Implicit 3D Orebody Boundary Modeling Based on Adaptive Finite Difference Method

Three-dimensional (3D) orebody boundary modeling primarily relies on spatial interpolation methods, such as radial basis functions (RBFs). However, these methods struggle with large datasets and require gradient or normal constraints for stable geometric extrapolation. This study proposes an adaptive finite difference implicit-modeling method, which avoids gradient information and can handle complex 3D orebody boundaries from large-scale, irregular datasets. We utilized difference operators for hanging and constrained octree nodes and applied adaptive density-based smoothing to reduce artifacts from sparse data, enabling complex boundary construction on nearly one million non-uniform control points. We used octree-based convolutional neural networks to fuse spatial features across octree levels, merging points with similar local geometries into the same finest-level cells. This enabled optimal adaptive octree mesh partitioning that accounts for spatial similarity among control points while controlling the total mesh count. Using this adaptive octree mesh, a finite difference scheme suitable for non-uniform mesh structures was constructed. The method outperforms traditional RBFs and uniform-grid finite difference methods in model accuracy, computational efficiency, and memory usage, exhibiting a robust performance across various data distribution patterns.