Re: Plotting 2D functions with discontinuities

*To*: mathgroup at smc.vnet.net*Subject*: [mg49546] Re: [mg49509] Plotting 2D functions with discontinuities*From*: Selwyn Hollis <sh2.7183 at misspelled.erthlink.net>*Date*: Fri, 23 Jul 2004 05:59:35 -0400 (EDT)*References*: <200407220645.CAA21038@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On Jul 22, 2004, at 2:45 AM, Micky Handel wrote: > Hello > I m interested in plotting functions with some discontinuities without > displaying the vertical line that Mathematica plots automatically. I > have > tried using the DiscontinuityPlot and the RLSCF packages that I found > and > downloaded. However, RLSCF does not function when my function is > defined by > a Which command, and the DiscontinuityPlot package does not work well > with > multiple plots. Is there another way of solving this problem? > Thanks > Micky Mickey, Here's a routine that I wrote form my MmaCalc package (see web link below). It's basically an improved version of DiscontinuityPlot. ShowDiscontinuous::usage = "ShowDiscontinuous[graphic] shows graphic after removing near-vertical segments from Line primitives."; Options[ShowDiscontinuous]={Threshold->1}; SetAttributes[ShowDiscontinuous,HoldFirst]; Needs["Utilities`FilterOptions`"]; der2= Compile[{x0,f0,x1,f1,x2,f2},((f2-f1)/(x2-x1)-(f1-f0)/(x1-x0))/(x2-x0)]; approxD2[{p0_,p1_,p2_}]:= der2@@Flatten[{p0,p1,p2}]; ShowDiscontinuous[graph_, (opts___)?OptionQ] := Module[{plot, plotdata, tells, newplotdata = {}, thresh, n, x, y, z}, thresh = 1000.*Threshold /. {opts} /. Options[ShowDiscontinuous]; plotdata = {First[plot=Block[{$DisplayFunction=Identity}, graph]]} /. {s___,{Line[data_]}} -> {{s},data}; If[Depth[plotdata]==6, plotdata=First[plotdata] ]; n=Length[plotdata]; Do[ tells = Flatten[(If[Abs[#1] < thresh, 0, #1] & ) /@ approxD2 /@ Partition[plotdata[[i,2]], 3, 1]]; tells = Flatten[{1,Position[tells,_Real]+1, Length[plotdata[[i,2]]]}]; x=y=-1; Scan[Block[{z=#}, If[x+1==y==z-1, tells=DeleteCases[tells,y]];x=y;y=z]&, tells]; tells = tells/.{1,q_,l_}->{1,l}; AppendTo[newplotdata, ({Sequence@@plotdata[[i,1]], Line[plotdata[[i,2,Range @@ #1]]]}&)/@ Partition[tells, 2]], {i, n}]; Show[Graphics[newplotdata], FilterOptions[Graphics,opts], DisplayFunction->$DisplayFunction, Last[plot]]]; (*Example*) Plot[Floor[x + .5] + .25, {x, -1, 5}]//ShowDiscontinuous ----- Selwyn Hollis http://www.appliedsymbols.com (edit reply-to to reply)

**References**:**Plotting 2D functions with discontinuities***From:*"Micky Handel" <hmicky@hotmail.com>