This paper presents analysis on two 3D mesh to 2D map strategies applied to unwrap images of rock tunnels and facilitate visualization of large datasets. First, we examined mesh parameterization algorithms which are used in computer graphics to convert a 3D mesh model to a 2D representation.We found that while these methods were automatic and could provide 2D maps with minimal metric distortion (ie: conservation of lengths in 3D when mapped to 2D), they exhibited twisted shapes and were not intuitive to interpret. Second, we proposed two novel approaches, combining mesh deformation algorithms, which are used in computer animation to reshape a 3D mesh to resemble a 3D plane, and projection onto a 2D plane. We found that while these methods required user interaction and introduced a greater amount of metric distortion, their outputs were fairly intuitive to interpret. To compare the relative merits of mesh parameterization and mesh deformation and projection, the different strategies are applied to a 8.2 m wide by 41 m long by 6.7 m high subsection of a mining tunnel. The metric distortion produced was calculated and their respective output 2D maps are presented and discussed.

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Keywords 3D images, Mesh deformation, Metric distortion, Surface parameterization, Terrestrial laser scanning, Tunnel mapping, Visualization
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Journal Tunnelling and Underground Space Technology
Lai, P., & Samson, C. (2016). Applications of mesh parameterization and deformation for unwrapping 3D images of rock tunnels. Tunnelling and Underground Space Technology, 58, 109–119. doi:10.1016/j.tust.2016.04.009