In this paper we improve an efficient implicit surface reconstruction method based on the surface following method for the radial basis functions interpolant. The method balances the reconstruction efficiency and the evaluation efficiency in the process of surface following. The growing strategy of the surface following method combines both the evaluation and reconstruction processes. Based on the analysis of the black-box fast multipole method (FMM) operations, we improve the FMM procedures for single point evaluation. The goal is to ensure that one point evaluation of the method obtains an optimum efficiency, so that it can be efficiently applied to the voxel growing method. Combined with the single point FMM, we improve the voxel growing method without manually specifying the seed points, and the leaf growing method is developed to avoid a mass of redundant computation. It ensures a smaller number of evaluation points and a higher evaluation efficiency in surface following. The numerical results of several data sets showed the reliability and performance of the efficient implicit surface reconstruction method. Compared with the existing methods, the improved method performs a better time and space efficiency.
In this paper, according to the analysis of optimum circuits, we present an efficient ventilation network solution based on minimum independent closed loops. Our main contribution is optimizing the circuit dividing strategy to improve the iteration convergence and the efficiency of a single iteration. In contrast to a traditional circuit, a minimum closed loop may contain one or more co-tree branches but fewer high-resistance branches and fan branches. It is helpful in solving the problem of divergence or slow convergence for complex ventilation networks. Moreover, we analyze the dividing rules of closed loops and improve the dividing algorithm of minimum independent closed loops. Compared with the traditional Hardy Cross iteration method, the improved solution method has better iteration convergence and computation efficiency. The experimental results of real-world mine ventilation networks show that the improved solution method converges rapidly within a small number of iterations. We also investigate the influence of network complexity, iterative precision, and initial airflow on the iteration convergence.
In this paper, we introduce combination constraints for modeling ore bodies based on multiple implicit fields interpolation. The basic idea of the method is to define a multi-labeled implicit function that combines different sub-implicit fields by the combination operations, including intersection, union and difference operators. The contribution of this paper resides in the application of combination of more general implicit fields with combination rules for the implicit modeling of ore bodies, such that the geologist can construct constraints honoring geological relationships more flexibly. To improve the efficiency of implicit surface reconstruction, a pruning strategy is used to avoid unnecessary calculations based on the hierarchical bounding box of the operation tree. Different RBF-based methods are utilized to study the implicit modeling cases of ore bodies. The experimental results of several datasets show that the combination constraints are useful to reconstruct implicit surfaces for ore bodies with mineralization rules involving multiple fields.
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