If your data has the best resolution, the easiest way would be to use scatter3. For instance:
[xx, yy, zz] = meshgrid(1:0.1:10); vv = cos(xx).*sin(yy).*sin(zz).^2; scatter3(xx(:),yy(:),zz(:),5,vv(:)); colormap(jet); colorbar;
The resulting image looks pretty similar to the cube in your question. Unfortunately, plotting takes a lot of time.
In your case, I would add fake data to increase the resolution:
val1 = [0.0378 0.0642 0.0824 0.0973; 0.0480 0.0770 0.0980 0.1142; 0.0541 0.0845 0.1068 0.1236; 0.0574 0.0899 0.1128 0.1311]; val2 = [0.0392 0.0750 0.1041 0.1277; 0.0520 0.0953 0.1277 0.1541; 0.0601 0.1068 0.1412 0.1689; 0.0655 0.1142 0.1500 0.1791]; val3 = [0.0392 0.0770 0.1122 0.1426; 0.0520 0.1014 0.1426 0.1764; 0.0608 0.1155 0.1595 0.1953; 0.0669 0.1257 0.1709 0.2081]; val4 = [0.0392 0.0770 0.1155 0.1493; 0.0520 0.1034 0.1500 0.1899; 0.0608 0.1196 0.1703 0.2122; 0.0669 0.1304 0.1831 0.2270]; [x, y, z] = meshgrid(1:4); ratio = zeros(4, 4, 4); ratio(:,:,1) = val1; ratio(:,:,2) = val2; ratio(:,:,3) = val3; ratio(:,:,4) = val4; ff = 25; [xx, yy, zz] = meshgrid(1/ff:1/ff:4); ratio_scaled = zeros(ff*4, ff*4, ff*4); for xi=1:4 for yi=1:4 for zi=1:4 ratio_scaled((xi - 1)*ff + 1 : xi*ff, (yi - 1)*ff + 1 : yi*ff, (zi - 1)*ff + 1 : zi*ff) = ratio(xi, yi, zi); end end end scatter3(xx(:),yy(:),zz(:),5,ratio_scaled(:)); colormap(jet); colorbar;
To change the resolution, just take different values for the ff variable.
** UPDATE **
To optimize performance and avoid unnecessary calculations, you can really use slices. For larger sizes, this is really great:
[xx, yy, zz] = meshgrid(1:0.05:10); vv = cos(xx).*sin(yy).*sin(zz).^2; xslice = [1, 10]; yslice = [1, 10]; zslice = [1, 10]; h = slice(xx,yy,zz,vv,xslice,yslice, zslice); set(h, 'EdgeColor', 'none'); axis vis3d; box on; colormap(jet); colorbar;
But in your case, the cube will look like this:
This is because the data is in the nodes of the grid, and not on the verge between them. To get the best result, you need to manipulate the input a bit. You can add another row in each dimension of the relationship and change the X, Y, Z axis to be able to cut the cube along the rows of data. Look at this:
ratio = zeros(4, 4, 4); ratio(:,:,1) = [0.0378 0.0642 0.0824 0.0973; 0.0480 0.0770 0.0980 0.1142; 0.0541 0.0845 0.1068 0.1236; 0.0574 0.0899 0.1128 0.1311]; ratio(:,:,2) = [0.0392 0.0750 0.1041 0.1277; 0.0520 0.0953 0.1277 0.1541; 0.0601 0.1068 0.1412 0.1689; 0.0655 0.1142 0.1500 0.1791]; ratio(:,:,3) = [0.0392 0.0770 0.1122 0.1426; 0.0520 0.1014 0.1426 0.1764; 0.0608 0.1155 0.1595 0.1953; 0.0669 0.1257 0.1709 0.2081]; ratio(:,:,4) = [0.0392 0.0770 0.1155 0.1493; 0.0520 0.1034 0.1500 0.1899; 0.0608 0.1196 0.1703 0.2122; 0.0669 0.1304 0.1831 0.2270]; %define limits of the axis x_min = 0.1; x_max = 0.4; y_min = 0.2; y_max = 0.8; z_min = 0.05;z_max = 0.2; %calculate the grid step x_step = (x_max - x_min)/(4-1); y_step = (y_max - y_min)/(4-1); z_step = (z_max - z_min)/(4-1); %define the mesh [xx, yy, zz] = meshgrid(x_min-x_step/2 : x_step : x_max+x_step/2, y_min-y_step/2 : y_step : y_max+y_step/2, z_min-z_step/2 : z_step : z_max+z_step/2); %extend all 3 dimensions of the ratio by one new row ratio(end+1, :, :) = ratio(end, :, :); ratio(:, end+1, :) = ratio(:, end, :); ratio(:, :, end+1) = ratio(:, :, end); %define the cutting slices xslice = [x_min-x_step/2, x_max+x_step/2]; yslice = [y_min-y_step/2, y_max+y_step/2]; zslice = [z_min-z_step/2, z_max+z_step/2]; h = slice(xx,yy,zz,ratio,xslice,yslice, zslice); %fix the axis axis([x_min-x_step/2 x_max+x_step/2 y_min-y_step/2 y_max+y_step/2 z_min-z_step/2 z_max+z_step/2]); %use EdgeColor to show/hide the edges %set(h, 'EdgeColor', 'none'); %hide all Ticks that you do not need set(gca, 'XTick', (x_min:x_step:x_max)); set(gca, 'YTick', (y_min:y_step:y_max)); set(gca, 'ZTick', (z_min:z_step:z_max)); %define the colormap colormap(jet); colorbar;
You will get the following result: