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From: nevjernik on 29 Mar 2010 06:22
Consider following simple piece of code which should represent plane
determined by two vectors:

******* Code Start **********
vector1 = {1, 2, 3}
vector2 = {2, 3, 4}
ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10, 10}]
******* Code End ************


Question: Why with this code I get some kind of "deformed" plane
apparently contracted in some directions, in a sense that distances of
points doesn't appear equal in all directions.

It can be better seen with circle of radius 2 drawn in that plane:

******* Code Start **********
vector1 = {1, 2, 3}
vector2 = {2, 3, 4}
Show[ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10,
10}, AxesOrigin -> {0, 0, 0}],
ParametricPlot3D[2 Cos[t] vector1 + 2 Sin[t] vector2, {t, 0, 2 Pi},
PlotStyle -> {Thick, Green}]]

******* Code End ************

I tried to use options like PlotRange, or BoxRatios, but with no efect
on plane or circle.

What I am doing wrong or missing?

Thanks

--
ne vesele mene bez vas
utakmice nedjeljom



From: dh on 29 Mar 2010 07:56
Hi,
your vectors are not orthogonal.
Therefore the do not constitute an orthogonal basis as you assume.
cheers, Daniel

On 29.03.2010 12:22, nevjernik wrote:
> Consider following simple piece of code which should represent plane
> determined by two vectors:
>
> ******* Code Start **********
> vector1 = {1, 2, 3}
> vector2 = {2, 3, 4}
> ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10, 10}]
> ******* Code End ************
>
>
> Question: Why with this code I get some kind of "deformed" plane
> apparently contracted in some directions, in a sense that distances of
> points doesn't appear equal in all directions.
>
> It can be better seen with circle of radius 2 drawn in that plane:
>
> ******* Code Start **********
> vector1 = {1, 2, 3}
> vector2 = {2, 3, 4}
> Show[ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10,
> 10}, AxesOrigin -> {0, 0, 0}],
> ParametricPlot3D[2 Cos[t] vector1 + 2 Sin[t] vector2, {t, 0, 2 Pi},
> PlotStyle -> {Thick, Green}]]
>
> ******* Code End ************
>
> I tried to use options like PlotRange, or BoxRatios, but with no efect
> on plane or circle.
>
> What I am doing wrong or missing?
>
> Thanks
>
> --
> ne vesele mene bez vas
> utakmice nedjeljom
>
>
>


--

Daniel Huber
Metrohm Ltd.
Oberdorfstr. 68
CH-9100 Herisau
Tel. +41 71 353 8585, Fax +41 71 353 8907
E-Mail:<mailto:dh(a)metrohm.com>
Internet:<http://www.metrohm.com>


From: David Park on 30 Mar 2010 06:01
And you can use Orthogonalize to obtain a better set of vectors.

{vector3, vector4} = Orthogonalize[{vector1, vector2}]

Show[ParametricPlot3D[{u vector3 + v vector4}, {u, -10, 10}, {v, -10,
10}, AxesOrigin -> {0, 0, 0}],
ParametricPlot3D[2 Cos[t] vector3 + 2 Sin[t] vector4, {t, 0, 2 Pi},
PlotStyle -> {Thick, Green}]]


David Park
djmpark(a)comcast.net
http://home.comcast.net/~djmpark/




From: nevjernik [mailto:hajde.da(a)mijenjamo.planetu]


Consider following simple piece of code which should represent plane
determined by two vectors:

******* Code Start **********
vector1 = {1, 2, 3}
vector2 = {2, 3, 4}
ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10, 10}]
******* Code End ************


Question: Why with this code I get some kind of "deformed" plane
apparently contracted in some directions, in a sense that distances of
points doesn't appear equal in all directions.

It can be better seen with circle of radius 2 drawn in that plane:

******* Code Start **********
vector1 = {1, 2, 3}
vector2 = {2, 3, 4}
Show[ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10,
10}, AxesOrigin -> {0, 0, 0}],
ParametricPlot3D[2 Cos[t] vector1 + 2 Sin[t] vector2, {t, 0, 2 Pi},
PlotStyle -> {Thick, Green}]]

******* Code End ************

I tried to use options like PlotRange, or BoxRatios, but with no efect
on plane or circle.

What I am doing wrong or missing?

Thanks

--
ne vesele mene bez vas
utakmice nedjeljom





From: Narasimham on 9 Apr 2010 03:33
On Mar 29, 3:22 pm, nevjernik <hajde...(a)mijenjamo.planetu> wrote:
> Consider following simple piece of code which should represent plane
> determined by two vectors:
>
> ******* Code Start **********
> vector1 = {1, 2, 3}
> vector2 = {2, 3, 4}
> ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10, 10}]
> ******* Code End ************
>
> Question: Why with this code I get some kind of "deformed" plane
> apparently contracted in some directions, in a sense that distances of
> points doesn't appear equal in all directions.
>
> It can be better seen with circle of radius 2 drawn in that plane:
>
> ******* Code Start **********
> vector1 = {1, 2, 3}
> vector2 = {2, 3, 4}
> Show[ParametricPlot3D[{u vector1 + v vector2}, {u, -10, 10}, {v, -10,
> 10}, AxesOrigin -> {0, 0, 0}],
> ParametricPlot3D[2 Cos[t] vector1 + 2 Sin[t] vector2, {t, 0, 2 Pi},
> PlotStyle -> {Thick, Green}]]
>
> ******* Code End ************
>
> I tried to use options like PlotRange, or BoxRatios, but with no efect
> on plane or circle.
>
> What I am doing wrong or missing?
>
> Thanks

In ParametricPlot3D three components are needed. So better:

vector1 = {1, 2, 3} ; vector2 = {2, 3, 4} ;Plot3D[{u vector1 + v
vector2}, {u, -10, 10}, {v, -10, 10}]

Narasimham



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