大比例尺成矿预测中高精度立方格预测模型快速构建算法

立方格模型是一种常用的大比例尺三维可视化预测模型。在计算机三维图形学中，立方格模型又被称为块段模型，该模型比较适合表示非均匀体数据的空间分布，在矿山大比例尺深边部成矿预测、三维反演、矿山储量估算等领域得到广泛应用。目前，构建高精度立方格预测模型的一般方法是将已有地质体、地表、构造等三维地学对象进行栅格化。针对栅格化过程中遇到的2个关键问题，即体形的空间形态复杂和需要计算的长方体数量大（≥10⁶），应用三维网格分割与种子填充（flood-fill）思想实现快速构建三维复杂体的立方格模型算法，其时间复杂度为O(n)。该算法的主要优点是花费相对小的空间代价高效地解决大量三角面与长方体的相交和空间查询计算问题。同时，应用该算法得到的立方格预测模型的长方体被划分为边界、内部和外部，便于开展预测要素综合模拟、矿山储量计算以及三维空间分析等其他后续地质应用。特别是将种子填充思想应用于高精度立方格模型构模，具有一定的创新性。本算法不仅适用于矢量体的快速栅格化，也适用于空间非自相交曲面（例如数字高程模型）的快速栅格化。

A Rapid Modeling Algorithm of High Precision Block Model on Large Scale Mineral Assessment in Three Dimension

Cubic model is one of methods for predicting blind orebodies. It is called block model in 3D computer graphics. Block model is one of the most important expressions and calculation model for geological body and it is suitable for expressing non-uniform distributed data. Block model is widely applied in 3D geophysical inversion, exploration and mineral assessment, etc. Currently, the general method of block modeling of complex geological body is to convert the surface model of a geological body to its block model. However, there are two key problems during the general process. One is numerical intersections calculation between triangles and voxels (cuboids)（≥10⁶）. The other is search of internal cuboids in complex geological body. In order to deal with the problems, the authors proposed a rapid block-modeling algorithm from complex geological body by applying uniform plane subdivision and flood-fill algorithms, whose time complexity is O(n). It is creative for applying two-dimension algorithm idea to successfully construct 3D block model. Besides, the algorithm is suitable for constructing block model from arbitrary surface in 3D except for self-intersection surfaces. At the end of the paper, the time complexity analysis and experiment are carried out and the result shows that the method is efficiency and general.