RE: Re: PlotVectorField

*To*: mathgroup at smc.vnet.net*Subject*: [mg34892] RE: [mg34819] Re: PlotVectorField*From*: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>*Date*: Wed, 12 Jun 2002 02:15:20 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

Selwyn, here another proposal, which should perform better (I expect, didn't test). Also this is more along you lines. Again I tried to simplify the cases: In[1]:= bounds = {{a, b}, {c, d}} = {{1, 2}, {-1, 0}}; In[2]:= xx = Sort[Table[Random[Real, bounds[[1]]], {10}]] In[3]:= yy = Sort[Table[Random[Real, bounds[[2]]], {10}]] In[4]:= z1 = Transpose[{xx, yy}] In[5]:= z = Append[Prepend[z1, {2.5, -1.1}], {2.2, 0.3}] In[7]:= Attributes[pull] = {HoldFirst} In[8]:= {head, tail} = {1, -1}; In[9]:= {atleft, atright, atbottom, attop} = Unevaluated[{Sequence[1, 1], Sequence[1, -1], Sequence[-1, 1], Sequence[-1, -1]}]; In[10]:= pull[z_, h_, hv_, dir_] := With[{r = (bounds[[hv, dir]] - z[[h*2, hv]])/(z[[h, hv]] - z[[h*2, hv]])}, z[[h]] = r z[[h]] + (1 - r)z[[h*2]] ] In[11]:= z In[12]:= Scan[Function[end, If[z[[end, 1]] < bounds[[atleft]], pull[z, end, atleft], If[z[[end, 1]] > bounds[[atright]], pull[z, end, atright]]]; If[z[[end, -1]] < bounds[[atbottom]], pull[z, end, atbottom], If[z[[end, -1]] > bounds[[attop]], pull[z, end, attop]]]; ], {head, tail}] In[13]:= z In[14]:= ListPlot[z, PlotRange -> bounds + {{-#, #}, {-#, #}} &[.1], Background -> Hue[.3, .1, 1], PlotStyle -> PointSize[.025], AspectRatio -> Automatic, PlotJoined -> True, Axes -> False, Epilog -> {Line[{{a, c}, {b, c}, {b, d}, {a, d}, {a, c}}], PointSize[.02], Point /@ z}] -- Hartmut > -----Original Message----- > From: shollis at armstrong.edu [mailto:shollis at armstrong.edu] To: mathgroup at smc.vnet.net > Sent: Saturday, June 08, 2002 11:22 AM > Subject: [mg34892] [mg34819] Re: PlotVectorField > > > I guess my original question was a bit cryptic, but Wolf's reply got > me thinking in the right direction. Actually what I was trying to do > was to overlay a vector field with several curves created with > ListPlot. The points given to ListPlot typically spill out beyond the > rectangle on which I want to plot, so I needed so way to restrict the > plot to the desired rectangle. PlotRange is the obvious way, but it > leads to the difficulties I was trying to describe. > > Anyway, I wonder what you all think about the following fix: Instead > of using PlotRange, I apply a ``pullback" function to the list of > points to make sure they all lie in the rectangle I want before I give > the list to ListPlot. The only points in the list that can possibly > spill out of the rectangle are the first and the last. So I made the > following functions for each edge of the rectangle a<=x<=b, c<=y<=d. > Each one just replaces the first/last point in the list with a convex > combination of first two/last two points in such a way that the result > is on the edge of the rectangle. > > pulla[z_,a_]:= Module[{r=(z[[1,1]]-a)/(z[[1,1]]-z[[2,1]])}, > ReplacePart[z, r*z[[2]]+(1-r)*z[[1]], 1]]; > pullb[z_,b_]:= Module[{r=(z[[-1,1]]-b)/(z[[-1,1]]-z[[-2,1]])}, > ReplacePart[z, r*z[[-2]]+(1-r)*z[[-1]], -1]]; > pullc[z_,c_]:= Module[{r=(z[[1,2]]-c)/(z[[1,2]]-z[[2,2]])}, > ReplacePart[z, r*z[[2]]+(1-r)*z[[1]], 1]]; > pulld[z_,d_]:= Module[{r=(z[[-1,2]]-d)/(z[[-1,2]]-z[[-2,2]])}, > ReplacePart[z, r*z[[-2]]+(1-r)*z[[-1]], -1]]; > > Then I put everything together like this: > > pullback[z_?MatrixQ,{a_,b_,c_,d_}]:=Module[{zz=z}, > If[If[If[If[If[If[If[If[zz[[1,1]]<a, > zz=pulla[zz,a],zz][[1,2]]<c, > zz=pullc[zz,c],zz][[-1,1]]>b, > zz=pullb[zz,b],zz][[-1,2]]>d, > zz=pulld[zz,d],zz][[-1,1]]<a, > zz=pullb[zz,a],zz][[-1,2]]<c, > zz=pulld[zz,c],zz][[1,1]]>b, > zz=pulla[zz,b],zz][[1,2]]>d, > zz=pullc[zz,d],zz];zz]; > > Now, pullback[pointlist, {a,b,c,d}] gives points that all lie in the > desired rectangle and still accurately produce the curve. > > If anyone has an ideas as to how this pullback function can be written > is a more ``MC" (Mathematica-ly Correct) way, I'd appreciate your > advice. > > Cheers, > Selwyn >