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Topic: Re: [mg4368] ParametricPlot3D: shading?
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 Allan Hayes Posts: 1,508 Registered: 12/6/04
Re: [mg4368] ParametricPlot3D: shading?
Posted: Jul 19, 1996 2:59 AM
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lawry@maths.ox.ac.uk (James Lawry)
[mg4368] ParametricPlot3D: shading?

Is concerned that
ParametricPlot3D[{x, y, 1, Hue[x]}, {x, 0, 1}, {y, 0, 1}]
colors according to the lighting, while
Plot3D[{1, Hue[x]}, {x, 0, 1}, {y, 0, 1}]
colors according to the directive Hue[x].

James,

Firstly, we can color ParametricPlot3D[..] according to directive
by turning the lighting off.
ParametricPlot3D[{x, y, 1, Hue[x]}, {x, 0, 1}, {y, 0, 1},
Lighting -> False
]

The reason that we don't need to do this for Plot3D[...] and why
it is hidden seems to lie in the following.

Although we have
sg = Plot3D[{1, Hue[x]}, {x, 0, 1}, {y, 0, 1}]
-SurfaceGraphics-
colored according to the directive Hue[x],
with, surprisingly
Options[sg, Lighting]
{Lighting -> True}

The SurfacGraphics object stores only matrices of heights color
directives, NOT the polygons that appear in the display.Check with
List@@sg

Presumably the polygons must be constructed to be displayed.
Let's simulate this by converting sg to a Graphics3D object

sg3d = Graphics3D[sg]
-Graphics3D-
Check that the polygons are there:
List@@sg3d

AND note that the option Lighting -> False has been automatically
prepended to the list of options. We can see this without searching
all of the code:

Options[sg3d, Lighting]
{Lighting -> False, Lighting -> True}

(1) We can see the graphics code by using InputForm instead of the
List@@ trick (which I used to emphasise that no processing was
involved)

InputForm[sg]

(2) It makes the preceding more manageable if we reduce the number
of plot points, by using PlotPoints -> 3 for example.

(3) Try

Show[sg3d, Lighting -> True]

Allan Hayes
hay@haystack.demon.co.uk

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