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I'm trying to create a vector plot with uniform vector scaling. I need the x and y ranges to be very different, because I need to highlight the angle between the vectors and the y=0 axis. This means that I can't use an automatic aspect ratio, however, changing the aspect ratio is changing the vector scaling in a way that I don't understand.
This is my code

Show[VectorPlot[{If[y>0, 1-2x, 1-x], If[y>0, -6/25+2/5x-3/2y, -7/25+2/5x-1/2y]},
{x,0.49,0.8}, {y,-0.01,0.01}, VectorStyle->Black, VectorPoints->Coarse, 
VectorScale->{0.05, 1, None}, AspectRatio->0.62], 
ContourPlot[y==0, {x,0.48,0.8}, {y,-0.01,0.01}, ContourStyle->{Black}]]

which gives the following vector plot

enter image description here

I specifically need the arrows on the top left to be approximately the same size as the rest of them, and to not cross the y=0 axis. I've also entered specific functions into sfun, for instance

Show[VectorPlot[{If[y>0, 1-2x, 1-x], If[y>0, -6/25+2/5x-3/2y, -7/25+2/5x-1/2y]},
{x,0.49,0.8}, {y,-0.01,0.01}, VectorStyle->Black, VectorPoints->Coarse, 
VectorScale->{0.05, 1, #2&}, AspectRatio->0.62], 
ContourPlot[y==0, {x,0.48,0.8}, {y,-0.01,0.01}, ContourStyle->{Black}]]

which should give a uniform vector length for the same y values, but instead gives the picture below, where there is the same vector length problem in the upper left corner.

enter image description here

Is there a way to scale the vectors so that this doesn't happen?

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    $\begingroup$ See mathematica.stackexchange.com/questions/71787/… $\endgroup$ – Michael E2 Jan 1 '16 at 22:30
  • $\begingroup$ I don't think it is really a duplicate. It turned out that figuring out the rescaling was a bit tricky, esp. because VectorPlot was changing the plot range so that it didn't not match the plot domain. See my answer. $\endgroup$ – Michael E2 Jan 1 '16 at 23:06
  • $\begingroup$ Similar: mathematica.stackexchange.com/a/32613 $\endgroup$ – Michael E2 Jan 1 '16 at 23:22
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You have to scale the (x,y)-components of the vectors so that they correspond to the horizontal and vertical units on the screen. That means scaling (1) according to the PlotRange and (2) according to the AspectRatio.

Show[VectorPlot[{If[y > 0, 1 - 2 x, 1 - x], 
   If[y > 0, -6/25 + 2/5 x - 3/2 y, -7/25 + 2/5 x - 1/2 y]}, {x, 0.49,
    0.8}, {y, -0.01, 0.01},
  VectorStyle -> Black, VectorPoints -> Coarse,
  VectorScale -> {1/20, 1, 
    Function[{x, y, fx, fy, norm}, 
     If[norm > 0, 
      norm/Sqrt[(fx/(0.8 - 0.49))^2 + (0.62 fy/(0.01 - (-0.01)))^2], 
      0]]},
  AspectRatio -> 0.62, PlotRange -> All],
 ContourPlot[y == 0, {x, 0.48, 0.79}, {y, -0.01, 0.01}, 
  ContourStyle -> {Black}]
 ]

Mathematica graphics

Note: Adding PlotRange -> All was essential. VectorPlot was automatically extending the plot range, making it difficult to get the rescaling correct.

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