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plotting - VectorPlot3D - vectors starting at points


Normally the vectors in VectorPlot3D are attached the middle. How to get them attached at the beginning (what is typical conventions in most textbooks) by use of VectorPlot3D?




Answer



Update V.11.3: In version 11.3+ the new option VectorMarkers can be used with Placed to control the position of vectors:


points = Tuples[{-1, 1}, {2}];    
Row[VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -2, 2}, {y, -2, 2}, 
   VectorPoints -> points, VectorMarkers -> Placed["Arrow" , #], 
   VectorScale -> {.5, .4}, ImageSize -> 300, 
   Prolog -> {Yellow, Opacity[.5], Rectangle[{-1, -1}, {1, 1}], 
      Opacity[1], Red, PointSize[Large], Point[points]}] & /@ {"Start", "End"}]

enter image description here



Original answer:


You can post-process the graphics output to shift the arrows:


points = Tuples[{-1, 1}, {2}];

vp1 = VectorPlot[{-1 - x^2 + y, 1 + x - y^2}, {x, -2, 2}, {y, -2, 2}, 
   VectorPoints -> points, VectorScale -> {.5, .4}, ImageSize -> 400, 
   Prolog -> {Yellow, Opacity[.5], Rectangle[{-1, -1}, {1, 1}], 
             Opacity[1], Red, PointSize[Large], Point[points]}];

vp1b = vp1 /. Arrow[x_] :> Arrow[{Mean[x], Mean[x] + Last[x] - First[x]}];

(* or  vp1 /. Arrow[x_] :> Translate[Arrow[x],Mean[x]-First[x]] *)

Row[{vp1, vp1b}, Spacer[10]]

enter image description here


Similarly, for VectorPlot3D:


points2 =Tuples[{-1, 1}, {3}];

vp2 = VectorPlot3D[{x, y, z}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2}, 
   VectorPoints -> points2, VectorScale -> .25, ImageSize -> 400];

vp2 = Show[vp2, Graphics3D@{Yellow, Opacity[.5], Cuboid[{-1, -1, -1}, {1, 1, 1}], 
     Opacity[1], Red, PointSize[.03], Sphere[points2, .2]}];
vp2b = vp2 /. Arrow[x_] :> Arrow[{Mean[x], Mean[x] + Last[x] - First[x]}];

Row[{vp2, vp2b}, Spacer[10]]

enter image description here


Update: A function that shifts the arrows to start from the designated points:


trF = MapAt[# /. Arrow[x_] :> Arrow[{Mean[x], Mean[x] + Last[x] - First[x]}] &, #, {1}] &;
(* or trF = MapAt[#/.Arrow[x_] :> Translate[Arrow[x],Mean[x]-First[x]]&,#,{1}]&; *)


Row[trF /@ {vp1, vp2}, Spacer[15]]

enter image description here


Update 2: For 3D arrow glyphs, we need to modify the replacement rule:


vp3 = VectorPlot3D[{x, y, z}, {x, -2, 2}, {y, -2, 2}, {z, -2, 2},
   VectorPoints->points2, VectorStyle -> "Arrow3D", VectorScale -> .25, ImageSize -> 400];
vp3 = Show[vp3,  Graphics3D@{Yellow, Opacity[.5], Cuboid[{-1, -1, -1}, {1, 1, 1}], 
     Opacity[1], Red, PointSize[.03], Sphere[points2, .2]}];
vp3b =vp3/. Arrow[Tube[x_, r__]]:>Arrow[Tube[{Mean[x], Mean[x] + Last[x] - First[x]}, r]];


Row[{vp3, vp3b}, Spacer[10]]

enter image description here


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