Map 2D data to a room plan?

Question

I need to map 2D measures taken at regular intervals in a room on the room floor plan in order to create a "heat map". Something like that:

^{Taken from https://www.purrmetrix.com/category/advice/ -- for illustration purpose only}

The room map can reasonably accurately be rendered as a polygon. However, I can't find:

• how to create the continuous "heat map" from discrete samples (using bilinear interpolation between the samples),
• nor how to put the room plan on the map, ensuring the "heat map" is clipped by the room boundaries.

I saw Mathematica has a full range of primitives to work with maps. But it seems there are more suitable to work with geodata, rather than simple 2D plans.

I didn't find really useful answers by searching on the net, probably because I lack the right keywords. Could you point me in the right direction?

Answer 1

I mentioned in comments that I doubted that the mapping functionality would be appropriate here, but an easier approach would be to model the room as a Polygon, then generate and save RegionMemberFunction from it, using RegionMember. I would then use ListDensityPlot to present your data, with that RegionMemberFunction as a RegionFunction option. Here is an example of the approach I mentioned in comments, using some made up data.

First, generate the room outline as a Polygon and the corresponding RegionMemberFunction, as well as some fake data in the form $(x,y,value)$:

room = Polygon[{{0, 0}, {6, 0}, {6, 2}, {2, 2}, {2, 4}, {0, 4}}];
rmf = RegionMember[room];
fakedata = Table[{x, y, Sin[x] Cos[y]}, {x, -1., 8}, {y, -1., 5}]~Flatten~1;

Plot the data within the polygon, adding the room polygon as an outline:

Show[
  Graphics[
    {FaceForm[], EdgeForm[Directive[Thickness[0.01], Black]], room},
    AspectRatio -> Automatic
  ],
  ListDensityPlot[
    fakedata,
    RegionFunction -> Function[{x, y, z}, rmf[{x, y}]],
    MaxPlotPoints -> 60
  ]
]

The MaxPlotPoints option within ListDensityPlot increases the precision of the drawing so that the density plot hews more closely to the shape of the room (the sharp corner was otherwise causing trouble).