Algorithm for three-dimensional curved block cutting analysis in solid modeling

Abstract

Geological solid modeling has been widely studied and applied in geological analysis relevant to rock engineering, mining, geophysics, geo-hazard assessment, and geographic information systems (GIS). The discontinuities and other faces that may be planes or surfaces need to be fully considered in an attempt to yield solids formed by the mutual intersection and cutting between faces in practical geological modeling. As one kind of geological solid modeling approach, 3D block cutting analysis can simultaneously identify tens of thousands of solids (blocks) from a complicated 3D discontinuity network without user intervention. However, this analysis can only address planes and build flat blocks. In this paper, we propose a method of 3D curved block cutting analysis. The corresponding algorithm is presented completely, with some key processes of analysis thoroughly accounted for, such as solving the surface-to-surface intersection, analyzing the composition of vertices, and analyzing relevant loops. Our proposed method fully exploits the advantages of topology and computational geometry. The 3D curved blocks can be accurately constructed and represented with minor computation and memory. Analysis examples showed that several hundreds of curved blocks can be automatically constructed within one minute using a microcomputer. This method is of significance for the development of geological solid modeling and can provide a reference for related studies.