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I have a list contour plot overlay by a 15x15 mesh grid. And I want to label the axes with numbers positioned at the center of the cells instead of the grid lines.

 data = {
 {1, 0, 2, 3, 4, 5, 6, 6, 7, 8, 8, 8, 8, 8, 8},
 {0, 0, 2, 3, 4, 4, 5, 6, 7, 7, 9, 9, 9, 9, 8},
 {0, 1, 2, 3, 4, 4, 5, 6, 6, 8, 9, 9, 9, 8, 9},
 {0, 2, 3, 4, 5, 6, 6, 6, 7, 8, 8, 9, 9, 8, 8},
 {0, 2, 3, 4, 5, 6, 7, 7, 8, 8, 9, 9, 9, 8, 7},
 {1, 2, 2, 4, 5, 6, 6, 7, 8, 8, 8, 8, 9, 8, 8},
 {1, 2, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 8, 8},
 {1, 2, 2, 3, 4, 5, 6, 7, 8, 8, 9, 9, 8, 8, 8},
 {2, 2, 3, 3, 4, 5, 6, 7, 9, 8, 8, 8, 8, 8, 7},
 {2, 2, 3, 3, 4, 5, 6, 7, 8, 8, 7, 7, 8, 7, 7},
 {1, 1, 1, 2, 4, 4, 6, 7, 8, 7, 7, 6, 6, 6, 7},
 {0, 1, 1, 2, 3, 4, 5, 7, 7, 7, 7, 6, 5, 5, 6},
 {0, 1, 2, 3, 4, 5, 6, 7, 5, 5, 6, 6, 5, 5, 5},
 {1, 2, 2, 2, 4, 4, 5, 6, 6, 4, 5, 6, 5, 5, 4},
 {3, 3, 3, 3, 3, 4, 6, 6, 7, 4, 4, 5, 5, 4, 2}};

ListContourPlot[
data, ColorFunction -> ColorData[{"Warm", "Reverse"}],
ContourLabels -> None, ContourStyle -> None, InterpolationOrder -> 4, 
Contours -> 10, Mesh -> 14,  MeshFunctions -> {#1 &, #2 &}, 
MeshStyle -> Black, ScalingFunctions -> {Identity, "Reverse"}, 
FrameTicks -> {{Table[{-i - 0.5, i}, {i, 0, 14, 1}], None}, {None, Table[{i + 0.5, i}, {i, 0, 14, 1}]}}]

enter image description here

However, the frame ticks doesn't fit to the grids completely. Is there any way to fix it?

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    $\begingroup$ Mesh->{Range[14]-0.5,-(Range[14]+0.5)} will line put mesh exactly on your ticks. Drop the 0.5 if you want the mesh shifted a half cell relative to the ticks. $\endgroup$
    – N.J.Evans
    Aug 30, 2017 at 17:56
  • $\begingroup$ I tried your methods, the ticks fit perfectly with the mesh. But the mesh become 14x14 instead of 15x15. I want it to be 15x15 because I want to assign coordinates for each of the elements in data. $\endgroup$
    – Kent Vk
    Aug 30, 2017 at 18:14
  • $\begingroup$ To modify @N.J.Evans comment, try it with either Mesh -> {Range[15] - 0.5, -(Range[15] + 0.5)} or Mesh -> {Range[15], -Range[15]}. Are they what you're looking for? $\endgroup$
    – aardvark2012
    Aug 31, 2017 at 3:43
  • $\begingroup$ No, I want 15x15 equal sized grids, with ticks labeled at the center to the cells. Changing Mesh->{Range[14]-0.5,-(Range[14]+0.5)}, Mesh->{Range[14],-(Range[14])}, Mesh->{Range[15]-0.5,-(Range[15]+0.5)} or Mesh->{Range[15],-(Range[15])} doesn't give 15x15 equal sized cells and the ticks labeled from 1 to 15. $\endgroup$
    – Kent Vk
    Aug 31, 2017 at 14:02

1 Answer 1

Reset to default
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I found what I want by modifying the frame ticks.

FrameTicks -> {{Table[{-(22/15) - 14/15 (i - 1), i}, {i, 1, 15, 1}], 
None}, {None, Table[{22/15 + 14/15 (i - 1), i}, {i, 1, 15, 1}]}}

The total width of a row is 14 units. By splitting it into 15 equal size cells each segment will have $14/15$ units and half of a unit is $7/15$ units. So the tick label 1 is in position $1+7/15=22/15$, label 2in position $(22/15)+14/15$, label 3 in position $(22/15)+14/15+14/15$ and this eventually forms an arithmetic progression.

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