Using same pure function for curve and surface mappings

• To: mathgroup at smc.vnet.net
• Subject: [mg124579] Using same pure function for curve and surface mappings
• From: Chris Young <cy56 at comcast.net>
• Date: Wed, 25 Jan 2012 07:06:40 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```By defining a pure function for a mapping, we can streamline the
process of mapping curves to a surface. I'm just a little worried that
the syntax coloring puts the "Saddle" in bright blue. Does this mean
it's still an undefined global?

http://home.comcast.net/~cy56/Mma/CurveMapViaPureFunction.nb

http://home.comcast.net/~cy56/Mma/CurveMapViaPureFunctionPic.png

\[HorizontalLine]Saddle = (f \[Function] {f[[1]], f[[2]],
f[[1]] * f[[2]]})

Manipulate[
Grid [
{
{
LocatorPane[
P,

Show[
ParametricPlot[\[HorizontalLine]Bez[P, t], {t, 0, 1}],
Graphics @ {Dotted, Line[P]},
PlotRange -> 2,
Axes -> True
],
{{-2, -2}, {2, 2}, {.25, .25}}
],
Show[
ParametricPlot3D[
\[HorizontalLine]Saddle @ {u, v}, {u, -2, 2}, {v, -2, 2},
PlotStyle -> Opacity[opac],
Mesh -> False
],
ParametricPlot3D[
\[HorizontalLine]Saddle @  \[HorizontalLine]Bez[P, t], {t, 0, 1}
]
/.
Line[pts_, rest___] :> Tube[pts, 0.05, rest],
PlotRange -> 2
]
}
}
],
{{P,
{{-1, -1}, {-1, -.5}, {-1, 0}, {-1, .5}, {-1, 1},
{  1, -1}, {   1, -.5}, {  1, 0}, {   1, .5}, {  1, 1}}}, Locator},
{{opac, 0.75}, 0, 1}
]

```

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