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I am surprised at the behavior of VectorPlot in the following sense: plotting a vector field and examining the output at a point $(x_0,y_0)$ reveals that Mathematica doesn't draw the tail of the arrow at $(x_0,y_0)$ but rather it draws the base of the arrowhead at $(x_0,y_0)$. (Of course, the output points the arrow in the correct direction.)

This is, in my opinion, confusing/misleading for students learning about vector fields.

Has anyone developed an efficient workaround to this, so that when we plot the vector field we get output that positions the tail of the arrowhead at the point $(x_0,y_0)$ rather than the base of the arrowhead?

Here is some output which perhaps more clearly portrays the issue:

pts = Flatten[Table[{i, j}, {i, -1, 1, .5}, {j, -1, 1, .5}], 1];
p1 = ListPlot[pts, PlotStyle -> {{Red, PointSize[Large]}}];
p2 = VectorPlot[{x + y, 1}, {x, -1, 1}, {y, -1, 1}, VectorPoints -> pts, VectorScale -> Medium];
Show[p2, p1]

enter image description here

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1 Answer 1

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The arrow is actually centred over the spot, so we simply need to shift the arrow by half its length:

Show[p2 /. Arrow[{p_, q_}] :> Arrow[{p + (q - p)/2, q + (q - p)/2}], p1]

enter image description here

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  • $\begingroup$ Thanks, this accomplishes what I desire. It seems to me that this should be the default behavior of VectorPlot. $\endgroup$
    – JohnD
    Jul 17, 2012 at 20:54
  • $\begingroup$ Have another Enlightened badge, Simon. :-) $\endgroup$
    – Mr.Wizard
    Jul 17, 2012 at 23:36
  • $\begingroup$ @Mr.Wizard, thank you. It's my first one actually :-) $\endgroup$ Jul 18, 2012 at 21:13
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    $\begingroup$ @texasAUtiger: Your reaction to the default behavior was mine as well. But on my part this is due primarily because math textbooks and teachers draw the fields with the tails at the specified points; hence the dissonance for students who look at the Mathematica result. But in truth the Mathematica default may be more reasonable: having the middle of the arrow at the point gives a more realistic representation of the flow through the point, rather than the flow away from the point. $\endgroup$
    – murray
    Jul 19, 2012 at 0:21
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    $\begingroup$ @texasAUtiger, something like myVectorPlot[x__]:=VectorPlot[x]/.Arrow[{p_,q_}]:>Arrow[{p+(q-p)/2,q+(q-p)/2}];SetAttributes[myVectorPlot,HoldAll] $\endgroup$ Jul 19, 2012 at 17:26

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