As an alternative to simple decimation and 2.5D Delaunay triangulation, this paper introduces methodologies known as epsilon-nets and Poisson surface reconstruction to reduce the size of large point clouds of geological scenes and generate a mesh. Epsilon-nets produce decimated point clouds free from undesirable organized patterns linked to data acquisition. Through the ε parameter, the user specifies the number of selected points which are then meshed in 3D by the Poisson surface reconstruction algorithm. Poisson meshes capture the topology of the rock face with a high fidelity and are robust enough to handle a degree of occlusion. These methodologies are demonstrated using an image of a rock face featuring large cubic blocks acquired at a camera-target distance of 3. m and containing 2044,140 points. The point cloud was decimated by a factor of 16 using an epsilon-net with ε≈0.0002, and the error, reported as the average Hausdorff distance (using the original point cloud as the source and the epsilon net as the target), was approximately 1. mm, which is on the same order of magnitude as the camera accuracy. Poisson surface reconstruction produced a realistic mesh and reduced noise, which conditioned the data for fracture analysis. A stereonet distinguished two sub-vertical joint sets that had been combined in previous studies. This case history is illustrated by color-coded displays of the strike and dip angles of mesh elements, highlighting ranges of angles of interest and capturing overhang areas.

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Keywords Epsilon-nets, Fracture orientation, Poisson surface reconstruction, Terrestrial laser scanning, Visualization
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Journal International Journal of Rock Mechanics and Mining Sciences
Lai, P., Samson, C, & Bose, P. (2014). Visual enhancement of 3D images of rock faces for fracture mapping. International Journal of Rock Mechanics and Mining Sciences, 72, 325–335. doi:10.1016/j.ijrmms.2014.09.016