• To: mathgroup at smc.vnet.net
• Subject: [mg24419] Re: [mg24393] fade to mauve
• From: "Preston Nichols" <pnichols at wittenberg.edu>
• Date: Tue, 18 Jul 2000 00:58:16 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```Dr. Purcell,

Perhaps you don't need big ViewPoints to get the result you want.

The online help for ViewPoint includes this:   "The view point is given in
a special scaled coordinate system in which the longest side of the
bounding box has length 1. The center of the bounding box is taken to have
coordinates {0, 0, 0}."

Here are some hemispheres of (exponentially) increasing radius, all with
the default ViewPoint:

Do[
ParametricPlot3D[
Exp[logr] {Sin[theta]Cos[phi], Sin[theta]Sin[phi], Cos[theta]},
{theta, Pi, 2 Pi}, {phi, 0, Pi},
ViewPoint -> {1.3, -2.4, 2.},
Axes->False],
{logr,1,10}]

The plots all look exactly the same in my Notebook.  (Double-click on one
of them to animate: no motion.)  You can change the Axes option to True to
assure yourself that the spheres really are growing.

Here are some hemispheres of constant radius, with ViewPoint of constant
direction and increasing length:

Do[
ParametricPlot3D[
{Sin[theta]Cos[phi], Sin[theta]Sin[phi], Cos[theta]},
{theta, Pi, 2 Pi}, {phi, 0, Pi},
ViewPoint -> radius {1.3, -2.4, 2.},
Axes->False],

Only now do we get the variation of perspective (look at the bounding
boxes), along with the "fade to mauve".

A general (perhaps disconcerting) conclusion:  to think of the ViewPoint as
the position vector of the "camera" relative to the center of the plot is
an oversimplification, though one which doesn't usually matter much.

I hope this helps,

Preston Nichols
Mathematics and Computer Science
Wittenberg University

At 11:13 PM 07/12/2000 -0400, Christopher J. Purcell wrote:
>Using Vers 4.0 and i think all the way back to 2.2, if you ParametricPlot
>anything, say a hemisphere:
>
>ParametricPlot3D[
>  radius{Sin[theta]Cos[phi], Sin[theta]Sin[phi], Cos[theta]}, {theta, Pi,
>    2 Pi}, {phi, 0, Pi}, ViewPoint -> radius *{1.3, -2.4, 2.}]
>
>where the ViewPoint is close to the default {1.3, -2.4, 2.} you get the
>usual nice shaded image. But when you increase the magnitude of Viewpoint,
>the colors and shading start to fade. For example if you repeat the above
>the shading has now faded to an ugly mauve (on a mac) even though the
>sphere has been scaled the same amount as ViewPoint. The same holds if you
>use Graphics3D to plot filled shaded polygons.
>
>When I draw big things and need to use big Viewpoints to get the
>perspective right, they lose their lighting.
>
>I don't see why it has to be this way.
>
>Dr. C. J. Purcell
>Defence Research Establishment Atlantic
>9 Grove St., Dartmouth, NS Canada B2Y 3Z7
>Tel: 902-426-3100-x389
>Fax: 902-426-9654
>
>
>

```

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