# How can I make a projection of ParametricPlot3D onto 2D surface without shading?

I have a Parametric Plot that has very high and low values. I used this answer Project RegionPlot3D to 2D using hue/color function to show third dimension to project the surface onto the 2D plane. This is the code:

ParametricPlot3D[{u, v, Exp[u]*Cos[u - v]}, {u, 1, 3}, {v, 1, 5},
Boxed -> False, ViewPoint -> {0, 0, Infinity}, Axes -> False,
ColorFunction -> "TemperatureMap", Mesh -> None, Background -> Black]


However when I do that the resulting image seems to still have the shading which is what I want to avoid. I also would like to change the color function so that the color function goes from white to a darker orange going through shade of orange only.

You could follow this example from the documentation and use Glow:

ParametricPlot3D[{u, v, Exp[u]*Cos[u - v]}, {u, 1, 3}, {v, 1, 5},
Boxed -> False, ViewPoint -> {0, 0, Infinity}, Axes -> False,
ColorFunction ->
Function[{x, y, z}, Glow[ColorData["TemperatureMap", z]]],
Mesh -> None, Lighting -> None]


Here is an example of adjusting the range of colors to be white to orange:

ParametricPlot3D[{u, v, Exp[u]*Cos[u - v]}, {u, 1, 3}, {v, 1, 5},
Boxed -> False, ViewPoint -> {0, 0, Infinity}, Axes -> False,
ColorFunction ->
Function[{x, y, z},
Glow[ColorData["TemperatureMap",
Rescale[z, {-10, 20}, {0.5, 0.95}]]]],
ColorFunctionScaling -> False, Mesh -> None, Lighting -> None]


• Thank you!! I actually tried to use glow but i was missing the z, I didn't know how to make it work Jul 20, 2020 at 22:39

You could use white ambient light and a custom ColorFunction based on a Blend of White and Darker@Orange.

ParametricPlot3D[{u, v, Exp[u]*Cos[u - v]}, {u, 1, 3}, {v, 1, 5}
, Boxed -> False
, ViewPoint -> {0, 0, Infinity}
, Axes -> False
, ColorFunction -> Function[{x, y, z, u, v}, Blend[{White, Darker@Orange}, z]]
, Mesh -> None
, Background -> Black
, Lighting -> {"Ambient", White}
]


• Thanks! :) this was very helful Jul 20, 2020 at 22:39

You can also use the option NormalsFunction:

ParametricPlot3D[{u, v, Exp[u] Cos[u - v]}, {u, 1, 3}, {v, 1, 5},
Boxed -> False,
ViewPoint -> {0, 0, ∞},
Axes -> False,
Mesh -> None,
ColorFunction -> "TemperatureMap",
NormalsFunction -> ({1, 1, 0} &)]


Use ColorFunction -> (Blend[{White, Orange}, #3] &) (as in Josh Bishop's answer) we get:

Use ColorFunction -> (Blend[{White, Yellow, Red}, #3] &) to get

• Thank you so much! the colors you put are perfect for what I needed Jul 20, 2020 at 22:40