Boolean Operations of Triangulated Solids and Their Applications in the 3d Geological Modelling

In this paper we present a new method for Boolean operations (intersection, union and difference) of triangulated solids, and its applications in three-dimensional (3D) computerized geological modelling (3DGM). This method is adapted to arbitrary (convex or concave), close geological solids. Three major steps are included in this method: (1) Calculate intersection points between triangles. Our work is mainly concerned with coplanar triangles, while non-planar cases are dealt with previous algorithm (Möller, 1997). Bounding box technique is employed to speed up this process. (2) Retriangulate the intersected triangles with the point-by-point insertion triangulation method, in order to keep consistent between pairs of solids. (3) Inclusion test between triangles and solids. This work can be reduced to testing whether a point is inside a solid or not. We extend the “Crossing Number Method” from 2D to 3D, and deal with some particular cases when the ray passes vertexes or edges of triangles. Boolean operations of triangulated solids have broad applications in engineering, geology, biological research, medical imaging, etc. We are concerned with the applications of this method and geological knowledge in 3DGM. Several examples, such as intrusions, ore bodies and tunnels, bifurcated geological bodies, are presented to validate the method.