一种面向三维地质剖面的形体表面重构算法

A Surface Reconstruction Algorithm for Geological Profile Data in 3D Space

在地学建模领域,三维表面形体重构方法大多是基于二维平行轮廓线,但有时会有既不平行也不交叉的剖面出现。为此,该文基于最短对角线法的基本思路,提出了一种面向地质剖面的三维空间轮廓线表面形体重构方法。该方法从平行剖面拓展到任意排列的剖面,在实现三维空间相关运算的基础上,通过基于均匀插值的三维非凸变换方法对原算法进行了改进,既适用于平行和非平行地质剖面的三维形体重构,同时又能处理真实地质剖面可能出现的复杂情形,譬如轮廓线不对中、轮廓线上点分布不均匀、轮廓线非凸等。最后,利用矿区真实地质剖面实现了形体重构,并通过与利用三维建模软件GOCAD得到的结果进行比较,验证了该算法对复杂地质体重构的实用性和健壮性。

From the existing researches of 3D-reconstruction we can find that most reconstruction algorithms are based on 2D planar contours and are widely applied in medical images and geological modeling. But in geological engineering and the modeling practice, it cannot always guarantee the geological cross-sections are parallel or free of intersection. Inspired by the shortest diagonal method, in this paper, a 3D geological surface reconstruction method tailored for geological profiles is presented, which is expanded from 2D to 3D space, not only allows the reconstruction from parallel geological cross-sections, but also achieves good performance when given arbitrary cross-sections. In this method, uniform interpolation is applied to passivate the sharp edges while maintaining the accuracy, and a new non-eonvex contours transformation algorithm is proposed to avoid the crossings in which commonly-used recursive operation is discarded and the complexity of algorithm is correspondingly reduced. This method is more adaptive and robust to handle complex scenarios existing in the geological sections such as non-aligned contours, non- convex contours and contours of uneven vertices, which is validated with the surface reconstruction test with practical geological profile data. The comparison with the commercial 3D modeling software GOCAD further shows good progressiveness and practicability of the method.