Re: Drawing Potatoes and a Problem with Piecewise

*To*: mathgroup at smc.vnet.net*Subject*: [mg80146] Re: Drawing Potatoes and a Problem with Piecewise*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Tue, 14 Aug 2007 06:48:48 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <f9p580$r58$1@smc.vnet.net>

David Park wrote: > Several years ago there was a question on MathGroup on how to draw a potato > in Mathematica. > > The SphericalDraw3D documentation has an example of a lumpy sphere and I > decided to turn this into a potato by stretching it by a factor of two along > the z axis. However, to get a reasonable looking potato it is necessary to > damp down the variations in radius near the ends with a weighting function. > So I constructed the following w weighting function using Piecewise. > > w[\[Theta]_] = Piecewise[ > {{1/2 (\[Theta]/(\[Pi]/4))^3, 0 <= \[Theta] < \[Pi]/4}, > {1 - 1/2 ((\[Pi]/2 - \[Theta])/(\[Pi]/4))^3, \[Pi]/ > 4 <= \[Theta] < \[Pi]/2}, > {1 + 1/2 ((\[Pi]/2 - \[Theta])/(\[Pi]/4))^3, \[Pi]/2 <= \[Theta] < > 3 \[Pi]/4}, > {1/2 ((\[Pi] - \[Theta])/(\[Pi]/4))^3, > 3 \[Pi]/4 <= \[Theta] <= \[Pi]}}] > Plot[w[\[Theta]], {\[Theta], 0, \[Pi]}, PlotPoints -> 20, > Frame -> True] > > The problem with this is that there are gaps in the function, which are more > or less visible depending on the number of PlotPoints. Am I defining > Piecewise incorrectly, or is there a bug with Piecewise in plotting > functions? <snip> David, The definition of w is correct (w is continuous). However, the trouble seems to come from the adaptive sampling, as we can see by evaluating the following expressions: Plot[ w[\[Theta]], { \[Theta], 0, Pi}, PlotPoints -> 45, Frame -> True, MaxRecursion -> 15] Plot[ w[\[Theta]], { \[Theta], 0, Pi}, PlotPoints -> 20, Frame -> True, MaxRecursion -> 0] Plot[ w[\[Theta]], { \[Theta], 0, Pi}, PlotPoints -> 20, Frame -> True] On my system, the first expression draws a smooth curve, while plot rendered by the second expression is cut on the left (but not on the right). (The last expression is the original one for comparison.) -- Jean-Marc

**problem using Ersek's RootSearch**

**Re: a problem about NDSolve and NIntegrate**

**Re: Drawing Potatoes and a Problem with Piecewise**

**Graphing an inequality**