Surface roughness of rock faces through the curvature of triangulated meshes

• Mapping curvature highlights heavily fractured rock faces.
• Curvature-based roughness measures provide estimates of roughness in meshes.
• Colour-coding of mesh elements allows visualisation of rougher/smoother surfaces.

In this paper, we examine three different measures of roughness based on a geometric property of surfaces known as curvature. These methods were demonstrated using an image of a large rock face made up of a smooth blocky limestone in contact with a rough friable dolostone. The point cloud analysed contained 10,334,288 points and was acquired at a distance of 3 m from the rock face. The point cloud was first decimated using an epsilon-net and then meshed using the Poisson surface reconstruction method before the proposed measures of roughness were applied. The first measure of roughness is defined as the difference in curvature between a mesh and a smoothed version of the same mesh. The second measure of roughness is a voting system applied to each vertex which identifies the subset of vertices which represent rough regions within the mesh. The third measure of roughness uses a combination of spatial partitioning data structures and data clustering in order to define roughness for a region in the mesh. The spatial partitioning data structure allows for a hierarchy of roughness values which is related to the size of the region being considered. All of the proposed measures of roughness are visualised using colour-coded displays which allows for an intuitive interpretation.