Linearly change the step size in a table












4














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



























    4














    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

























      4












      4








      4







      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













      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









      marko

      856




      856






















          4 Answers
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          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





















          • 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.
            – marko
            Nov 22 '18 at 10:19










          • @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 $y$.
            – Szabolcs
            Nov 22 '18 at 10:21












          • 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.
            – marko
            Nov 22 '18 at 10:29










          • @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 :-)
            – Szabolcs
            Nov 22 '18 at 10:39












          • 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
            – marko
            Nov 22 '18 at 12:35





















          2














          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





















          • 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.
            – marko
            Nov 22 '18 at 9:25



















          2














          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































            1














            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





















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              4 Answers
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              active

              oldest

              votes








              4 Answers
              4






              active

              oldest

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              active

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              4














              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





















              • 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.
                – marko
                Nov 22 '18 at 10:19










              • @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 $y$.
                – Szabolcs
                Nov 22 '18 at 10:21












              • 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.
                – marko
                Nov 22 '18 at 10:29










              • @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 :-)
                – Szabolcs
                Nov 22 '18 at 10:39












              • 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
                – marko
                Nov 22 '18 at 12:35


















              4














              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





















              • 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.
                – marko
                Nov 22 '18 at 10:19










              • @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 $y$.
                – Szabolcs
                Nov 22 '18 at 10:21












              • 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.
                – marko
                Nov 22 '18 at 10:29










              • @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 :-)
                – Szabolcs
                Nov 22 '18 at 10:39












              • 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
                – marko
                Nov 22 '18 at 12:35
















              4












              4








              4






              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












              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









              Szabolcs

              158k13432926




              158k13432926












              • 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.
                – marko
                Nov 22 '18 at 10:19










              • @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 $y$.
                – Szabolcs
                Nov 22 '18 at 10:21












              • 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.
                – marko
                Nov 22 '18 at 10:29










              • @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 :-)
                – Szabolcs
                Nov 22 '18 at 10:39












              • 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
                – marko
                Nov 22 '18 at 12:35




















              • 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.
                – marko
                Nov 22 '18 at 10:19










              • @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 $y$.
                – Szabolcs
                Nov 22 '18 at 10:21












              • 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.
                – marko
                Nov 22 '18 at 10:29










              • @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 :-)
                – Szabolcs
                Nov 22 '18 at 10:39












              • 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
                – marko
                Nov 22 '18 at 12:35


















              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.
              – marko
              Nov 22 '18 at 10:19




              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.
              – marko
              Nov 22 '18 at 10:19












              @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 $y$.
              – Szabolcs
              Nov 22 '18 at 10:21






              @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 $y$.
              – Szabolcs
              Nov 22 '18 at 10:21














              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.
              – marko
              Nov 22 '18 at 10:29




              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.
              – marko
              Nov 22 '18 at 10:29












              @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 :-)
              – Szabolcs
              Nov 22 '18 at 10:39






              @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 :-)
              – Szabolcs
              Nov 22 '18 at 10:39














              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
              – marko
              Nov 22 '18 at 12:35






              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
              – marko
              Nov 22 '18 at 12:35













              2














              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





















              • 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.
                – marko
                Nov 22 '18 at 9:25
















              2














              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





















              • 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.
                – marko
                Nov 22 '18 at 9:25














              2












              2








              2






              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












              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. Stork

              23.4k22051




              23.4k22051












              • 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.
                – marko
                Nov 22 '18 at 9:25


















              • 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.
                – marko
                Nov 22 '18 at 9:25
















              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.
              – marko
              Nov 22 '18 at 9:25




              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.
              – marko
              Nov 22 '18 at 9:25











              2














              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




























                2














                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


























                  2












                  2








                  2






                  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














                  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









                  J42161217

                  3,767220




                  3,767220























                      1














                      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


























                        1














                        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
























                          1












                          1








                          1






                          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












                          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









                          marko

                          856




                          856






























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