Argthtjtr

I am trying to create a table of points, where the size of the step would change linearly from a certain value to another. Bellow is a simple code to demonstrate a table of points with a constant step in X and Y direction.

MasterMesh=Flatten[Table[{XX , YY, 0}, {XX, -1/2, 1/2, 0.2}, {YY, -1/2, 1/2, 0.2}], 1];

ListPointPlot3D[MasterMesh]

My goal would ultimately be, to create a raster of point that is something like shown in the figure bellow (drawn clumsily), where the distances between the new points (marked red bellow) are supposed to change linearly in a way that L1:L2:L3:L4:L5=1:2:3:4:5.

Any help will be much appreciated!

g1 = Prepend[Accumulate@Range[5], 0]

(* {0, 1, 3, 6, 10, 15} *)



g2 = Prepend[Accumulate@Reverse@Range[5], 0]

(* {0, 5, 9, 12, 14, 15} *)



Join @@ MapIndexed[{First[#2], #1, 0} &,

   Subdivide[g1, g2, 5],

   {2}

   ] // ListPointPlot3D

MasterMesh =

  Flatten[Table[{1.7^x, 1.7^y, 0},

    {x, 1, 2, .1},

    {y, 1, 2, .1}], 1];

ListPointPlot3D[MasterMesh]

You can change n and range

n = 5

range = .5

d = 2 range/n

x = FoldList[# + 1/(n*(n + 1)/2)*#2*2 range &, -range, Range@n];

h = Table[{x[[i]], j, 0}, {i, n + 1}, {j, -range, range, d}];

g = Table[Diagonal@Table[{i, k, 0}, {i, x[[j]], -x[[-j]], 

  Abs[x[[j]] + x[[-j]]]/(n + 1)}, {k, -range, range, d}], {j, 2, n}];

ListPointPlot3D[Join[{h[[1]]}, g, {h[[n + 1]]}],PlotStyle -> PointSize[Large]]    

n=12 and range=2