Abstract
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.
Highlights
Reconstructing a surface from a series of geological sampling points is a well-studied problem in geological modeling, computer graphics, and reverse engineering, etc
We present a two-step surface reconstruction method to extract the implicit surface for the radial basis functions (RBF) method without specified seed voxels efficiently
Based on the above analysis, we present the signed marching cubes method (SMC) to accelerate the speed of surface reconstruction combined with the signed fast multipole method
Summary
Reconstructing a surface from a series of geological sampling points is a well-studied problem in geological modeling, computer graphics, and reverse engineering, etc. To visualize the interpolated implicit function, the implicit surface reconstruction method [5–7] should be used to extract the target isosurface of the interpolated implicit function. There are many implicit surfaces reconstruction methods used to extract isosurfaces, including the marching cubes (MC) methods [10–16], the marching tetrahedra (MT) methods [17,18], and the Delaunay triangulation methods [19–21]. Based on the given implicit function, the basic idea of the marching cubes method is to triangulate the sampling points by evaluating the corresponding function values. The target isosurface is extracted by triangulating the sampling points to approximate the target isosurface based on the eight vertices of each cube and a predefined lookup table. Raman et al [23] extended the lookup table, which differentiates scalar values equal to the isovalue from scalar values greater than the isovalue, in order to improve the quality of reconstructed mesh. For the correctness of the mesh topology, there are several methods [24] presented to resolve the ambiguity of the isosurface for any cube configuration
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