spud + spot = spod

A modest mathematical formulation.

Begin with a common spud:

[Graphics:HTMLFiles/index_1.gif]

[Graphics:HTMLFiles/index_2.gif]

[Graphics:HTMLFiles/index_3.gif]

Next, after slicing off the bottom, define a convenient paring of our tuber:

In[1]:=

$rmax = 3. ; rexp = .7 ; spudspin[t_] := ParametricPlot3D[{r^rexp Cos[theta + r/(2.5 * rmax)], ... l[.1], SphericalRegion -> True, DisplayFunction -> Identity] ; spud = spudspin[-π] ;$

And take a look at our handiwork:

In[5]:=

$Show[GraphicsArray[{ spud //. (ViewPoint -> _) -> (ViewPoint -> {0, 2, 1}), spud //. ... ViewPoint -> _) -> (ViewPoint -> {0, 4, 4}) }], DisplayFunction -> $DisplayFunction] ;$

[Graphics:HTMLFiles/index_6.gif]

A comic interlude...

Now let's define some alternate lighting:

In[6]:=

lz = .5 ; lth = N[2 π/3] ; lph = N[6 π/20] ; redSpots = {{{Cos[lth + lph], Sin[lth + ... h - lph/7], lz - .2}, RGBColor[0, 0, .15]}} ; fullSpots = Join[redSpots, greenSpots, blueSpots] ;

...and use them:

In[13]:=

$Show[GraphicsArray[{ { spud //. (ViewPoint -> _) -> (ViewPoint -> {0, 4, 4}), spud / ... ces -> _) -> (LightSources -> fullSpots)} } }], DisplayFunction -> $DisplayFunction] ;$

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...and view the last from slightly different vantage points:

In[14]:=

$spudspot = spud //. (LightSources -> _) -> (LightSources -> fullSpots) ; Show[Graphic ... ewPoint -> _) -> (ViewPoint -> {0, 0, 10}) }], DisplayFunction -> $DisplayFunction] ;$

[Graphics:HTMLFiles/index_12.gif]

Hey! that last looks rather like a SPOD, eh? So let's move in for a closer look, rinsing off our spud for a brighter appearance under the lights.

In[16]:=

$Show[GraphicsArray[{ Graphics3D[{SurfaceColor[GrayLevel[1], GrayLevel[1], 1], Part[spud, 1]}, ... pudspot, 1]}, Part[spudspot, 2] //. (ViewPoint -> _) -> (ViewPoint -> {0, 0, 6})] }]] ;$

[Graphics:HTMLFiles/index_14.gif]

Move along, there's nothing to see here...

So let's put the pieces together and take them for a spin...

In[17]:=

Table[Show[ Graphics3D[ {SurfaceColor[GrayLevel[1], GrayLevel[1], 1], Part[spudspin[a], 1]}, P ... playFunction -> $DisplayFunction, LightSources -> fullSpots], {a, 0, π/5, π/50}] ;

...and also available as a full length movie (just watch for 120 minutes)

For further amusement, consider snagging the Mathematica Notebook I used Spud2SPOD.zip and, if you haven't a copy of Mathematica lying around, grab the Math Reader which should let you do some handy things like view and resize, copy and paste, just not recalculate.

Converted by Mathematica (May 14, 2003)

Last Updated: Wednesday, May 14, 2003 10:58:59 AM Posted: 5/14/03 10:57 AM Expire: never
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