Research On Methods Of Calculating Minkowski Sum Of Polyhedra Based On Redundant Filtering

As an important branch in the field of computational geometry research, Minkowski sum has great significances in the aspects of theory and application research. Some research results have been widely applied in robotics, dynamic simulation and computer graphics etc. In recent years, the methods of calculating the Minkowski sum of polyhedra have always been attracting extensive attention. However, there are still deficiencies in terms of computational efficiency, suitability and robustness. Based on the research status of Minkowski sum and comprehensive analysis of key points in the methods of calculating Minkowski sum of polyhedra, this paper has further studied the methods of calculating the Minkowski sum of polyhedra to improve the computational efficiency, suitability and accuracy.Firstly, in view of the problem of repetitive computation in the process of Minkowski sum calculation of convex polyhedra, a new method of calculating Minkowski sum of convex polyhedra based on redundant filtering is put forward. According to the constructing theory of the Minkowski sum of polyhedra, the redundant edges and redundant surfaces are defined. The algorithm for calculating the Minkowski sum of convex polyhedra is designed through the redundant identification and filtering strategies. The simulation experiments are conducted to verify the proposed algorithms.Secondly, aiming at reducing the complexity in the process of subdivision and non-practicability in calculation, this paper proposes a subdivision method of concave polyhedra based on threshold. Based on the convex decomposition theory of polyhedra, a valid subdivision strategy for Minkwski sum calculation of concave polyhedra is given through introducing the concept of subdivision measurement, relative subdivision and subdivision threshold. The subdivision algorithm with threshold value is designed and verified by simulation.Thirdly, in view of the existing problems such as low efficiency and robustness in the process of merging and the sub-Minkowski calculation of polyhedra in calculating Minkowski sum of concave polyhedra at present, this paper has proposed a new method of calculating Minkowski sum of concave polyhedra based on redundancy filtering and threshold subdivision. Based on the calculation framework of Minkowski of polyhedra: decomposition, summation and merger, the method for concave polyhedra makes use of the threshold subdivision strategy and combines with the redundant filtering method to design the algorithm of calculating Minkowski sum of concave polyhedra by using convex convexity judging principle and convex polyhedra merging optimization strategy.The validity of the method is tested through simulation experiments.Finally, in view of the existing geometric defects and the low efficiency in the methods of calculating Minkowski sum of rotating polyhedra. By introducing the concept of critical information identification, this paper puts forward a kind of method of calculating Minkowski sum based on redundant filtering method of convex polyhedra and critical information. The method applies the rotating polyhedra Gaussian mapping and the corresponding relationship between mapping and rotating.The method of calculating Minkowski sum of ratating convex polyhedron is designed through critical information and redundant filtering strategy.The validity of the method is tested through simulation experiments.