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In a ListPlot3D[ ] I want to have the Mesh at the same positions as the ticks. For some reason this isn't default if both are chosen Automatic.

So my question is if there is some function to read (or reproduce) the automatically generated Ticks as a list e.g. xTicksList and yTicksList and than use this like

Mesh-> {xTicksList,yTicksList}

Alternative solutions are of course also welcome. But no solutions with explicite values, this isn't what I want, because finally I want to use this in a more general recipe.

Edit:

Easy call:

SetDirectory["./"]
data = Import["file.dat"];
ListPlot3D[data, ViewPoint -> {0, -2, 4}]

Data to work on:

     -1.300000000000       0.210526315789       0.980235619886
     -1.163157894737       0.210526315789       0.979505821537
     -1.026315789474       0.210526315789       1.097953636927
     -0.889473684211       0.210526315789       1.102989687180
     -0.752631578947       0.210526315789       1.098700823572
     -0.615789473684       0.210526315789       1.125990693356
     -0.478947368421       0.210526315789       1.211353461701
     -0.342105263158       0.210526315789       1.815613507388
     -0.205263157895       0.210526315789       1.045807948880
     -0.068421052632       0.210526315789       0.000001971641
      0.068421052632       0.210526315789       0.000001971641
      0.205263157895       0.210526315789       1.045807948880
      0.342105263158       0.210526315789       1.815613507388
      0.478947368421       0.210526315789       1.211353461701
      0.615789473684       0.210526315789       1.125990693356
      0.752631578947       0.210526315789       1.098700823572
      0.889473684211       0.210526315789       1.102989687180
      1.026315789474       0.210526315789       1.097953636927
      1.163157894737       0.210526315789       0.979505821537
      1.300000000000       0.210526315789       0.980235619886
     -1.300000000000       0.421052631579       0.980942994071
     -1.163157894737       0.421052631579       0.981933173223
     -1.026315789474       0.421052631579       1.103154056150
     -0.889473684211       0.421052631579       1.107281088495
     -0.752631578947       0.421052631579       1.106941920492
     -0.615789473684       0.421052631579       1.146919259544
     -0.478947368421       0.421052631579       1.309678535944
     -0.342105263158       0.421052631579       0.584224780318
     -0.205263157895       0.421052631579       0.700847812228
     -0.068421052632       0.421052631579       0.000006770074
      0.068421052632       0.421052631579       0.000006770074
      0.205263157895       0.421052631579       0.700847812228
      0.342105263158       0.421052631579       0.584224780318
      0.478947368421       0.421052631579       1.309678535944
      0.615789473684       0.421052631579       1.146919259544
      0.752631578947       0.421052631579       1.106941920492
      0.889473684211       0.421052631579       1.107281088495
      1.026315789474       0.421052631579       1.103154056150
      1.163157894737       0.421052631579       0.981933173223
      1.300000000000       0.421052631579       0.980942994071
     -1.300000000000       0.631578947368       0.982279600261
     -1.163157894737       0.631578947368       0.986279051512
     -1.026315789474       0.631578947368       1.111702792051
     -0.889473684211       0.631578947368       1.114982129224
     -0.752631578947       0.631578947368       1.122873224846
     -0.615789473684       0.631578947368       1.194737734850
     -0.478947368421       0.631578947368       1.930464394003
     -0.342105263158       0.631578947368       0.560661235292
     -0.205263157895       0.631578947368       0.615345975499
     -0.068421052632       0.631578947368       0.964754106066
      0.068421052632       0.631578947368       0.964754106066
      0.205263157895       0.631578947368       0.615345975499
      0.342105263158       0.631578947368       0.560661235292
      0.478947368421       0.631578947368       1.930464394003
      0.615789473684       0.631578947368       1.194737734850
      0.752631578947       0.631578947368       1.122873224846
      0.889473684211       0.631578947368       1.114982129224
      1.026315789474       0.631578947368       1.111702792051
      1.163157894737       0.631578947368       0.986279051512
      1.300000000000       0.631578947368       0.982279600261
     -1.300000000000       0.842105263158       0.984506863561
     -1.163157894737       0.842105263158       0.993017144639
     -1.026315789474       0.842105263158       1.123329136135
     -0.889473684211       0.842105263158       1.127086080172
     -0.752631578947       0.842105263158       1.151323601756
     -0.615789473684       0.842105263158       1.316936571158
     -0.478947368421       0.842105263158       0.533092973179
     -0.342105263158       0.842105263158       0.546076002707
     -0.205263157895       0.842105263158       0.576957097781
     -0.068421052632       0.842105263158       0.684846595150
      0.068421052632       0.842105263158       0.684846595150
      0.205263157895       0.842105263158       0.576957097781
      0.342105263158       0.842105263158       0.546076002707
      0.478947368421       0.842105263158       0.533092973179
      0.615789473684       0.842105263158       1.316936571158
      0.752631578947       0.842105263158       1.151323601756
      0.889473684211       0.842105263158       1.127086080172
      1.026315789474       0.842105263158       1.123329136135
      1.163157894737       0.842105263158       0.993017144639
      1.300000000000       0.842105263158       0.984506863561
     -1.300000000000       1.052631578947       0.988041894481
     -1.163157894737       1.052631578947       1.002844293634
     -1.026315789474       1.052631578947       1.137460222080
     -0.889473684211       1.052631578947       1.145431494008
     -0.752631578947       1.052631578947       1.204639094902
     -0.615789473684       1.052631578947       2.034283267433
     -0.478947368421       1.052631578947       0.527426104920
     -0.342105263158       1.052631578947       0.536322515501
     -0.205263157895       1.052631578947       0.555643903601
     -0.068421052632       1.052631578947       1.542776620591
      0.068421052632       1.052631578947       1.542776620591
      0.205263157895       1.052631578947       0.555643903601
      0.342105263158       1.052631578947       0.536322515501
      0.478947368421       1.052631578947       0.527426104920
      0.615789473684       1.052631578947       2.034283267433
      0.752631578947       1.052631578947       1.204639094902
      0.889473684211       1.052631578947       1.145431494008
      1.026315789474       1.052631578947       1.137460222080
      1.163157894737       1.052631578947       1.002844293634
      1.300000000000       1.052631578947       0.988041894481
     -1.300000000000       1.263157894737       0.993507698008
     -1.163157894737       1.263157894737       1.016663871059
     -1.026315789474       1.263157894737       1.153029591526
     -0.889473684211       1.263157894737       1.173527252601
     -0.752631578947       1.263157894737       1.324259264609
     -0.615789473684       1.263157894737       0.520310839569
     -0.478947368421       1.263157894737       0.523127565540
     -0.342105263158       1.263157894737       0.529437718570
     -0.205263157895       1.263157894737       0.542365083073
     -0.068421052632       1.263157894737       1.251779214963
      0.068421052632       1.263157894737       1.251779214963
      0.205263157895       1.263157894737       0.542365083073
      0.342105263158       1.263157894737       0.529437718570
      0.478947368421       1.263157894737       0.523127565540
      0.615789473684       1.263157894737       0.520310839569
      0.752631578947       1.263157894737       1.324259264609
      0.889473684211       1.263157894737       1.173527252601
      1.026315789474       1.263157894737       1.153029591526
      1.163157894737       1.263157894737       1.016663871059
      1.300000000000       1.263157894737       0.993507698008
     -1.300000000000       1.473684210526       1.001780955507
     -1.163157894737       1.473684210526       1.035419641030
     -1.026315789474       1.473684210526       1.168300600319
     -0.889473684211       1.473684210526       1.218742366781
     -0.752631578947       1.473684210526       1.820497914358
     -0.615789473684       1.473684210526       0.517801652652
     -0.478947368421       1.473684210526       0.519782526335
     -0.342105263158       1.473684210526       0.524378305806
     -0.205263157895       1.473684210526       1.497512379500
     -0.068421052632       1.473684210526       1.158442502764
      0.068421052632       1.473684210526       1.158442502764
      0.205263157895       1.473684210526       1.497512379500
      0.342105263158       1.473684210526       0.524378305806
      0.478947368421       1.473684210526       0.519782526335
      0.615789473684       1.473684210526       0.517801652652
      0.752631578947       1.473684210526       1.820497914358
      0.889473684211       1.473684210526       1.218742366781
      1.026315789474       1.473684210526       1.168300600319
      1.163157894737       1.473684210526       1.035419641030
      1.300000000000       1.473684210526       1.001780955507
     -1.300000000000       1.684210526316       1.013974303940
     -1.163157894737       1.684210526316       1.059492763356
     -1.026315789474       1.684210526316       1.180869891090
     -0.889473684211       1.684210526316       1.299514133592
     -0.752631578947       1.684210526316       0.516453133533
     -0.615789473684       1.684210526316       0.515737848476
     -0.478947368421       1.684210526316       0.517124685004
     -0.342105263158       1.684210526316       0.520545139810
     -0.205263157895       1.684210526316       1.214149849511
     -0.068421052632       1.684210526316       1.111669990419
      0.068421052632       1.684210526316       1.111669990419
      0.205263157895       1.684210526316       1.214149849511
      0.342105263158       1.684210526316       0.520545139810
      0.478947368421       1.684210526316       0.517124685004
      0.615789473684       1.684210526316       0.515737848476
      0.752631578947       1.684210526316       0.516453133533
      0.889473684211       1.684210526316       1.299514133592
      1.026315789474       1.684210526316       1.180869891090
      1.163157894737       1.684210526316       1.059492763356
      1.300000000000       1.684210526316       1.013974303940
     -1.300000000000       1.894736842105       1.031151313623
     -1.163157894737       1.894736842105       1.087145840815
     -1.026315789474       1.894736842105       1.188079272660
     -0.889473684211       1.894736842105       1.480552497483
     -0.752631578947       1.894736842105       0.514891129597
     -0.615789473684       1.894736842105       0.514017825943
     -0.478947368421       1.894736842105       0.514975893386
     -0.342105263158       1.894736842105       1.653213278836
     -0.205263157895       1.894736842105       1.132316352893
     -0.068421052632       1.894736842105       1.083852929370
      0.068421052632       1.894736842105       1.083852929370
      0.205263157895       1.894736842105       1.132316352893
      0.342105263158       1.894736842105       1.653213278836
      0.478947368421       1.894736842105       0.514975893386
      0.615789473684       1.894736842105       0.514017825943
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      0.889473684211       1.894736842105       1.480552497483
      1.026315789474       1.894736842105       1.188079272660
      1.163157894737       1.894736842105       1.087145840815
      1.300000000000       1.894736842105       1.031151313623
     -1.300000000000       2.105263157895       1.053263797252
     -1.163157894737       2.105263157895       1.112054099666
     -1.026315789474       2.105263157895       1.187887756512
     -0.889473684211       2.105263157895       2.414939312234
     -0.752631578947       2.105263157895       0.513547775105
     -0.615789473684       2.105263157895       0.512568414028
     -0.478947368421       2.105263157895       0.513214034428
     -0.342105263158       2.105263157895       1.234630789787
     -0.205263157895       2.105263157895       1.093026423469
     -0.068421052632       2.105263157895       1.065649778360
      0.068421052632       2.105263157895       1.065649778360
      0.205263157895       2.105263157895       1.093026423469
      0.342105263158       2.105263157895       1.234630789787
      0.478947368421       2.105263157895       0.513214034428
      0.615789473684       2.105263157895       0.512568414028
      0.752631578947       2.105263157895       0.513547775105
      0.889473684211       2.105263157895       2.414939312234
      1.026315789474       2.105263157895       1.187887756512
      1.163157894737       2.105263157895       1.112054099666
      1.300000000000       2.105263157895       1.053263797252
     -1.300000000000       2.315789473684       1.076657703675
     -1.163157894737       2.315789473684       1.123492475408
     -1.026315789474       2.315789473684       1.179776702031
     -0.889473684211       2.315789473684       0.517636004512
     -0.752631578947       2.315789473684       0.512380796022
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     -0.478947368421       2.315789473684       0.519172187319
     -0.342105263158       2.315789473684       1.138037117826
     -0.205263157895       2.315789473684       1.070113678169
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      1.300000000000       2.315789473684       1.076657703675
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     -0.752631578947       2.526315789474       0.511360095534
     -0.615789473684       2.526315789474       0.510277474936
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     -0.342105263158       2.526315789474       1.094672456667
     -0.205263157895       2.526315789474       1.055241265973
     -0.068421052632       2.526315789474       1.043728713057
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      1.300000000000       2.526315789474       1.091865153557
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      0.889473684211       2.947368421053       0.514306616086
      1.026315789474       2.947368421053       1.124857239675
      1.163157894737       2.947368421053       1.064870984592
      1.300000000000       2.947368421053       1.070982617491
     -1.300000000000       3.157894736842       1.047866508842
     -1.163157894737       3.157894736842       1.041164829929
     -1.026315789474       3.157894736842       1.103940126372
     -0.889473684211       3.157894736842       0.513409767406
     -0.752631578947       3.157894736842       0.508961575187
     -0.615789473684       3.157894736842       1.326407622207
     -0.478947368421       3.157894736842       1.082011967173
     -0.342105263158       3.157894736842       1.044357195862
     -0.205263157895       3.157894736842       1.031641411387
     -0.068421052632       3.157894736842       1.027100715053
      0.068421052632       3.157894736842       1.027100715053
      0.205263157895       3.157894736842       1.031641411387
      0.342105263158       3.157894736842       1.044357195862
      0.478947368421       3.157894736842       1.082011967173
      0.615789473684       3.157894736842       1.326407622207
      0.752631578947       3.157894736842       0.508961575187
      0.889473684211       3.157894736842       0.513409767406
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share|improve this question
    
Take a look at AbsoluteOptions[] –  belisarius Apr 29 at 17:52
    
Yes I thought about this too, but then I have to Plot everything twice (what takes some time) ... but if there is no other way I'll try this. –  PeMa Apr 29 at 18:16
    
:-) AbsoluteOptions[] gives: {Ticks -> Automatic} . –  PeMa Apr 29 at 18:30
    
Related: minor grid lines (2D case). Please provide data to work on. –  Kuba Apr 29 at 18:43
    
I added some data. In the plot you see 6 Mesh lines from 0 to 1 on the x-axes while there are only 5 Ticks. –  PeMa Apr 29 at 19:33

2 Answers 2

up vote 4 down vote accepted

Create a custom ticks function that, with some additional tuning/styling, can reproduce the Automatic-ally produced ticks:

ClearAll[tickF];
tickF[div1_, div2_: - 1] := (If[div2 == -1,
        Thread[{#, #, {.02, 0}}, List, 2] &@FindDivisions[{#1, #2}, div1],
        Join @@ MapAt[Join @@ # &, {Thread[{#, #, {.02, 0}}, List, 2] &@#[[1]], 
           Thread[{#, "", {.01, 0}}, List, 2] & /@ #[[2]]} &@
                  FindDivisions[{#1, #2}, {div1, div2}], {2}]]) &

Usage:

plt1 = Plot3D[Sin[x y], {x, 0, 4}, {y, 0, 4}, FaceGrids -> All,ImageSize -> 400, 
    Ticks -> Evaluate@({(t1 = {##}; tickF[8, 5][##]) &,
            (t2 = {##}; tickF[8, 5][##]) &,
           (t3 = {##}; N /@ tickF[8, 5][##]) &}),
    Mesh -> {(tickF[8] @@ t1)[[All, 1]], (tickF[8] @@ t2)[[All, 1]]}];
plt2 = Plot3D[Sin[x y], {x, 0, 4}, {y, 0, 4}, FaceGrids -> All, ImageSize -> 400,
    Mesh -> None];
Row[{plt2, plt1}, Spacer[5]]//Panel

enter image description here

With OP's data

lp2 = ListPlot3D[data, ViewPoint -> {0, -2, 4},  ImageSize -> 400];
lp1 = ListPlot3D[data, ViewPoint -> {0, -2, 4},  ImageSize -> 400, 
   Ticks -> Evaluate@({(t1 = {##}; tickF[4, 5][##]) &,
           (t2 = {##}; tickF[4, 5][##]) &,
           (t3 = {##}; N /@ tickF[4, 5][##]) &}),
Mesh -> {(tickF[4] @@ t1)[[All, 1]], (tickF[4] @@ t2)[[All, 1]]}];
Row[{lp2, lp1}, Spacer[5]] // Panel

enter image description here

share|improve this answer
    
I'm not sure that the generated divisions will always match the elusive internal routine.In my machine a PlotRange of {x, 10, 40} (as an example) gives different results –  belisarius Apr 30 at 1:24
    
@belisarius, I agree; we don't know how the second argument of FindDivisions is selected internally. I also get different x-ticks for {x,10,40}; it does take some trial-and-error to find that tickF[5, 5] gives the same ticks. –  kguler Apr 30 at 1:44
    
In fact I don't believe the internal stuff was done using FindDivisions[](it was new in V.7) –  belisarius Apr 30 at 1:50
    
@belisarius, can't recollect the source of my hunch that internal tick generation uses FindDivisions; definitely nothing "official" - most likely some comments/Q/As on this site :) –  kguler Apr 30 at 1:57
    
Did I understand it right, that you tried to imitate mathematica's internal procedure to create the ticks, but it's not entirely working? –  PeMa Apr 30 at 5:23

I know this seems utterly complicated for the task at hand, but as FullGraphics[] isn't implemented for Graphics3D[] and AbsoluteOptions[] doesn't work for Ticks[], I don't know an easier way:

s1 = ListPlot3D[data, Ticks -> #, PlotStyle -> None, Mesh -> None] & /@ 
               {{Automatic, None, None}, {None, Automatic, None}};
mesh = Map[ToExpression@ StringJoin[#[[All, 1]]] &, (GatherBy[#, #[[2]] &] & /@ 
           (Cases[#, Text[t_, {_, y_}, __] :> {t, y}, Infinity] & /@ (First@
           ImportString[ExportString[#, "EPS" ], "EPS"] & /@  s1))), {2}];

ListPlot3D[data, Mesh -> mesh]

Mathematica graphics

share|improve this answer
    
Amazing, thanks! But I need to modify this, to get meshlines at minor ticks as well. So, is there a way to write a scale to the minor ticks? –  PeMa Apr 30 at 5:14

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