Efficient visibility criterion for discontinuities discretised by triangular surface meshes

This study proposes a computationally efficient algorithm for determining which pairs of points among many predetermined pairs in three dimensions will maintain straight line visibility between one another in the presence of an arbitrary surface mesh of triangles. This is carried out in the context of meshless numerical methods with the goal of implementing near-real-time discontinuity propagation simulation. A brief overview is given of existing discontinuity modelling techniques for meshless methods. Such techniques necessitate determination of which key pairs of points (nodes and quadrature points) lack straight line visibility due to the discontinuity, which is proposed to be modelled with a surface mesh of triangles. The efficiency of this algorithm is achieved by allocating all quadrature points and surface mesh triangles to the cells of an overlayed three-dimensional grid in order to rapidly identify for each triangle an approximately minimal set of quadrature points whose nodal connectivities may be interrupted due to the presence of the triangle, hence eliminating most redundant visibility checking computations. Triangles are automatically split such that any size of overlayed cubic grid cells can be employed, and the parameters governing triangle splitting and binning have been examined experimentally in order to optimise the visibility algorithm.