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I'm proving to plot and edit some wolfram alpha laminae, but when I try it, I don't have any result, for example:

(from:http://blog.wolframalpha.com/data/uploads/2013/07/Curvespt31.cdf)

yamahaEquation = 
  WolframAlpha[
   "Yamaha symbol\[Hyphen]like equation", \
{{"DefiningInequalitiesPod:Lamina", 1}, "ComputableData"}];

GraphicsRow[{
  yamahaRegionPlot = 
   RegionPlot[
    Evaluate[yamahaEquation[[1]]],  {x, -0.5, 0.6}, {y, -0.6, 0.6}, 
    PlotPoints -> 50, MaxRecursion -> 1, Frame -> False],
  Plot3D[Evaluate[ yamahaEquation[[1, 1]] ],  {x, -0.5, 
    0.6}, {y, -0.6, 0.6}, Mesh -> False, MaxRecursion -> 6, 
   RegionFunction -> (Norm[{#1, #2}] <= 1/2 &), 
   ViewPoint -> {0, 0, 4}, Boxed -> False, Axes -> False]}] => (Blank image)

or

WolframAlpha["ferrari symbol like equation"] => WolframAlpha["ferrari symbol like equation", {{"Result", 1}, 
  "ComputableData"}] => Missing["NotAvailable"]

Somebody knows how to resolve it?

Thanks

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    – Mahdi
    Commented Apr 29, 2015 at 8:10

1 Answer 1

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The "Yamaha Equation" lamina is a function of two variables {x, y} and a parameter a. So, you need to supply something numeric for the a before you can plot.

yamahaRegionPlot = RegionPlot[
  Evaluate[yamahaEquation[[1]]] /. {a -> 1},  {x, -0.5, 0.6}, {y, -0.6, 0.6}, 
  PlotPoints -> 50, 
  Frame -> False];

yamaha3D = Plot3D[
  Evaluate[yamahaEquation[[1, 1]]] /. {a -> 1}, {x, -0.5, 0.6}, {y, -0.6, 0.6}, 
  Mesh -> False, 
  MaxRecursion -> 6, 
  RegionFunction -> (Norm[{#1, #2}] <= 1/2 &), 
  ViewPoint -> {0, 0, 4}, 
  Boxed -> False, 
  Axes -> False]

Although it would be a pain to check every lamina to see if there is an extra parameter like this, there is actually a fairly easy way out, because Mathematic already incorporates a lot of Wolfram|Alpha functionality (since v10). In this case there is function LaminaData that you can use:

yamahaEquation = LaminaData["YamahaEquation", "Inequalities"]

(* -> Function[a, Function[{x, y}, inequalities... ]] *)

This gives you the inequalities as a function of {x, y} nested inside a function of the parameter a. You can see that there is a parameter, by running

parameter = LaminaData["YamahaEquation", "Variables"]

(* -> {a} *)

The LaminaData function gives you easy access to a lot of other nice data about the laminae, so check out the documentation.

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