Re: PlotVectorField

*To*: mathgroup at smc.vnet.net*Subject*: [mg34819] Re: PlotVectorField*From*: shollis at armstrong.edu (Selwyn Hollis)*Date*: Sat, 8 Jun 2002 05:21:34 -0400 (EDT)*References*: <adpg01$j55$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

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