Is it possible to rotate the Isolines on a Surface Using `MeshFunction`?
Clash Royale CLAN TAG#URR8PPP
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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]]]]
plotting graphics
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add a comment |
$begingroup$
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]]]]
plotting graphics
$endgroup$
add a comment |
$begingroup$
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]]]]
plotting graphics
$endgroup$
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]]]]
plotting graphics
plotting graphics
asked Feb 25 at 4:47
BBirdsellBBirdsell
462314
462314
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
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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.
Manipulate[Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8, BoxRatios -> Automatic,
MeshFunctions -> AngleVector[-θ].#, #2 &,
AngleVector[π/2 - θ].#, #2 &,
PlotStyle -> Directive[Lighting -> "Neutral",
FaceForm[White, Specularity[0.2, 10]]]],
θ, 0, 2 π]
Note that this rotates the mesh clockwise; use MeshFunctions -> AngleVector[θ].#, #2 &, AngleVector[π/2 + θ].#, #2 &
instead if the anticlockwise version is desired.
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(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
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done (I took the liberty to replace theWith
withManipulate
to better show the advantages of this method)
$endgroup$
– Lukas Lang
Feb 25 at 8:40
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Thanks a lot, @Lukas! TheManipulate
is indeed much nicer.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
add a comment |
$begingroup$
You can use MeshFunctions -> (Function /@ (RotationMatrix[θ].#, #2))
to rotate by angle θ
:
θ = 75 Degree;
meshfunctions = Function /@ (RotationMatrix[θ].#, #2);
Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8,
MeshFunctions -> meshfunctions, Mesh -> 3, 8,
BoxRatios -> 4, 8, 1, Boxed -> False, Axes -> False,
ImageSize -> Large,
PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]
For 45 Degree
rotation you can use the simpler MeshFunctions -> # + #2 &, # - #2 &
to get
$endgroup$
add a comment |
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
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.
Manipulate[Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8, BoxRatios -> Automatic,
MeshFunctions -> AngleVector[-θ].#, #2 &,
AngleVector[π/2 - θ].#, #2 &,
PlotStyle -> Directive[Lighting -> "Neutral",
FaceForm[White, Specularity[0.2, 10]]]],
θ, 0, 2 π]
Note that this rotates the mesh clockwise; use MeshFunctions -> AngleVector[θ].#, #2 &, AngleVector[π/2 + θ].#, #2 &
instead if the anticlockwise version is desired.
$endgroup$
$begingroup$
(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
$begingroup$
done (I took the liberty to replace theWith
withManipulate
to better show the advantages of this method)
$endgroup$
– Lukas Lang
Feb 25 at 8:40
$begingroup$
Thanks a lot, @Lukas! TheManipulate
is indeed much nicer.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
add a comment |
$begingroup$
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.
Manipulate[Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8, BoxRatios -> Automatic,
MeshFunctions -> AngleVector[-θ].#, #2 &,
AngleVector[π/2 - θ].#, #2 &,
PlotStyle -> Directive[Lighting -> "Neutral",
FaceForm[White, Specularity[0.2, 10]]]],
θ, 0, 2 π]
Note that this rotates the mesh clockwise; use MeshFunctions -> AngleVector[θ].#, #2 &, AngleVector[π/2 + θ].#, #2 &
instead if the anticlockwise version is desired.
$endgroup$
$begingroup$
(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
$begingroup$
done (I took the liberty to replace theWith
withManipulate
to better show the advantages of this method)
$endgroup$
– Lukas Lang
Feb 25 at 8:40
$begingroup$
Thanks a lot, @Lukas! TheManipulate
is indeed much nicer.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
add a comment |
$begingroup$
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.
Manipulate[Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8, BoxRatios -> Automatic,
MeshFunctions -> AngleVector[-θ].#, #2 &,
AngleVector[π/2 - θ].#, #2 &,
PlotStyle -> Directive[Lighting -> "Neutral",
FaceForm[White, Specularity[0.2, 10]]]],
θ, 0, 2 π]
Note that this rotates the mesh clockwise; use MeshFunctions -> AngleVector[θ].#, #2 &, AngleVector[π/2 + θ].#, #2 &
instead if the anticlockwise version is desired.
$endgroup$
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.
Manipulate[Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8, BoxRatios -> Automatic,
MeshFunctions -> AngleVector[-θ].#, #2 &,
AngleVector[π/2 - θ].#, #2 &,
PlotStyle -> Directive[Lighting -> "Neutral",
FaceForm[White, Specularity[0.2, 10]]]],
θ, 0, 2 π]
Note that this rotates the mesh clockwise; use MeshFunctions -> AngleVector[θ].#, #2 &, AngleVector[π/2 + θ].#, #2 &
instead if the anticlockwise version is desired.
edited Feb 25 at 9:34
answered Feb 25 at 6:55
J. M. is slightly pensive♦J. M. is slightly pensive
98.2k10306466
98.2k10306466
$begingroup$
(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
$begingroup$
done (I took the liberty to replace theWith
withManipulate
to better show the advantages of this method)
$endgroup$
– Lukas Lang
Feb 25 at 8:40
$begingroup$
Thanks a lot, @Lukas! TheManipulate
is indeed much nicer.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
add a comment |
$begingroup$
(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
$begingroup$
done (I took the liberty to replace theWith
withManipulate
to better show the advantages of this method)
$endgroup$
– Lukas Lang
Feb 25 at 8:40
$begingroup$
Thanks a lot, @Lukas! TheManipulate
is indeed much nicer.
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
$begingroup$
(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
$begingroup$
(If anyone is kind enough to edit my post to include the resulting image, please do so.)
$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 6:56
$begingroup$
done (I took the liberty to replace the
With
with Manipulate
to better show the advantages of this method)$endgroup$
– Lukas Lang
Feb 25 at 8:40
$begingroup$
done (I took the liberty to replace the
With
with Manipulate
to better show the advantages of this method)$endgroup$
– Lukas Lang
Feb 25 at 8:40
$begingroup$
Thanks a lot, @Lukas! The
Manipulate
is indeed much nicer.$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
$begingroup$
Thanks a lot, @Lukas! The
Manipulate
is indeed much nicer.$endgroup$
– J. M. is slightly pensive♦
Feb 25 at 9:31
add a comment |
$begingroup$
You can use MeshFunctions -> (Function /@ (RotationMatrix[θ].#, #2))
to rotate by angle θ
:
θ = 75 Degree;
meshfunctions = Function /@ (RotationMatrix[θ].#, #2);
Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8,
MeshFunctions -> meshfunctions, Mesh -> 3, 8,
BoxRatios -> 4, 8, 1, Boxed -> False, Axes -> False,
ImageSize -> Large,
PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]
For 45 Degree
rotation you can use the simpler MeshFunctions -> # + #2 &, # - #2 &
to get
$endgroup$
add a comment |
$begingroup$
You can use MeshFunctions -> (Function /@ (RotationMatrix[θ].#, #2))
to rotate by angle θ
:
θ = 75 Degree;
meshfunctions = Function /@ (RotationMatrix[θ].#, #2);
Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8,
MeshFunctions -> meshfunctions, Mesh -> 3, 8,
BoxRatios -> 4, 8, 1, Boxed -> False, Axes -> False,
ImageSize -> Large,
PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]
For 45 Degree
rotation you can use the simpler MeshFunctions -> # + #2 &, # - #2 &
to get
$endgroup$
add a comment |
$begingroup$
You can use MeshFunctions -> (Function /@ (RotationMatrix[θ].#, #2))
to rotate by angle θ
:
θ = 75 Degree;
meshfunctions = Function /@ (RotationMatrix[θ].#, #2);
Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8,
MeshFunctions -> meshfunctions, Mesh -> 3, 8,
BoxRatios -> 4, 8, 1, Boxed -> False, Axes -> False,
ImageSize -> Large,
PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]
For 45 Degree
rotation you can use the simpler MeshFunctions -> # + #2 &, # - #2 &
to get
$endgroup$
You can use MeshFunctions -> (Function /@ (RotationMatrix[θ].#, #2))
to rotate by angle θ
:
θ = 75 Degree;
meshfunctions = Function /@ (RotationMatrix[θ].#, #2);
Plot3D[Cos[x y/2], x, 0, 4, y, 0, 8,
MeshFunctions -> meshfunctions, Mesh -> 3, 8,
BoxRatios -> 4, 8, 1, Boxed -> False, Axes -> False,
ImageSize -> Large,
PlotStyle -> Directive[Lighting -> "Neutral", FaceForm[White, Specularity[0.2, 10]]]]
For 45 Degree
rotation you can use the simpler MeshFunctions -> # + #2 &, # - #2 &
to get
edited Feb 26 at 0:12
answered Feb 25 at 5:17
kglrkglr
189k10206424
189k10206424
add a comment |
add a comment |
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