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} ]