I need a loose replication of
this plot from Wikipedia. My best attempt so far seems to have some unwanted padding around the vector plot, on the bottom layer.
Am I missing anything to properly align the two coordinate systems? Is there an alternative implementation?
Define a potential field and its gradient:
f = Function[{x, y}, -(Cos^2 + Cos^2)^2];
g = Function[{x, y}, Evaluate@D[f[x, y], {{x, y}}]];
Make 2D plot for the texture
tx = VectorDensityPlot[g[x, y], {x, -Pi/2, Pi/2}, {y, -Pi/2, Pi/2},
Frame -> False, PlotRangePadding -> None, ColorFunction -> "DarkRainbow", VectorPoints -> 30]
Combine 3D filed plot with 2D vector plot of its gradient via texture
Show[Plot3D[f[x, y], {x, -Pi/2, Pi/2}, {y, -Pi/2, Pi/2},
ColorFunction -> "DarkRainbow", PlotStyle -> Opacity[.8], MeshStyle -> Opacity[.3]],
Graphics3D[{Texture[tx],
Polygon[{{-Pi/2, -Pi/2, -4}, {Pi/2, -Pi/2, -4}, {Pi/2, Pi/2, -4}, {-Pi/2, Pi/2, -4}},
VertexTextureCoordinates -> {{0, 0}, {1, 0}, {1, 1}, {0, 1}}]}, Lighting -> "Neutral"]]
