Wanner, ThomasO'Neil, Patrick2018-10-222018-10-222017https://hdl.handle.net/1920/11241Point cloud data arises naturally from 3D scanners, LiDAR sensors, and industrial computed tomography among other sources. Most point clouds obtained through experimental means exhibit some level of noise, inhibiting mesh reconstruction algorithms and topological data analysis techniques. To alleviate the problems caused by noise, smoothing algorithms are often employed as a preprocessing step before attempting to reconstruct the sampled measure. Moving least squares is one such technique, however it is designed to work on surfaces in R^3 . As many interesting point clouds naturally live in higher dimensions, we seek a method for smoothing higher dimensional point clouds. To this end, we turn to the distance-to-measure function.191 pagesenCopyright 2017 Patrick O'NeilMathematicsComputational GeometryComputational TopologyPiecewise-Smooth Dynamical SystemsPoint CloudsVoronoi DiagramsDissertation