Linearly change the step size in a table












4












$begingroup$


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]


enter image description here



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.
enter image description here



Any help will be much appreciated!










share|improve this question









$endgroup$

















    4












    $begingroup$


    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]


    enter image description here



    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.
    enter image description here



    Any help will be much appreciated!










    share|improve this question









    $endgroup$















      4












      4








      4





      $begingroup$


      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]


      enter image description here



      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.
      enter image description here



      Any help will be much appreciated!










      share|improve this question









      $endgroup$




      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]


      enter image description here



      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.
      enter image description here



      Any help will be much appreciated!







      list-manipulation table data






      share|improve this question













      share|improve this question











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      share|improve this question










      asked Nov 22 '18 at 8:40









      markomarko

      856




      856






















          4 Answers
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          oldest

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          4












          $begingroup$

          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


          enter image description here






          share|improve this answer









          $endgroup$













          • $begingroup$
            Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
            $endgroup$
            – marko
            Nov 22 '18 at 10:19










          • $begingroup$
            @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
            $endgroup$
            – Szabolcs
            Nov 22 '18 at 10:21












          • $begingroup$
            Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
            $endgroup$
            – marko
            Nov 22 '18 at 10:29










          • $begingroup$
            @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
            $endgroup$
            – Szabolcs
            Nov 22 '18 at 10:39












          • $begingroup$
            Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
            $endgroup$
            – marko
            Nov 22 '18 at 12:35





















          2












          $begingroup$

          MasterMesh =
          Flatten[Table[{1.7^x, 1.7^y, 0},
          {x, 1, 2, .1},
          {y, 1, 2, .1}], 1];
          ListPointPlot3D[MasterMesh]





          share|improve this answer









          $endgroup$













          • $begingroup$
            Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
            $endgroup$
            – marko
            Nov 22 '18 at 9:25



















          2












          $begingroup$

          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]]


          enter image description here



          n=12 and range=2     


          enter image description here






          share|improve this answer











          $endgroup$





















            1












            $begingroup$

            Maybe someone will find this useful, so here is my code to achieve mesh distortion in both directions. It is achieved using the answer by Szabolcs and the Line-line intersection equation, taken from Wikipedia.



            NumElements1 = 10;
            NumElements2 = 4;
            ratio = 2;

            x[n_, ratio_] :=
            Normalize[
            Accumulate[
            Join[{0}, Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]], Max]
            reversex[n_, ratio_] :=
            Normalize[
            Accumulate[
            Join[{0},
            Reverse[Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]]], Max]

            g1 = x[NumElements1, ratio];
            g2 = reversex[NumElements1, ratio];

            g3 = x[NumElements2, ratio];
            g4 = reversex[NumElements2, ratio];

            Flatten[Table[
            MapThread[{(-#1 + (#1 - #2)*
            g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) -
            1), (#1*(g3[[i]] - g4[[i]]) -
            g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) - 1), 0} &, {g1,
            g2}], {i, 1, NumElements2 + 1}], 1] // ListPointPlot3D


            By changing ratio and NumElements1 and NumElements2, you can get the desired output. For the data above I get this:
            enter image description here






            share|improve this answer









            $endgroup$














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              4 Answers
              4






              active

              oldest

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              4 Answers
              4






              active

              oldest

              votes









              active

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              active

              oldest

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              4












              $begingroup$

              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


              enter image description here






              share|improve this answer









              $endgroup$













              • $begingroup$
                Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
                $endgroup$
                – marko
                Nov 22 '18 at 10:19










              • $begingroup$
                @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:21












              • $begingroup$
                Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
                $endgroup$
                – marko
                Nov 22 '18 at 10:29










              • $begingroup$
                @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:39












              • $begingroup$
                Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
                $endgroup$
                – marko
                Nov 22 '18 at 12:35


















              4












              $begingroup$

              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


              enter image description here






              share|improve this answer









              $endgroup$













              • $begingroup$
                Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
                $endgroup$
                – marko
                Nov 22 '18 at 10:19










              • $begingroup$
                @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:21












              • $begingroup$
                Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
                $endgroup$
                – marko
                Nov 22 '18 at 10:29










              • $begingroup$
                @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:39












              • $begingroup$
                Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
                $endgroup$
                – marko
                Nov 22 '18 at 12:35
















              4












              4








              4





              $begingroup$

              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


              enter image description here






              share|improve this answer









              $endgroup$



              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


              enter image description here







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Nov 22 '18 at 9:33









              SzabolcsSzabolcs

              165k14450954




              165k14450954












              • $begingroup$
                Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
                $endgroup$
                – marko
                Nov 22 '18 at 10:19










              • $begingroup$
                @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:21












              • $begingroup$
                Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
                $endgroup$
                – marko
                Nov 22 '18 at 10:29










              • $begingroup$
                @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:39












              • $begingroup$
                Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
                $endgroup$
                – marko
                Nov 22 '18 at 12:35




















              • $begingroup$
                Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
                $endgroup$
                – marko
                Nov 22 '18 at 10:19










              • $begingroup$
                @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:21












              • $begingroup$
                Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
                $endgroup$
                – marko
                Nov 22 '18 at 10:29










              • $begingroup$
                @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
                $endgroup$
                – Szabolcs
                Nov 22 '18 at 10:39












              • $begingroup$
                Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
                $endgroup$
                – marko
                Nov 22 '18 at 12:35


















              $begingroup$
              Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
              $endgroup$
              – marko
              Nov 22 '18 at 10:19




              $begingroup$
              Thank you for this answer. In a way, this code does what I asked in the question. The only drawback is that I need the distance between the first and last point in X or Y direction to be controlled independently and not related to the number of subdivisions. As is stands now, if I want 5 subdivisions in Y direction, I get the min and max Y coordinate of 1 and 6 respectively. Changing the number of subdivisions to 10, makes them 1 and 11.
              $endgroup$
              – marko
              Nov 22 '18 at 10:19












              $begingroup$
              @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
              $endgroup$
              – Szabolcs
              Nov 22 '18 at 10:21






              $begingroup$
              @marko I don't understand your comment. In my code, the mesh size is set independently in the two directions. I also do not understand which direction you are referring to as $x$ and $y$.
              $endgroup$
              – Szabolcs
              Nov 22 '18 at 10:21














              $begingroup$
              Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
              $endgroup$
              – marko
              Nov 22 '18 at 10:29




              $begingroup$
              Sorry for the unclear comment. As it stands now, the number of subdivisions (set to 5) defined in Subdivide[g1, g2, 5] defines also the length of the mesh in this direction (the direction I called "Y"). Setting the number of divisions to 10, will change the length of the mesh to 10. Is there a way to keep this constant? Similarly, I wish to keep the length of the mesh in the other direction constant (now it is 15), regardless of the number of divisions. Let's say that I wish the mesh to be of length 10 in both directions. Hopefully this is more clear.
              $endgroup$
              – marko
              Nov 22 '18 at 10:29












              $begingroup$
              @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
              $endgroup$
              – Szabolcs
              Nov 22 '18 at 10:39






              $begingroup$
              @marko You can scale the mesh by inserting the required scaling factor in front of the first or second element of {First[#2], #1, 0} in MapIndexed. A bit inconvenient, as you'd need to sync the factor with the value in Range and Subdivide, but it will work :-)
              $endgroup$
              – Szabolcs
              Nov 22 '18 at 10:39














              $begingroup$
              Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
              $endgroup$
              – marko
              Nov 22 '18 at 12:35






              $begingroup$
              Thank you. I managed to get it working, using the code bellow, where I define number of elements in both directions and the length (for a hyperbolic paraboloid) NumElements1 = 16; NumElements2 = 10; len = 2; g1 = Prepend[Accumulate@Range[NumElements2], 0]; g2 = Prepend[Accumulate@Reverse@Range[NumElements2], 0]; Flatten[MapIndexed[{len/ Last[g1]*#1, (len/(NumElements1 + 1))*(First[#2] - 1), (len/Last[g1]*#1 - len/2)^2 - ((len/(NumElements1 + 1))*(First[#2] - 1) - len/2)^2} &, Subdivide[g1, g2, NumElements1], {2}], 1] // ListPointPlot3D
              $endgroup$
              – marko
              Nov 22 '18 at 12:35













              2












              $begingroup$

              MasterMesh =
              Flatten[Table[{1.7^x, 1.7^y, 0},
              {x, 1, 2, .1},
              {y, 1, 2, .1}], 1];
              ListPointPlot3D[MasterMesh]





              share|improve this answer









              $endgroup$













              • $begingroup$
                Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
                $endgroup$
                – marko
                Nov 22 '18 at 9:25
















              2












              $begingroup$

              MasterMesh =
              Flatten[Table[{1.7^x, 1.7^y, 0},
              {x, 1, 2, .1},
              {y, 1, 2, .1}], 1];
              ListPointPlot3D[MasterMesh]





              share|improve this answer









              $endgroup$













              • $begingroup$
                Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
                $endgroup$
                – marko
                Nov 22 '18 at 9:25














              2












              2








              2





              $begingroup$

              MasterMesh =
              Flatten[Table[{1.7^x, 1.7^y, 0},
              {x, 1, 2, .1},
              {y, 1, 2, .1}], 1];
              ListPointPlot3D[MasterMesh]





              share|improve this answer









              $endgroup$



              MasterMesh =
              Flatten[Table[{1.7^x, 1.7^y, 0},
              {x, 1, 2, .1},
              {y, 1, 2, .1}], 1];
              ListPointPlot3D[MasterMesh]






              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Nov 22 '18 at 8:51









              David G. StorkDavid G. Stork

              24.9k22155




              24.9k22155












              • $begingroup$
                Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
                $endgroup$
                – marko
                Nov 22 '18 at 9:25


















              • $begingroup$
                Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
                $endgroup$
                – marko
                Nov 22 '18 at 9:25
















              $begingroup$
              Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
              $endgroup$
              – marko
              Nov 22 '18 at 9:25




              $begingroup$
              Your code indeed produces something similar to what I would need, but the step length is not increasing in a way that I wish. For the set of data that you provided, it goes: L1=0.19, L2=0.21, L3=0.24. Also the max distance in X or Y direction, location of the first point and the step change seem to be all dependable on each other.
              $endgroup$
              – marko
              Nov 22 '18 at 9:25











              2












              $begingroup$

              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]]


              enter image description here



              n=12 and range=2     


              enter image description here






              share|improve this answer











              $endgroup$


















                2












                $begingroup$

                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]]


                enter image description here



                n=12 and range=2     


                enter image description here






                share|improve this answer











                $endgroup$
















                  2












                  2








                  2





                  $begingroup$

                  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]]


                  enter image description here



                  n=12 and range=2     


                  enter image description here






                  share|improve this answer











                  $endgroup$



                  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]]


                  enter image description here



                  n=12 and range=2     


                  enter image description here







                  share|improve this answer














                  share|improve this answer



                  share|improve this answer








                  edited Nov 22 '18 at 14:34

























                  answered Nov 22 '18 at 12:13









                  J42161217J42161217

                  4,598324




                  4,598324























                      1












                      $begingroup$

                      Maybe someone will find this useful, so here is my code to achieve mesh distortion in both directions. It is achieved using the answer by Szabolcs and the Line-line intersection equation, taken from Wikipedia.



                      NumElements1 = 10;
                      NumElements2 = 4;
                      ratio = 2;

                      x[n_, ratio_] :=
                      Normalize[
                      Accumulate[
                      Join[{0}, Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]], Max]
                      reversex[n_, ratio_] :=
                      Normalize[
                      Accumulate[
                      Join[{0},
                      Reverse[Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]]], Max]

                      g1 = x[NumElements1, ratio];
                      g2 = reversex[NumElements1, ratio];

                      g3 = x[NumElements2, ratio];
                      g4 = reversex[NumElements2, ratio];

                      Flatten[Table[
                      MapThread[{(-#1 + (#1 - #2)*
                      g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) -
                      1), (#1*(g3[[i]] - g4[[i]]) -
                      g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) - 1), 0} &, {g1,
                      g2}], {i, 1, NumElements2 + 1}], 1] // ListPointPlot3D


                      By changing ratio and NumElements1 and NumElements2, you can get the desired output. For the data above I get this:
                      enter image description here






                      share|improve this answer









                      $endgroup$


















                        1












                        $begingroup$

                        Maybe someone will find this useful, so here is my code to achieve mesh distortion in both directions. It is achieved using the answer by Szabolcs and the Line-line intersection equation, taken from Wikipedia.



                        NumElements1 = 10;
                        NumElements2 = 4;
                        ratio = 2;

                        x[n_, ratio_] :=
                        Normalize[
                        Accumulate[
                        Join[{0}, Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]], Max]
                        reversex[n_, ratio_] :=
                        Normalize[
                        Accumulate[
                        Join[{0},
                        Reverse[Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]]], Max]

                        g1 = x[NumElements1, ratio];
                        g2 = reversex[NumElements1, ratio];

                        g3 = x[NumElements2, ratio];
                        g4 = reversex[NumElements2, ratio];

                        Flatten[Table[
                        MapThread[{(-#1 + (#1 - #2)*
                        g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) -
                        1), (#1*(g3[[i]] - g4[[i]]) -
                        g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) - 1), 0} &, {g1,
                        g2}], {i, 1, NumElements2 + 1}], 1] // ListPointPlot3D


                        By changing ratio and NumElements1 and NumElements2, you can get the desired output. For the data above I get this:
                        enter image description here






                        share|improve this answer









                        $endgroup$
















                          1












                          1








                          1





                          $begingroup$

                          Maybe someone will find this useful, so here is my code to achieve mesh distortion in both directions. It is achieved using the answer by Szabolcs and the Line-line intersection equation, taken from Wikipedia.



                          NumElements1 = 10;
                          NumElements2 = 4;
                          ratio = 2;

                          x[n_, ratio_] :=
                          Normalize[
                          Accumulate[
                          Join[{0}, Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]], Max]
                          reversex[n_, ratio_] :=
                          Normalize[
                          Accumulate[
                          Join[{0},
                          Reverse[Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]]], Max]

                          g1 = x[NumElements1, ratio];
                          g2 = reversex[NumElements1, ratio];

                          g3 = x[NumElements2, ratio];
                          g4 = reversex[NumElements2, ratio];

                          Flatten[Table[
                          MapThread[{(-#1 + (#1 - #2)*
                          g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) -
                          1), (#1*(g3[[i]] - g4[[i]]) -
                          g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) - 1), 0} &, {g1,
                          g2}], {i, 1, NumElements2 + 1}], 1] // ListPointPlot3D


                          By changing ratio and NumElements1 and NumElements2, you can get the desired output. For the data above I get this:
                          enter image description here






                          share|improve this answer









                          $endgroup$



                          Maybe someone will find this useful, so here is my code to achieve mesh distortion in both directions. It is achieved using the answer by Szabolcs and the Line-line intersection equation, taken from Wikipedia.



                          NumElements1 = 10;
                          NumElements2 = 4;
                          ratio = 2;

                          x[n_, ratio_] :=
                          Normalize[
                          Accumulate[
                          Join[{0}, Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]], Max]
                          reversex[n_, ratio_] :=
                          Normalize[
                          Accumulate[
                          Join[{0},
                          Reverse[Table[1 + (i - 1)/(n - 1) (ratio - 1), {i, 1, n}]]]], Max]

                          g1 = x[NumElements1, ratio];
                          g2 = reversex[NumElements1, ratio];

                          g3 = x[NumElements2, ratio];
                          g4 = reversex[NumElements2, ratio];

                          Flatten[Table[
                          MapThread[{(-#1 + (#1 - #2)*
                          g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) -
                          1), (#1*(g3[[i]] - g4[[i]]) -
                          g3[[i]])/((#1 - #2)*(g3[[i]] - g4[[i]]) - 1), 0} &, {g1,
                          g2}], {i, 1, NumElements2 + 1}], 1] // ListPointPlot3D


                          By changing ratio and NumElements1 and NumElements2, you can get the desired output. For the data above I get this:
                          enter image description here







                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered Jan 3 at 8:56









                          markomarko

                          856




                          856






























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