Re: ListDensityPlot with irregular data and InterpolationOrder

*To*: mathgroup at smc.vnet.net*Subject*: [mg88584] Re: ListDensityPlot with irregular data and InterpolationOrder*From*: Szabolcs Horvát <szhorvat at gmail.com>*Date*: Fri, 9 May 2008 03:23:55 -0400 (EDT)*Organization*: University of Bergen*References*: <fvudo3$ec7$1@smc.vnet.net>

Bill Rowe wrote: > On 5/7/08 at 7:10 AM, szhorvat at gmail.com (Szabolcs Horv=C3=A1t) wrote: > >> This is not explicitly documented (or at least I could not find any >> mention of it), but from looking at the plots it seems to me that >> with ListDensityPlot (and related functions), an InterpolationOrder >> higher than 1 only work with data that lies on a regular grid. > >> So for example the following data cannot be plotted with >> InterpolationOrder higher than 1: > >> data = {#1, #2, Sin[#1] Sin[#2]} & @@@ RandomReal[2 Pi, {100, 2}]; > >> Is this correct? > > The array you create above is a regular array and as far as I > can see there is no problem with using an InterpolationOrder > greater than 1. That is, using your code above to assign values > to data > > > ListDensityPlot[data] > ListDensityPlot[data,InterpolationOrder->1] > ListDensityPlot[data,InterpolationOrder->3] > > all execute with no error messages. > > True, all three graphics appear identical. But I believe this is > due the functional relationship you created. > > Do the following > > data=RandomReal[2 Pi, {5,5}]; > > then > > ListDensityPlot[data] > ListDensityPlot[data,InterpolationOrder->1] > ListDensityPlot[data,InterpolationOrder->3] > > All three should execute with no error and the images will not > be the same due to the different interpolation order. Exactly this is what I mean, i.e. that when passing arbitrary data points to ListDensityPlot (instead of data on a regular grid), InterpolationOrder seems to only have an effect if we use InterpolationOrder -> 0. Otherwise the result will be the same as with InterpolationOrder -> None. So it seems that ListDensityPlot can only interpolate on a grid, but not in a more general situation. This is not a problem, of course, but I got a bit confused because it gives no error message!