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How show axes labels with AxesOrigin->{0,0,0} in 3D?

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  How show axes labels with AxesOrigin->{0,0,0} in 3D? Murray Eisenberg <murray@math.umass.edu> - 2011-06-06 10:24 +0000
    Re: How show axes labels with AxesOrigin->{0,0,0} in 3D? "Nasser M. Abbasi" <nma@12000.org> - 2011-06-07 10:47 +0000
    Re: How show axes labels with AxesOrigin->{0,0,0} in 3D? Helen Read <readhpr@gmail.com> - 2011-06-07 10:47 +0000

#2971 — How show axes labels with AxesOrigin->{0,0,0} in 3D?

Since Mathematica 7, 3D graphics has allowed the AxesOrigin option so 
that, for example, the axes can go through the origin {0,0,0}, just like 
the way that mathematicians (or at least college calculus teachers) do 
it and teach their students to do it.

That works, but...

If you include an AxesLabel option, the labels do not appear, e.g., from:

    Plot3D[x^2 - y^2, {x, -2, 2}, {y, -2, 2},
           AxesOrigin -> {0, 0, 0},
           AxesLabel -> {x, y, z},
           BoxRatios -> {1, 1, 1}, Boxed -> False]

Is there some way to make the axes labels appear (other than to add them 
manually using the Text function, say in an Epilog)?

[And is this just another instance of WRI protracted stubbornness even 
in admitting that having 3D axes emanating from the origin is a 
permissible way of handling 3D graphics?  (Scientific/engineering 
convention seems overwhelmingly to favor axes along edges of a 3D 
graphic, whereas in math -- as I suggested, at least in multivariable 
calculus -- axes emanating from the origin is the norm.)

-- 
Murray Eisenberg                     murray@math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower      phone 413 549-1020 (H)
University of Massachusetts                413 545-2859 (W)
710 North Pleasant Street            fax   413 545-1801
Amherst, MA 01003-9305

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#2992

On 6/6/2011 3:24 AM, Murray Eisenberg wrote:
> Since Mathematica 7, 3D graphics has allowed the AxesOrigin option so
> that, for example, the axes can go through the origin {0,0,0}, just like
> the way that mathematicians (or at least college calculus teachers) do
> it and teach their students to do it.
>
> That works, but...
>
> If you include an AxesLabel option, the labels do not appear, e.g., from:
>
>      Plot3D[x^2 - y^2, {x, -2, 2}, {y, -2, 2},
>             AxesOrigin ->  {0, 0, 0},
>             AxesLabel ->  {x, y, z},
>             BoxRatios ->  {1, 1, 1}, Boxed ->  False]
>
> Is there some way to make the axes labels appear (other than to add them
> manually using the Text function, say in an Epilog)?
>
> [And is this just another instance of WRI protracted stubbornness even
> in admitting that having 3D axes emanating from the origin is a
> permissible way of handling 3D graphics?  (Scientific/engineering
> convention seems overwhelmingly to favor axes along edges of a 3D
> graphic, whereas in math -- as I suggested, at least in multivariable
> calculus -- axes emanating from the origin is the norm.)
>

Hello;

The axes labels are there, just hard to see. Here is a proof:

Plot3D[x^2 - y^2,
  {x, -2, 2},
  {y, -2, 2},
  AxesOrigin -> {0, 0, 0},
  AxesLabel -> {Style[x, Red, 40], Style[y, Red, 40],
    Style[z, Red, 40]},
  BoxRatios -> {1, 1, 1},
  Boxed -> False]

I consider axes labels for 3D not be well implemented in Mathematica. Please
see this discussion

http://stackoverflow.com/questions/6182804/mathematica-help-me-understand-mathematica-3d-coordinates-system

--Nasser

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#2995

On 6/6/2011 6:24 AM, Murray Eisenberg wrote:
> Since Mathematica 7, 3D graphics has allowed the AxesOrigin option so
> that, for example, the axes can go through the origin {0,0,0}, just like
> the way that mathematicians (or at least college calculus teachers) do
> it and teach their students to do it.
>
> That works, but...
>
> If you include an AxesLabel option, the labels do not appear, e.g., from:
>
>      Plot3D[x^2 - y^2, {x, -2, 2}, {y, -2, 2},
>             AxesOrigin ->  {0, 0, 0},
>             AxesLabel ->  {x, y, z},
>             BoxRatios ->  {1, 1, 1}, Boxed ->  False]
>
> Is there some way to make the axes labels appear (other than to add them
> manually using the Text function, say in an Epilog)?

The labels are there, it's just difficult to see them, and they are 
strangely (poorly, really) placed. Try this.

plot1=Plot3D[x^2 - y^2, {x, -2, 2}, {y, -2, 2}, AxesOrigin -> {0, 0, 0},
  AxesLabel -> {x, y, z}, BoxRatios -> {1, 1, 1}, Boxed -> False,
  AxesStyle -> Directive[Bold, 16]]


The labels certainly are not where I would put them. Compare:

plot2=Plot3D[x^2 - y^2, {x, -2, 2}, {y, -2, 2}, AxesLabel -> {x, y, z},
  BoxRatios -> {1, 1, 1}, Boxed -> False,
  AxesStyle -> Directive[Bold, 16]]


And if you change the ViewPoint to more or less approximate the way we 
draw it on the board in calculus class, the placement of the labels is 
even worse.

Compare:

Show[plot2,ViewPoint -> {2.362691025323322`, 1.7097627408932812`,
   1.7159261314840222`}]

Show[plot1,ViewPoint -> {2.362691025323322`, 1.7097627408932812`,
   1.7159261314840222`}]

In the latter, now the x label is in a very misleading place, and the y 
and z labels are right on top of each other to the point of illegibility.


-- 
Helen Read
University of Vermont

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