Re: Function Coloring with ParametricPlot3D

• To: mathgroup at smc.vnet.net
• Subject: [mg31282] Re: [mg31264] Function Coloring with ParametricPlot3D
• From: Omega Consulting <omega_consulting at yahoo.com>
• Date: Fri, 26 Oct 2001 04:28:29 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```At 08:59 PM 10/23/2001, David Park wrote:
>Dear MathGroup,
>
>There is a percularity of the ParametricPlot3D command with color
>specification as the fourth element that bugs me.
>
>(snip)
>
>What I would like to do is have Mathematica determine a single function
>value for each square, perhaps by averaging the values at the four corners,
>and then apply my color function to that single value. In that case there
>would be no blending, unless I decide to do the blending in my color
>function.
>
>Does anyone know how to work around this?
>
>David Park

You can color your ParametricPlot manually.

Here's a function that averages the points in a Polygon and gets the color
at that point.

col[pts_] :=Module[{x,y,z},
{x,y,z}=(Plus@@pts)/(Length@pts);
cfun[x,y]
]

Then use a replacement rule to add a color primitive to each Polygon.

Show[ParametricPlot3D[{x, y, 0}, {x, 0, 10}, {y, 0, 10},
PlotPoints -> 8, Lighting -> False,  DisplayFunction->Identity] /.
Polygon[pts_]:>{col[pts], Polygon[pts]},
DisplayFunction->\$DisplayFunction];

--------------------------------------------------------------
Omega Consulting