Re: Plotting Piecewise Functions with Discontinuites

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1949] Re: Plotting Piecewise Functions with Discontinuites*From*: wiener at finance.wharton.upenn.edu (Zvi Wiener)*Date*: Sat, 26 Aug 1995 00:09:25 -0400*Organization*: University of Pennsylvania

Paul J. Simonich (simonichpj%dfms%usafa at dfmail.usafa.af.mil) wrote: : I'm trying to plot a piecewise function with a discontinuity at x=3: : f[x_]:=Which[x<=-3,3, : x>=-3 && x<=3, Abs[x], : x>3,-3] : Plot[f[x],{x,-7,7},AxesLabel->{x,y},PlotRange->All]; : Mathematica draws a veritcal line connecting the points of discontinuity. : Is there a "simple way" to get Mathematica to not evaluate the function : exactly at the point of discontinuity besides using Show[ ] with two : separate plots? : Thanks in Advance. : Capt Paul Simonich : Dept of Mathematical Sciences : US Air Force Academy (* Subject: Re: plotting graphs with asymptotes Tom Wickham-Jones at Wolfram, solved this problem elegantly a few months ago in response to a similar query. I made a nice NeXT notebook---mail me if you can take NeXTMail. But here is Tom's code: *) Unprotect[Plot]; Plot[ f_, {x_, lims__ /; Length[ {lims}] > 2}, opts___] := Module[ (* Tom Wickham-Jones, WRI *) {temp, eps = 10^-15, d}, temp = Partition[{lims}, 2, 1]; (* make pairs offset by 1 *) temp = ( d = (#[[2]] - #[[1]])*eps; (* get a delta *) # + {d, -d} (* shrink both ends by delta *) )& (* map over pairs to get shrunken pairs *) /@ temp; temp = Plot[f, Evaluate[Prepend[#,x]], (* iter triplets *) DisplayFunction -> Identity, opts ]& /@ temp; Show[temp, DisplayFunction -> $DisplayFunction] ] Protect[Plot]; (* I call this "elegant" because you use this extended Plot in an already existing Mma syntax (that of NIntegrate) by specifying extra internal points at singularities: Plot[Tan[x], {x, 0, Pi/2, 3Pi/2, 2Pi}] *) Zvi Wiener Lehman Brothers, Inc. zwiene at lehman.com