provides an efficient and fast way to plan a path with the maximal clearance among the moving and changing obstacles. In comparison to raster based techniques and methods using the Delaunay triangulation (Voronoi diagram), it requires less time to preprocess and generates paths with a larger clearance.

Phase diagram of the Ti-V-C system at 1000 and 1200 C

Picha R., Kroupa A., Brož P.

Archives of Metallurgy

2001

Vol. 46, iss. 2

139-144

The ternary Ti-V-C system was studied experimentally at 1000 and 1200°C. Phase diagram data for this system and relevant subsystems has been collected and theoretical assessment was caried out. New thermodynamic parameters in Hillert-Staffansson model were assessed. Experimental results, both own and taken from literature were compared with calculated phase diagrams in order to support and verify suggested data. Reasonable agreement was obtained between the calculation and the experiments.

Zbadano doświadczalnie układ Ti-V-C w temperaturach 1000 oraz 1200°C. Zebrano i krytycznie opracowano dane dotyczące tego układu oraz składowych układów podwójnych. Określono parametry termodynamiczne w modelu Hillerta-Staffanssona. W celu weryfikacji danych porównano obliczony wykres fazowy z rezultatami badań własnych i z literatury. Stwierdzono dobrą zgodność pomiędzy rezultatami z obliczeń oraz z badań.