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I want to combine some ListContourPlot3D and Graphics3D to present, on one 3D plot, the projection of the contour plots on each face of the cube and a region of defined amplitude. Here is a working example.

Contour plots on each face together with a region of defined amplitude

I also want to add shading on the projected contours so that it appears more realistic. I succeeded in obtaining a realistic result using VertexNormals.

Projection of the contour plots with realistic lighting

When I add the ListContourPlot3D, the shading changed and looked bad.

Complete picture with mixed up shading Do you have any suggestions for keeping the shading as in Fig. 2 (GraphContour in the code below) even when the ListContourPlot3D plot is added. (GraphComplete)?

(*Define the vector for use in VertexNormals*)
{p1, p2,p3} = {{1, 0, 0}, {1, 1, 1}, {0, 0, 1}};
n = Cross[p2 - p1, p3 - p1];
(*Define constants for the boundary of the table*)
Rmin = -0.5; Rmax = 0.5; Rstep = 0.1; Rlength = (Rmax - Rmin)/Rstep; R0 = Rlength/2;

sphere = 
  Table[(Rx^2 + 0.6 Ry^2 + 0.5 Rz^2), 
    {Rx, Rmin, Rmax,Rstep}, {Ry, Rmin, Rmax, Rstep}, {Rz, Rmin, Rmax, Rstep}];

(*Plot of the region representing value of 5%*)
SphereP = 
  ListContourPlot3D[sphere/Max[sphere], 
    Contours -> {0.05}, AxesLabel -> {"x", "y", "z"},
    DataRange -> {{Rmin, Rmax}, {Rmin, Rmax}, {Rmin, Rmax}},
    MeshStyle -> Directive[Red, Opacity[0]], 
    Lighting -> "Neutral", Boxed -> False, 
    ContourStyle -> Directive[Orange, Opacity[0.9]],
    AxesEdge -> {{-1, -1}, {1, -1}, {-1, -1}}];

(*Define contour plot for projection on the cube faces*)
ContourXZ = 
  ListContourPlot[
    Table[(sphere[[Rx]][[R0]][[Rz]])/Max[sphere], {Rx, 1, Rlength}, {Rz, 1, Rlength}],
    DataRange -> {{Rmin, Rmax}, {Rmin, Rmax}}, Contours -> 10, 
    Axes -> False, PlotRangePadding -> 0, Frame -> False, 
    PlotLegends -> None, ClippingStyle -> Automatic, PlotRange -> {0, 1},
    ColorFunction -> ColorData[{"SunsetColors", "Reverse"}]];
level = Rmin; (*Level at which the contour appears*)
grIntXZ = 
  Graphics3D[
    {Texture[ImageData @ Rasterize[ContourXZ, "Image"]], EdgeForm[], 
     Polygon[{{Rmin, Rmin, level}, {Rmax, Rmin, level}, 
              {Rmax, Rmax,level}, {Rmin, Rmax, level}}, 
    VertexNormals -> {n, n, n, -n}, 
    VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]}, 
    Lighting -> "Neutral"];
ContourXY = 
  ListContourPlot[
    Table[(sphere[[Rx]][[Ry]][[R0]])/Max[sphere], {Rx, 1,Rlength}, {Ry, 1, Rlength}],
    DataRange -> {{Rmin, Rmax}, {Rmin, Rmax}}, Contours -> 10,
    Axes -> False, PlotRangePadding -> 0, Frame -> False,
    PlotLegends -> None, ClippingStyle -> Automatic, PlotRange -> {0, 1},
    ColorFunction -> ColorData[{"SunsetColors", "Reverse"}]];
level = -0.5; (*Level at which the contour appears*)
 grIntXY = 
   Graphics3D[
     {Texture[ContourXY], EdgeForm[], 
      Polygon[{{level, Rmin, Rmin }, {level, Rmax, Rmin}, 
               {level, Rmax,Rmax}, {level, Rmin, Rmax}}, 
     VertexNormals -> {n, -n, n, n}, 
     VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]},
     Lighting -> "Neutral"];
level = +0.5; (*Level at which the contour appears*)
ContourYZ =
  ListContourPlot[
    Table[(sphere[[R0]][[Ry]][[Rz]])/Max[sphere], {Ry, 1,Rlength}, {Rz, 1, Rlength}], 
    DataRange -> {{Rmin 10^6, Rmax 10^6}, {Rmin 10^6, Rmax 10^6}}, 
    Contours -> 10, Axes -> False, PlotRangePadding -> 0, Frame -> False,
    PlotLegends -> None, ClippingStyle -> Automatic,
    PlotRange -> {0, 1}, ColorFunction -> ColorData[{"SunsetColors", "Reverse"}]];
grIntYZ = 
  Graphics3D[
    {Texture[ContourYZ], EdgeForm[], 
     Polygon[{{Rmin , level, Rmin }, {Rmax, level, Rmin}, 
              {Rmax,level, Rmax}, { Rmin, level, Rmax }}, 
    VertexNormals -> {-n, n, n, n}, 
    VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]},
    Lighting -> "Neutral"];
(*Without the ListContourPlot3D, the shading are nice and realists*)

GraphContour = 
  Show[grIntXZ, grIntXY, grIntYZ, 
    PlotRange -> All,BoxRatios -> {1, 0.9,0.9}];
(*Everything get disturbed when adding the ListContourPlot3D*)

GraphComplete = 
  Show[SphereP, grIntXZ, grIntXY, grIntYZ, 
    PlotRange -> All, BoxRatios -> {1, 0.9, 0.9}];
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If you are playing with ellypse I highly recommend using Graphics3D primitives like in this answer: How to render 3D ellipse. Notice that there are two-axis ellipse but just add 3rd parametr for ScalingTransform. –  Kuba Nov 29 '13 at 6:13
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1 Answer

Not really an answer but comments do not allow graphics.

Your results might be due to the drivers of the graphics card. Your code produces the intended result on mine:

enter image description here

By the way, you might want to check Edit->Preferences->Appearance->Graphics->Antialiasing quality (the contour lines of your graphics are not aliased).

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