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 present an improved approach to the surface reconstruction of orebody from sets of interpreted cross sections that allows for shape control with geometry constraints. The soft and hard constraint rules based on adaptive sampling are proposed. As only the internal and external position relations of sections are calculated, it is unnecessary to estimate the normal directions of sections. Our key contribution is proposing an iterative closest point correction algorithm. It can be used for iterative correction of the distance field based on the constraint rules and the internal and external position relations of the model. We develop a rich variety of geometry constraints to dynamically control the shape trend of orebody for structural geologists. As both of the processes of interpolation and iso-surface extraction are improved, the performance of this method is excellent. Combined with the interactive tools of constraint rules, our approach is shown to be effective on non-trivial sparse sections. We show the reconstruction results with real geological datasets and compare the method with the existing reconstruction methods.
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.
To interpolate large drillhole data sets efficiently in implicit modeling of orebody, we optimize the solution of the RBF equation based on the two-level domain decomposition method. The solution performance is improved by balancing the two goals of the convergence rate and the iteration efficiency. The solution method converts the large domain into small subdomains which can be solved directly. The optimum division of subdomains can improve both the convergence of iteration and the efficiency of a single iteration, whereas the subdivision of a trivial subdomain leads the iteration failed to converge. For the efficiency of a single iteration, the kernel independent fast multipole method is used to calculate the matrix-vector product efficiently. Moreover, the initial solution of iteration and center reduction strategy are optimized for the dynamic updating of implicit surface. Combined with the preconditioned Krylov subspace method, the optimized solution method was implemented. The experimental results of several drillhole data sets show that the optimized solution method converges rapidly within a small number of iterations.
In this paper, we explore a new approach, a two-step surface reconstruction method to extract the target isosurface from a given implicit function efficiently. Our main contribution is that we improve the surface reconstruction process by accelerating the speed of evaluation using signed marching cubes. The basic strategy is to filter the invalid voxels that do not intersect with the target isosurface in a low-cost manner, and to evaluate the valid voxels that intersect with the target isosurface accurately. The improved signed marching cubes method consists of a rough evaluation step and an exact evaluation step. The coarse evaluation step evaluates the points of all voxels using the fast multipole method with a lower order. After the rough evaluation step, the voxels that intersect with the target isosurface are screened out. Then, the exact evaluation step evaluates the points of filtered voxels using the fast multipole method with a higher order. The experimental results show that, compared with the traditional marching cubes method, the improved reconstruction method reduces the amounts of calculation for invalid voxels that do not intersect with the target isosurfaces, which is useful to improve the efficiency of surface reconstruction.
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