Is it possible to rotate the Isolines on a Surface Using `MeshFunction`?












5












$begingroup$


This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.



Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},

BoxRatios->{4,8,1},

Boxed->False,

Axes->False,

ImageSize->Large,

Mesh->{3,8},

PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]


enter image description here



enter image description here






plotting graphics







share|improve this question









$endgroup$

















    5












    $begingroup$


    This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.



    Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},
    
BoxRatios->{4,8,1},
    
Boxed->False,
    
Axes->False,
    
ImageSize->Large,
    
Mesh->{3,8},
    
PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]


    enter image description here



    enter image description here






    plotting graphics







    share|improve this question









    $endgroup$















      5












      5








      5





      $begingroup$


      This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.



      Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},
      
BoxRatios->{4,8,1},
      
Boxed->False,
      
Axes->False,
      
ImageSize->Large,
      
Mesh->{3,8},
      
PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]


      enter image description here



      enter image description here






      plotting graphics







      share|improve this question









      $endgroup$




      This came up in a different context but some expertise in 3D surfaces or the graphic options would be appreciated. I'm trying to extrapolate the curves from any given surface and things seem to be going quite smoothly. All the curves can be grabbed in one more step as a GraphicsComplex. Perfect for more processing. However, now I'm trying to rotate the isolines to get even more control. This is possible in other software but I'm not sure how it was achieved. I assume there is some way to use the MeshFunction to rotate the Mesh through at least 45 degrees but all my searching hasn't brought up anything helpful. A less practical approach might be to find the intersecting curve of a regularly spaced vertical planes.



      Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8},
      
BoxRatios->{4,8,1},
      
Boxed->False,
      
Axes->False,
      
ImageSize->Large,
      
Mesh->{3,8},
      
PlotStyle->Directive[Lighting->"Neutral",FaceForm[White,Specularity[0.2,10]]]]


      enter image description here



      enter image description here






      plotting graphics




      plotting graphics






      share|improve this question













      share|improve this question











      share|improve this question




      share|improve this question










      asked 2 hours ago









      BBirdsellBBirdsell

      430313




      430313






















          2 Answers
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          $begingroup$

          Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 
          
 Boxed -> False, Axes -> False, ImageSize -> Large, 
          
 MeshFunctions -> {# + #2 &, # - #2 &},
          
 Mesh -> {3, 8}, 
          
 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]


          enter image description here






          share|improve this answer









          $endgroup$





















            0












            $begingroup$

            Since we have the identity



            RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}


            one can use this to construct a mesh that is arbitrarily oriented; e.g.



            With[{θ = π/4}, 
            
     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 
            
            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 
            
                              AngleVector[π/2 - θ].{#, #2} &}]]


            and you can change the value of θ for other orientations.






            share|improve this answer









            $endgroup$













            • $begingroup$
              (If anyone is kind enough to edit my post to include the resulting image, please do so.)
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              – J. M. is computer-less♦
              21 mins ago











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            2 Answers
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            active

            oldest

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            2 Answers
            2






            active

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            active

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            active

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            3












            $begingroup$

            Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 
            
 Boxed -> False, Axes -> False, ImageSize -> Large, 
            
 MeshFunctions -> {# + #2 &, # - #2 &},
            
 Mesh -> {3, 8}, 
            
 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]


            enter image description here






            share|improve this answer









            $endgroup$


















              3












              $begingroup$

              Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 
              
 Boxed -> False, Axes -> False, ImageSize -> Large, 
              
 MeshFunctions -> {# + #2 &, # - #2 &},
              
 Mesh -> {3, 8}, 
              
 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]


              enter image description here






              share|improve this answer









              $endgroup$
















                3












                3








                3





                $begingroup$

                Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 
                
 Boxed -> False, Axes -> False, ImageSize -> Large, 
                
 MeshFunctions -> {# + #2 &, # - #2 &},
                
 Mesh -> {3, 8}, 
                
 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]


                enter image description here






                share|improve this answer









                $endgroup$



                Plot3D[Cos[(x y)/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> {4, 8, 1}, 
                
 Boxed -> False, Axes -> False, ImageSize -> Large, 
                
 MeshFunctions -> {# + #2 &, # - #2 &},
                
 Mesh -> {3, 8}, 
                
 PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]


                enter image description here







                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered 2 hours ago









                kglrkglr

                185k10202421




                185k10202421























                    0












                    $begingroup$

                    Since we have the identity



                    RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}


                    one can use this to construct a mesh that is arbitrarily oriented; e.g.



                    With[{θ = π/4}, 
                    
     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 
                    
            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 
                    
                              AngleVector[π/2 - θ].{#, #2} &}]]


                    and you can change the value of θ for other orientations.






                    share|improve this answer









                    $endgroup$













                    • $begingroup$
                      (If anyone is kind enough to edit my post to include the resulting image, please do so.)
                      $endgroup$
                      – J. M. is computer-less♦
                      21 mins ago
















                    0












                    $begingroup$

                    Since we have the identity



                    RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}


                    one can use this to construct a mesh that is arbitrarily oriented; e.g.



                    With[{θ = π/4}, 
                    
     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 
                    
            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 
                    
                              AngleVector[π/2 - θ].{#, #2} &}]]


                    and you can change the value of θ for other orientations.






                    share|improve this answer









                    $endgroup$













                    • $begingroup$
                      (If anyone is kind enough to edit my post to include the resulting image, please do so.)
                      $endgroup$
                      – J. M. is computer-less♦
                      21 mins ago














                    0












                    0








                    0





                    $begingroup$

                    Since we have the identity



                    RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}


                    one can use this to construct a mesh that is arbitrarily oriented; e.g.



                    With[{θ = π/4}, 
                    
     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 
                    
            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 
                    
                              AngleVector[π/2 - θ].{#, #2} &}]]


                    and you can change the value of θ for other orientations.






                    share|improve this answer









                    $endgroup$



                    Since we have the identity



                    RotationMatrix[θ] == {AngleVector[-θ], AngleVector[π/2 - θ]}


                    one can use this to construct a mesh that is arbitrarily oriented; e.g.



                    With[{θ = π/4}, 
                    
     Plot3D[Cos[x y/2], {x, 0, 4}, {y, 0, 8}, BoxRatios -> Automatic, 
                    
            MeshFunctions -> {AngleVector[-θ].{#, #2} &, 
                    
                              AngleVector[π/2 - θ].{#, #2} &}]]


                    and you can change the value of θ for other orientations.







                    share|improve this answer












                    share|improve this answer



                    share|improve this answer










                    answered 22 mins ago









                    J. M. is computer-less♦J. M. is computer-less

                    96.8k10303462




                    96.8k10303462












                    • $begingroup$
                      (If anyone is kind enough to edit my post to include the resulting image, please do so.)
                      $endgroup$
                      – J. M. is computer-less♦
                      21 mins ago


















                    • $begingroup$
                      (If anyone is kind enough to edit my post to include the resulting image, please do so.)
                      $endgroup$
                      – J. M. is computer-less♦
                      21 mins ago
















                    $begingroup$
                    (If anyone is kind enough to edit my post to include the resulting image, please do so.)
                    $endgroup$
                    – J. M. is computer-less♦
                    21 mins ago




                    $begingroup$
                    (If anyone is kind enough to edit my post to include the resulting image, please do so.)
                    $endgroup$
                    – J. M. is computer-less♦
                    21 mins ago


















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