Get 2D temperature map from 3D geometry with temperatures stored in FaceVertexCData?

Minimum viable example:

% Define a simple 6 sided cube with dimensions 0-1 in X, Y, and Z
vertices = [0,0,1;  % 1 Front-Top-Left (FTL)
            1,0,1;  % 2 Front-Top-Right (FTR)
            1,0,0;  % 3 Front-Bottom-Right (FBoR)
            0,0,0;  % 4 Front-Bottom-Left (FBoL)
            0,1,1;  % 5 Back-Top-Left (BaTL)
            1,1,1;  % 6 Back-Top-Right (BaTR)
            1,1,0;  % 7 Back-Bottom-Right (BaBoR)
            0,1,0]; % 8 Back-Bottom-Left (BaBoL)
faces = [1,2,3,4;  % 1 Front
         2,6,7,3;  % 2 Right
         6,5,8,7;  % 3 Back
         5,1,4,8;  % 4 Left
         1,5,6,2;  % 5 Top
         4,3,7,8]; % 6 Bottom
temps = [5;10;15;20;25;30]; % One temperature per face
% Plot the cube
fig1 = figure;
ax1 = axes(fig1);
patch('Faces',faces,'Vertices',vertices,'FaceColor','flat','EdgeColor','none','FaceVertexCData',temps,'Parent',ax1);
% Rotate to an isometric type of view angle
ax1.View = [-42.5 28];
% Turn off axes
ax1.XAxis.Visible = 'off';
ax1.YAxis.Visible = 'off';
ax1.ZAxis.Visible = 'off';
% Set data aspect ratio to 1 1 1
daspect(ax1,[1 1 1]);

% -------------------------------------------------------------------------
% Code goes here that should produce a 2D matrix that looks something like:
% (15x15 as example, but would need to be more like 1024x1024 up to 
%  4096x4096 in real world use cases)
%       1  2  3  4  5  6  7  8  9 10 11 12 13 14 15
% 1  % 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 
% 2  % 00 00 00 00 00 00 25 00 00 00 00 00 00 00 00 
% 3  % 00 00 00 00 00 25 25 25 00 00 00 00 00 00 00 
% 4  % 00 00 00 00 25 25 25 25 25 00 00 00 00 00 00 
% 5  % 00 00 00 25 25 25 25 25 25 25 00 00 00 00 00 
% 6  % 00 00 20 25 25 25 25 25 25 10 00 00 00 00 00 
% 7  % 00 00 20 20 20 25 25 25 10 10 00 00 00 00 00 
% 8  % 00 00 20 20 20 20 25 10 10 10 00 00 00 00 00 
% 9  % 00 00 20 20 20 20 20 10 10 10 00 00 00 00 00 
% 10 % 00 00 20 20 20 20 20 10 10 10 00 00 00 00 00 
% 11 % 00 00 00 20 20 20 20 10 10 00 00 00 00 00 00 
% 12 % 00 00 00 00 20 20 20 10 00 00 00 00 00 00 00 
% 13 % 00 00 00 00 00 20 20 10 00 00 00 00 00 00 00 
% 14 % 00 00 00 00 00 00 20 00 00 00 00 00 00 00 00 
% 15 % 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 
%
% Real world use cases would include projection from multiple different
% angles onto complex 3D geometries containing in excess of 100k polygons.
% There will also be cases where part of the geometry overlaps other parts
% of the geometry, and the solution needs to account for only the visible
% geometry from the specific look angle and ignore all other facets out of
% sight behind the 'closest to the camera' faces. The current plotting
% solution plots one patch object per body as children of an hgtransform
% and there can be hundreds of bodies in a model.

I hope this makes sense. I have searched far and wide for a simple way to do this but have come up empty-handed so far. Any help would be appreciated!

Answer 1

[albrittbrat]

I cross posted this on stack exchange after I got no answers here, and someone gave a wonderful, thorough answer over there:

https://stackoverflow.com/questions/78403361/matlab-how-to-create-2d-pixel-map-of-data-stored-in-3d-patch-objects-faceverte