When the point cloud represents a surface, then it is possible to create a triangulated mesh for more rapidly visualizing the object. Plotting points clouds takes some non-trivial processing since the renderer has to plot many points and do so with occlusion handling and scale awareness. A must faster means to visualize objects whose surface are modelled by the point cloud would be to simply the points to surfaces, then to plot those surfaces. The main idea is that there will be far less surfaces to plot than there are points. Furthermore occlusion handling, and possible even scale handling, is much easier with surfaces.

Given an unordered point cloud, the process of generating surface patches that attempt to reproduce the actual surface is known as mesh triangulation or surface triangulation. For planar point clouds or volumetric point clouds (cannot be planar), it is possible to triangulate or tesselate the surface using Delaunay triangulation. For further understanding, refer to the slides from MIT CSAIL. These methods work with convex hull type processing, so they don't quite do the trick.

Here, you will explore an alternative strategy to surface mesh triangulation, which is a naive version of the advancing fronts method. Read on here.

Explore and Deliverables: In addition to the surface triangulations for the sample point clouds and one object from the earlier point cloud, discuss the performance of the method as the main parameter ($\rho_{near}$) is adjusted. What happens? Is it sensible? Can you relate its value to what you see happening? Can you relate it to concepts you might know from signal processing or some ECE class you've taken?

/* For Matlab folks, an exemplar implementation of Delaunay triangulation can be found here.

For PCL folks, there's no sample code you can use this time :( However you may check the C++ implementation of Delaunay triangulation from here. Try to integrate it into your PCL pipeline. */

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