How to use Normal to recover translated points
I'm working through a coding exercise to program a matrix of Lissajour Curves in Mathematica but have encountered an obstacle when trying to recover the translated Point to then do further processing on them (as seen through the link). I've encountered problems trying to recovering the updated coordinates of translated points using Normal before. In this case I've gone so far as to try to rebuild that solution in my current notebook to no avail. It seems like there should be some application of Normal to Graphics[graphicsdata] that would generate the updated point coordinates in a list. I'm not sure what I'm missing about how Normal works but it would be useful to understand it as I try to advance my Mathematica program complexity.
angle = Drop[Range[0,Pi 2,(2 Pi)/20],-1];
cols = 5;
rows = 3;
radius = .45;
functionXY[anglevar_]:= {radius * Cos[anglevar],radius * Sin[anglevar]}
translatevectors = Flatten[{Table[{x,0},{x,cols}],Table[{0,-y},{y,rows}]},1];
points = Point /@ functionXY /@ angle;
graphicsdata = Table[Translate[#, translatevectors[[n]]] &/@ points,{n,Length@translatevectors}];
Graphics[graphicsdata]
list-manipulation graphics geometry
asked 6 hours ago
BBirdsell
377313
add a comment |
I'm working through a coding exercise to program a matrix of Lissajour Curves in Mathematica but have encountered an obstacle when trying to recover the translated Point to then do further processing on them (as seen through the link). I've encountered problems trying to recovering the updated coordinates of translated points using Normal before. In this case I've gone so far as to try to rebuild that solution in my current notebook to no avail. It seems like there should be some application of Normal to Graphics[graphicsdata] that would generate the updated point coordinates in a list. I'm not sure what I'm missing about how Normal works but it would be useful to understand it as I try to advance my Mathematica program complexity.
angle = Drop[Range[0,Pi 2,(2 Pi)/20],-1];
cols = 5;
rows = 3;
radius = .45;
functionXY[anglevar_]:= {radius * Cos[anglevar],radius * Sin[anglevar]}
translatevectors = Flatten[{Table[{x,0},{x,cols}],Table[{0,-y},{y,rows}]},1];
points = Point /@ functionXY /@ angle;
graphicsdata = Table[Translate[#, translatevectors[[n]]] &/@ points,{n,Length@translatevectors}];
Graphics[graphicsdata]
list-manipulation graphics geometry
asked 6 hours ago
BBirdsell
377313
maybenormal = # /. Translate[(prim : Alternatives[Point, Line, Circle])[x_, y___], t_] :> prim[TranslationTransform[t]@x, y] &; normal@Graphics[graphicsdata]? `
– kglr
6 hours ago
add a comment |
I'm working through a coding exercise to program a matrix of Lissajour Curves in Mathematica but have encountered an obstacle when trying to recover the translated Point to then do further processing on them (as seen through the link). I've encountered problems trying to recovering the updated coordinates of translated points using Normal before. In this case I've gone so far as to try to rebuild that solution in my current notebook to no avail. It seems like there should be some application of Normal to Graphics[graphicsdata] that would generate the updated point coordinates in a list. I'm not sure what I'm missing about how Normal works but it would be useful to understand it as I try to advance my Mathematica program complexity.
angle = Drop[Range[0,Pi 2,(2 Pi)/20],-1];
cols = 5;
rows = 3;
radius = .45;
functionXY[anglevar_]:= {radius * Cos[anglevar],radius * Sin[anglevar]}
translatevectors = Flatten[{Table[{x,0},{x,cols}],Table[{0,-y},{y,rows}]},1];
points = Point /@ functionXY /@ angle;
graphicsdata = Table[Translate[#, translatevectors[[n]]] &/@ points,{n,Length@translatevectors}];
Graphics[graphicsdata]
list-manipulation graphics geometry
asked 6 hours ago
BBirdsell
377313
I'm working through a coding exercise to program a matrix of Lissajour Curves in Mathematica but have encountered an obstacle when trying to recover the translated Point to then do further processing on them (as seen through the link). I've encountered problems trying to recovering the updated coordinates of translated points using Normal before. In this case I've gone so far as to try to rebuild that solution in my current notebook to no avail. It seems like there should be some application of Normal to Graphics[graphicsdata] that would generate the updated point coordinates in a list. I'm not sure what I'm missing about how Normal works but it would be useful to understand it as I try to advance my Mathematica program complexity.
angle = Drop[Range[0,Pi 2,(2 Pi)/20],-1];
cols = 5;
rows = 3;
radius = .45;
functionXY[anglevar_]:= {radius * Cos[anglevar],radius * Sin[anglevar]}
translatevectors = Flatten[{Table[{x,0},{x,cols}],Table[{0,-y},{y,rows}]},1];
points = Point /@ functionXY /@ angle;
graphicsdata = Table[Translate[#, translatevectors[[n]]] &/@ points,{n,Length@translatevectors}];
Graphics[graphicsdata]
list-manipulation graphics geometry
list-manipulation graphics geometry
asked 6 hours ago
BBirdsell
377313
asked 6 hours ago
BBirdsell
377313
asked 6 hours ago
BBirdsell
377313
asked 6 hours ago
BBirdsell
377313
asked 6 hours ago
BBirdsell
377313
377313
maybenormal = # /. Translate[(prim : Alternatives[Point, Line, Circle])[x_, y___], t_] :> prim[TranslationTransform[t]@x, y] &; normal@Graphics[graphicsdata]? `
– kglr
6 hours ago
add a comment |
maybenormal = # /. Translate[(prim : Alternatives[Point, Line, Circle])[x_, y___], t_] :> prim[TranslationTransform[t]@x, y] &; normal@Graphics[graphicsdata]? `
– kglr
6 hours ago
maybe
normal = # /. Translate[(prim : Alternatives[Point, Line, Circle])[x_, y___], t_] :> prim[TranslationTransform[t]@x, y] &; normal@Graphics[graphicsdata]? `– kglr
6 hours ago
maybe
normal = # /. Translate[(prim : Alternatives[Point, Line, Circle])[x_, y___], t_] :> prim[TranslationTransform[t]@x, y] &; normal@Graphics[graphicsdata]? `– kglr
6 hours ago
add a comment |
1 Answer
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As mentioned in the linked q/a, the section Properties and Relations in Scale, Translate and GeometricTransformation says:
When possible, Normal will transform the coordinates explicitly.
When Normal does not work, you can post-process the translated primitives to regular primitives with translated coordinates:
normal = # /. Translate[Point[x_], t_] :> Point[TranslationTransform[t]@x] &;
points = Cases[normal@Graphics[graphicsdata], Point[x_] :> x, ∞];
Show[ListPlot[points, AspectRatio -> Automatic, Axes -> False,
PlotStyle -> Directive[AbsolutePointSize[7], Opacity[.7, Red]]],
Graphics[graphicsdata]]
answered 4 hours ago
kglr
176k9198404
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
As mentioned in the linked q/a, the section Properties and Relations in Scale, Translate and GeometricTransformation says:
When possible, Normal will transform the coordinates explicitly.
When Normal does not work, you can post-process the translated primitives to regular primitives with translated coordinates:
normal = # /. Translate[Point[x_], t_] :> Point[TranslationTransform[t]@x] &;
points = Cases[normal@Graphics[graphicsdata], Point[x_] :> x, ∞];
Show[ListPlot[points, AspectRatio -> Automatic, Axes -> False,
PlotStyle -> Directive[AbsolutePointSize[7], Opacity[.7, Red]]],
Graphics[graphicsdata]]
answered 4 hours ago
kglr
176k9198404
add a comment |
As mentioned in the linked q/a, the section Properties and Relations in Scale, Translate and GeometricTransformation says:
When possible, Normal will transform the coordinates explicitly.
When Normal does not work, you can post-process the translated primitives to regular primitives with translated coordinates:
normal = # /. Translate[Point[x_], t_] :> Point[TranslationTransform[t]@x] &;
points = Cases[normal@Graphics[graphicsdata], Point[x_] :> x, ∞];
Show[ListPlot[points, AspectRatio -> Automatic, Axes -> False,
PlotStyle -> Directive[AbsolutePointSize[7], Opacity[.7, Red]]],
Graphics[graphicsdata]]
answered 4 hours ago
kglr
176k9198404
add a comment |
As mentioned in the linked q/a, the section Properties and Relations in Scale, Translate and GeometricTransformation says:
When possible, Normal will transform the coordinates explicitly.
When Normal does not work, you can post-process the translated primitives to regular primitives with translated coordinates:
normal = # /. Translate[Point[x_], t_] :> Point[TranslationTransform[t]@x] &;
points = Cases[normal@Graphics[graphicsdata], Point[x_] :> x, ∞];
Show[ListPlot[points, AspectRatio -> Automatic, Axes -> False,
PlotStyle -> Directive[AbsolutePointSize[7], Opacity[.7, Red]]],
Graphics[graphicsdata]]
answered 4 hours ago
kglr
176k9198404
As mentioned in the linked q/a, the section Properties and Relations in Scale, Translate and GeometricTransformation says:
When possible, Normal will transform the coordinates explicitly.
When Normal does not work, you can post-process the translated primitives to regular primitives with translated coordinates:
normal = # /. Translate[Point[x_], t_] :> Point[TranslationTransform[t]@x] &;
points = Cases[normal@Graphics[graphicsdata], Point[x_] :> x, ∞];
Show[ListPlot[points, AspectRatio -> Automatic, Axes -> False,
PlotStyle -> Directive[AbsolutePointSize[7], Opacity[.7, Red]]],
Graphics[graphicsdata]]
answered 4 hours ago
kglr
176k9198404
edited 1 hour ago
answered 4 hours ago
kglr
176k9198404
answered 4 hours ago
kglr
176k9198404
answered 4 hours ago
kglr
176k9198404
176k9198404
add a comment |
add a comment |
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maybe
normal = # /. Translate[(prim : Alternatives[Point, Line, Circle])[x_, y___], t_] :> prim[TranslationTransform[t]@x, y] &; normal@Graphics[graphicsdata]? `– kglr
6 hours ago