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Notice that the point at the top of South America still shows the local minimum that is evident in the cell-centered plots above, thus this method should still preserve gradients and oscillations in the data. The main downside of this method (triangulation) is that it becomes painfully slow for large grids. We may have a couple ways around this. First, it can be expected that most of the time is spent doing the triangulation; the plotting itself should be relatively fast (TODO: confirm). Thuswe might expect that a significant amount of time is spent calculating the Delaunay triangulation. It turns out this is only partly true, as the following timing results show (using meshes ne4, ne30, ne120, ne240, ne512):
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This shows the time to plot (or calculate a triangulation, in the case of the “triangulation” data) for the range of mesh sizes using three different methods: the dual grid approach above (mpl implementation), calling tripcolor without specifying a triangulation, and finally using tripcolor but first calculating the triangulation separately. Thus, it appears that a similar amount of time is spent in both the calculation of the triangulation and the plotting of the data (caveat: sample size of one for these timing figures, so huge uncertainty here; TODO: update with average timing over multiple passes). Still, we should be able to perform the triangulation once per grid, and save the results to use at plotting time. This should cut the actual plotting time in half, if the results above can be trusted. So the first option is to do this using the MPL routines, and just save the data. However, we already have something that looks something like this in the SEMapping.nc file that is output in each case run directory. This file contains information about the quadrilaterals that are formed by groups of four GLL nodes. Unfortunately, we don’t have a corresponding quadpcolor routine in MPL to plot data in quads directly. However, one can imagine splitting each quadrilateral in two triangles by connecting opposite vertices, and then creating a triangulation object from the resulting triangles. This is fairly easy to do in python:
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