# How do I get a beautiful image overlay from data and a model function?

I have a set of experimental data that I wish to make into a density plot. Then I have to overlay an image of a model function f(x, y, z) = Sin(x/z)Sin(y) on the density image such that parameters a, b and w are used to control the size and position of the model image on the density image. I actually succeeded halfway as shown in the following code:

canto = Import["forcemapf.xls"];
ListDensityPlot[canto, Axes -> False, Frame -> False]


This produce image1. I now used comton in:

Manipulate[
ImageCompose[
comton,
ImageResize[
ColorReplace[
Image[
DensityPlot3D[Sin[x/z] Sin[y], {x, -3, 3}, {y, -3, 3}, {z, -3, 3},
Axes -> False, Boxed -> False, ColorFunction -> Hue]],
White -> Transparent],
s]],
{s, 50, 300, 1}]


However, I still got the following problems

1. I currently have only s (controlling the size of the model image) and could not get the other control parameters to work.
2. I would love to use ListPlotDensity after ImageCompose instead of an image (comton). I am not really sure if this is even possible.
3. I wish to have legend (probably using PlotLegends) of the model function f(x, y, z) placed by the right hand side. I tried several methods but still did not succeed; one of the methods gave the legend but the model image disappeared. Another method meanwhile worked with the image overlay but the legend did work with ImageCompose.
4. I could not use other control parameters (w, a and b) unless the objects are certain types of images. My attempt is as follows (image2 is here):

Manipulate[ ImageCompose[ comton, ImageResize[ ColorReplace[comtona, White -> Transparent], White -> Transparent, w], {a, b}], {w, 50, 300, 1}, {a, 50, 130,10}, {b, 50, 130, 10}]

I would be grateful if you guys can help in checking out where I am getting it wrong.

• Does the data canto match the set of 3D points {x,y,z}? – Alex Trounev Jan 28 at 12:48
• @Alex Trounev, thanks. canto represent a 3D data imported to be plotted. It has nothing to do with 3D points {x,y,z}; these points are for the function f(x,y,z)=Sin(x/z)Sin(y)! – Dean Jan 28 at 13:15
• Then the data should look like {x,y,z,f[x,y,z]}` – Alex Trounev Jan 28 at 13:22