An Orientation on Surface Reconstruction

When reconstructing a surface from irregularly spaced data, sampled from a closed surface in 3D, we need to decide how to identify a good triangulation. As a measure of quality we consider various differential geometrical properties, such as integral Gaussian curvature, integral mean curvature and area. We furthermore study a non-functional approach, which is based on a mapping procedure. A locally optimal triangulation is then identified as a fixed point under the map. The optimisation methods all require an initial triangulation as a starting point. To find an initial triangulation, we look at growing and shrinking approaches.