How can we color 3D objects in specific direction?

Question

Update

I would like to control the direction of the color gradient to get similar to this plot but in 3D

Original

pol = {{1/2, 0, 0}, {1, 0, 0}, {5/4, Sqrt[3]/4, 0}, {1, Sqrt[3]/2, 
    0}, {1/2, Sqrt[3]/2, 0}, {1/4, Sqrt[3]/4, 0}, {1/2, 0, 0}};
Graphics3D[{Polygon[pol, 
   VertexColors -> {Red, Red, White, Black, Black, White}]}, 
 Boxed -> False];     

How can we make the gradient of color in a specific direction? for example along the green line in this fig or any arbitrary one such that it starts with red color from the bottom edge and white everywhere at the middle (white line) and smoothly goes to black at the top edge?

Answer 1

Updated

• We use {x - x0, y - y0} . AngleVector[t] to calculate the sign distance from the line through the center {x0,y0} of the polygon.

• Use Rescale to limit the range of the distance to the interval [0,1].

• Set the Blend color from Red to White then to Blue.

pol = {{1/2, 0, 0}, {1, 0, 0}, {5/4, Sqrt[3]/4, 0}, {1, Sqrt[3]/2, 
    0}, {1/2, Sqrt[3]/2, 0}, {1/4, Sqrt[3]/4, 0}, {1/2, 0, 0}};
{x0, y0, z0} = RegionCentroid@Polygon@pol;
t = π/2;
RegionPlot3D[Polygon@pol, PlotPoints -> 100, MaxRecursion -> 6, 
 Mesh -> None, 
 ColorFunction -> 
  Function[{x, y, z}, 
   Blend[{{0, Red}, {.5, White}, {1, Blue}}, 
    Rescale[{x - x0, y - y0} . AngleVector[t], {-(Sqrt[3]/4), 
      Sqrt[3]/4}]]], ColorFunctionScaling -> False, 
 Lighting -> {{"Ambient", White}}, PerformanceGoal -> "Quality", 
 Boxed -> False, Axes -> False]

Original

Maybe similar with this result.

• Along the y direction.

RegionPlot3D[Polygon@pol, PlotPoints -> 100, MaxRecursion -> 4, 
 ColorFunction -> 
  Function[{x, y, z}, Blend[{{0, Red}, {.5, White}, {1, Red}}, y]], 
 ColorFunctionScaling -> True, Boxed -> False]

• Or set the color function be the distance from the line through the center of polygon.

{x0, y0, z0} = RegionCentroid@Polygon@pol;
ani = Manipulate[
  RegionPlot3D[Polygon@pol, PlotPoints -> 80, MaxRecursion -> 4, 
   Mesh -> None, 
   ColorFunction -> 
    Function[{x, y, z}, 
     Blend[{{1, Red}, {0, White}}, 
      2.5 Abs[{x - x0, y - y0} . AngleVector[t]]]], 
   ColorFunctionScaling -> False, Lighting -> "Neutral", 
   PerformanceGoal -> "Quality", Boxed -> False, Axes -> False], {t, 
   0, 2 Pi}]

Answer 2

A rough approximation

$Version

(* "13.1.0 for Mac OS X x86 (64-bit) (June 16, 2022)" *)

Clear["Global`*"]

pol = {{1/2, 0, 0}, {1, 0, 0}, {5/4, Sqrt[3]/4, 0}, {1, Sqrt[3]/2, 0}, {1/2, 
    Sqrt[3]/2, 0}, {1/4, Sqrt[3]/4, 0}, {1/2, 0, 0}};

Manipulate[
 pol2 = Insert[
   Insert[pol, p*pol[[4]] + (1 - p)*pol[[5]], 5],
   p*pol[[1]] + (1 - p)*pol[[2]], 2];
 Graphics3D[{
   Red,
   Polygon[pol2,
    VertexColors -> {
      Blend[{Red, White}, 1/2 - p], Red, Blend[{Red, White}, p - 1/2], White,
      Blend[{Black, White}, 1/2 - p], Black, Blend[{Black, White}, p - 1/2],
      White}],
   Thick,
   Green, Line[{pol2[[2]], pol2[[6]]}]},
  Boxed -> False],
 {{p, 0.5}, 0, 1, 0.05, Appearance -> "Labeled"}]