Graphing random points on the XY-plane
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I am trying to generate around 10-20 points on the xy- plane in the domain $[-10,10]times[-10,10]$ (in 3D) and I am having trouble. I want to draw the plane in 3D, graph the random (they do not have to be random but at least nicely dispersed) points, and then graph vertical lines through these points. I found this How to generate random points in a region? and tried to adopt it for a plane in 3D but since i am very new to Mathematica I cannot seem to make it work. I am aware of the RandomPoint command but the problem is i need to describe the region and I do not know how to describe the region of xy-plane. I tried z=0 but I think it only accepts "worded" regions.
Any help would be appreciated.
plotting graphics3d random
edited Mar 5 at 18:32
m_goldberg
87.4k872198
asked Mar 5 at 17:14
SorfoshSorfosh
1403
$endgroup$
add a comment |
$begingroup$
I am trying to generate around 10-20 points on the xy- plane in the domain $[-10,10]times[-10,10]$ (in 3D) and I am having trouble. I want to draw the plane in 3D, graph the random (they do not have to be random but at least nicely dispersed) points, and then graph vertical lines through these points. I found this How to generate random points in a region? and tried to adopt it for a plane in 3D but since i am very new to Mathematica I cannot seem to make it work. I am aware of the RandomPoint command but the problem is i need to describe the region and I do not know how to describe the region of xy-plane. I tried z=0 but I think it only accepts "worded" regions.
Any help would be appreciated.
plotting graphics3d random
edited Mar 5 at 18:32
m_goldberg
87.4k872198
asked Mar 5 at 17:14
SorfoshSorfosh
1403
$endgroup$
$begingroup$
If you want to useRandomPoint, there'sImplicitRegion:RandomPoint[ ImplicitRegion[Abs@x < 10 && Abs@y < 10 && z == 0, {x, y, z}], 100]will give you 100 points in the specified region. Alternatively, you could also generate points in 2D usingRandomReal[10,{100,2}]and add the z coordinate usingAppend[0]/@pts
$endgroup$
– Lukas Lang
Mar 5 at 17:22
add a comment |
$begingroup$
I am trying to generate around 10-20 points on the xy- plane in the domain $[-10,10]times[-10,10]$ (in 3D) and I am having trouble. I want to draw the plane in 3D, graph the random (they do not have to be random but at least nicely dispersed) points, and then graph vertical lines through these points. I found this How to generate random points in a region? and tried to adopt it for a plane in 3D but since i am very new to Mathematica I cannot seem to make it work. I am aware of the RandomPoint command but the problem is i need to describe the region and I do not know how to describe the region of xy-plane. I tried z=0 but I think it only accepts "worded" regions.
Any help would be appreciated.
plotting graphics3d random
edited Mar 5 at 18:32
m_goldberg
87.4k872198
asked Mar 5 at 17:14
SorfoshSorfosh
1403
$endgroup$
I am trying to generate around 10-20 points on the xy- plane in the domain $[-10,10]times[-10,10]$ (in 3D) and I am having trouble. I want to draw the plane in 3D, graph the random (they do not have to be random but at least nicely dispersed) points, and then graph vertical lines through these points. I found this How to generate random points in a region? and tried to adopt it for a plane in 3D but since i am very new to Mathematica I cannot seem to make it work. I am aware of the RandomPoint command but the problem is i need to describe the region and I do not know how to describe the region of xy-plane. I tried z=0 but I think it only accepts "worded" regions.
Any help would be appreciated.
plotting graphics3d random
plotting graphics3d random
edited Mar 5 at 18:32
m_goldberg
87.4k872198
asked Mar 5 at 17:14
SorfoshSorfosh
1403
edited Mar 5 at 18:32
m_goldberg
87.4k872198
asked Mar 5 at 17:14
SorfoshSorfosh
1403
edited Mar 5 at 18:32
m_goldberg
87.4k872198
edited Mar 5 at 18:32
m_goldberg
87.4k872198
edited Mar 5 at 18:32
m_goldberg
87.4k872198
87.4k872198
asked Mar 5 at 17:14
SorfoshSorfosh
1403
asked Mar 5 at 17:14
SorfoshSorfosh
1403
asked Mar 5 at 17:14
SorfoshSorfosh
1403
1403
$begingroup$
If you want to useRandomPoint, there'sImplicitRegion:RandomPoint[ ImplicitRegion[Abs@x < 10 && Abs@y < 10 && z == 0, {x, y, z}], 100]will give you 100 points in the specified region. Alternatively, you could also generate points in 2D usingRandomReal[10,{100,2}]and add the z coordinate usingAppend[0]/@pts
$endgroup$
– Lukas Lang
Mar 5 at 17:22
add a comment |
$begingroup$
If you want to useRandomPoint, there'sImplicitRegion:RandomPoint[ ImplicitRegion[Abs@x < 10 && Abs@y < 10 && z == 0, {x, y, z}], 100]will give you 100 points in the specified region. Alternatively, you could also generate points in 2D usingRandomReal[10,{100,2}]and add the z coordinate usingAppend[0]/@pts
$endgroup$
– Lukas Lang
Mar 5 at 17:22
$begingroup$
If you want to use
RandomPoint, there's ImplicitRegion: RandomPoint[ ImplicitRegion[Abs@x < 10 && Abs@y < 10 && z == 0, {x, y, z}], 100] will give you 100 points in the specified region. Alternatively, you could also generate points in 2D using RandomReal[10,{100,2}] and add the z coordinate using Append[0]/@pts$endgroup$
– Lukas Lang
Mar 5 at 17:22
$begingroup$
If you want to use
RandomPoint, there's ImplicitRegion: RandomPoint[ ImplicitRegion[Abs@x < 10 && Abs@y < 10 && z == 0, {x, y, z}], 100] will give you 100 points in the specified region. Alternatively, you could also generate points in 2D using RandomReal[10,{100,2}] and add the z coordinate using Append[0]/@pts$endgroup$
– Lukas Lang
Mar 5 at 17:22
add a comment |
2 Answers
2
active
oldest
votes
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You can use RandomPoint with InfinitePlane and draw lines using InfiniteLine:
plane = InfinitePlane[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}];
pts = RandomPoint[plane, 20, {{-10, 10}, {-10, 10}, {0, 0}}];
Graphics3D[{plane, Red, InfiniteLine[#, {0, 0, 1}] & /@ pts, Blue,
Sphere[pts, .1]}, PlotRange -> {{-10, 10}, {-10, 10}, {-5, 5}}]
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
$endgroup$
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
1
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
add a comment |
$begingroup$
Maybe this will work for you.
First define a function for generating $n$ random points on the xy-plane.
pts[n_] := {#1, #2, 0} & @@@ RandomReal[{-10., 10.}, {n, 2}]
Then
SeedRandom[42];
Module[{n = 20, p0} ,
p0 = pts[n];
Graphics3D[
{{AbsolutePointSize[4], Point[p0]},
{Red, Thick, HalfLine[#, {0, 0, 1}] & /@ p0}},
PlotRange -> {{-10, 10}, {-10, 10}, {0, 10}}]]
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
$endgroup$
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
$begingroup$
You can use RandomPoint with InfinitePlane and draw lines using InfiniteLine:
plane = InfinitePlane[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}];
pts = RandomPoint[plane, 20, {{-10, 10}, {-10, 10}, {0, 0}}];
Graphics3D[{plane, Red, InfiniteLine[#, {0, 0, 1}] & /@ pts, Blue,
Sphere[pts, .1]}, PlotRange -> {{-10, 10}, {-10, 10}, {-5, 5}}]
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
$endgroup$
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
1
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
add a comment |
$begingroup$
You can use RandomPoint with InfinitePlane and draw lines using InfiniteLine:
plane = InfinitePlane[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}];
pts = RandomPoint[plane, 20, {{-10, 10}, {-10, 10}, {0, 0}}];
Graphics3D[{plane, Red, InfiniteLine[#, {0, 0, 1}] & /@ pts, Blue,
Sphere[pts, .1]}, PlotRange -> {{-10, 10}, {-10, 10}, {-5, 5}}]
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
$endgroup$
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
1
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
add a comment |
$begingroup$
You can use RandomPoint with InfinitePlane and draw lines using InfiniteLine:
plane = InfinitePlane[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}];
pts = RandomPoint[plane, 20, {{-10, 10}, {-10, 10}, {0, 0}}];
Graphics3D[{plane, Red, InfiniteLine[#, {0, 0, 1}] & /@ pts, Blue,
Sphere[pts, .1]}, PlotRange -> {{-10, 10}, {-10, 10}, {-5, 5}}]
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
$endgroup$
You can use RandomPoint with InfinitePlane and draw lines using InfiniteLine:
plane = InfinitePlane[{{0, 0, 0}, {1, 0, 0}, {0, 1, 0}}];
pts = RandomPoint[plane, 20, {{-10, 10}, {-10, 10}, {0, 0}}];
Graphics3D[{plane, Red, InfiniteLine[#, {0, 0, 1}] & /@ pts, Blue,
Sphere[pts, .1]}, PlotRange -> {{-10, 10}, {-10, 10}, {-5, 5}}]
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
edited Mar 5 at 17:53
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
answered Mar 5 at 17:37
halmirhalmir
10.5k2544
10.5k2544
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
1
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
add a comment |
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
1
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
$begingroup$
Wow, that is perfect. Now if i wanted to change the direction vector of the line depending on the points, how would i do that? I tried changing ${0,0,1}$ to ${#[[2]], #[[1]], sqrt[#[[2]]^2 + #[[1]]^2]}$ but that didn't work.
$endgroup$
– Sorfosh
Mar 5 at 19:18
1
1
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
@Sorfosh it works fine to me. Did you type sqrt instead Sqrt ?
$endgroup$
– halmir
Mar 5 at 20:23
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
$begingroup$
oh... wow. I forgot it is case sensitive. Thank you! :P
$endgroup$
– Sorfosh
Mar 5 at 21:41
add a comment |
$begingroup$
Maybe this will work for you.
First define a function for generating $n$ random points on the xy-plane.
pts[n_] := {#1, #2, 0} & @@@ RandomReal[{-10., 10.}, {n, 2}]
Then
SeedRandom[42];
Module[{n = 20, p0} ,
p0 = pts[n];
Graphics3D[
{{AbsolutePointSize[4], Point[p0]},
{Red, Thick, HalfLine[#, {0, 0, 1}] & /@ p0}},
PlotRange -> {{-10, 10}, {-10, 10}, {0, 10}}]]
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
$endgroup$
add a comment |
$begingroup$
Maybe this will work for you.
First define a function for generating $n$ random points on the xy-plane.
pts[n_] := {#1, #2, 0} & @@@ RandomReal[{-10., 10.}, {n, 2}]
Then
SeedRandom[42];
Module[{n = 20, p0} ,
p0 = pts[n];
Graphics3D[
{{AbsolutePointSize[4], Point[p0]},
{Red, Thick, HalfLine[#, {0, 0, 1}] & /@ p0}},
PlotRange -> {{-10, 10}, {-10, 10}, {0, 10}}]]
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
$endgroup$
add a comment |
$begingroup$
Maybe this will work for you.
First define a function for generating $n$ random points on the xy-plane.
pts[n_] := {#1, #2, 0} & @@@ RandomReal[{-10., 10.}, {n, 2}]
Then
SeedRandom[42];
Module[{n = 20, p0} ,
p0 = pts[n];
Graphics3D[
{{AbsolutePointSize[4], Point[p0]},
{Red, Thick, HalfLine[#, {0, 0, 1}] & /@ p0}},
PlotRange -> {{-10, 10}, {-10, 10}, {0, 10}}]]
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
$endgroup$
Maybe this will work for you.
First define a function for generating $n$ random points on the xy-plane.
pts[n_] := {#1, #2, 0} & @@@ RandomReal[{-10., 10.}, {n, 2}]
Then
SeedRandom[42];
Module[{n = 20, p0} ,
p0 = pts[n];
Graphics3D[
{{AbsolutePointSize[4], Point[p0]},
{Red, Thick, HalfLine[#, {0, 0, 1}] & /@ p0}},
PlotRange -> {{-10, 10}, {-10, 10}, {0, 10}}]]
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
edited Mar 5 at 18:25
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
answered Mar 5 at 17:39
m_goldbergm_goldberg
87.4k872198
87.4k872198
add a comment |
add a comment |
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$begingroup$
If you want to use
RandomPoint, there'sImplicitRegion:RandomPoint[ ImplicitRegion[Abs@x < 10 && Abs@y < 10 && z == 0, {x, y, z}], 100]will give you 100 points in the specified region. Alternatively, you could also generate points in 2D usingRandomReal[10,{100,2}]and add the z coordinate usingAppend[0]/@pts$endgroup$
– Lukas Lang
Mar 5 at 17:22