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Modern state of computer technologies allows a formulation and solutions new intricate problem which depends on construction of complex mathematical models and methods of their solution. Thus, when designing and building a visual model of thermal processes at welding turbine blades of aircraft engines, must be extremely accurate model the welding bath, the welding seam and region adjacent to them. Getting the exact solution of this problem requires simultaneous solution the whole complex of heat physical and geometrical problems which demand significant computing resources. This paper's main result is presenting a generalized effective parallel-and-recursive algorithm with the optimal bound of time complexity O(log2 N) which solves in unified manner the variety of interrelated geometrical problems for the construction of visual models of complex phenomena and processes.