[?] Get plot with just axes crossing at the origin?

Questions
,
1

Hi, when I plot (3D) a 2 variable scalar function in wolfram Mathemática I always get the function in a box formed by the axis. How could I get rid of that box and just see the surface I´m plotting and the three ortogonal axis crossing at the origin??

2

In dimension 2 it’s easy:

Graphics[Circle[], Axes -> True, AxesStyle -> Arrowheads[.1]]

In dimension 3 the box can be deleted with Boxed->False and perhaps Axes->False too. To get the arrows one roundabout way is this:

pl = Graphics3D[{Opacity[.1], Sphere[]}];
{{xmin, xmax}, {ymin, ymax}, {zmin, zmax}} = 
  PlotRange /. AbsoluteOptions[pl, PlotRange];
Show[pl, Graphics3D[{Arrow[{{xmin, 0, 0}, {xmax, 0, 0}}], 
   Arrow[{{0, ymin, 0}, {0, ymax, 0}}], 
   Arrow[{{0, 0, zmin}, {0, 0, zmax}}]}], Boxed -> False]

It can be automated, if necessary. Anyone knows a more elegant solution?

3

An alternative to Gianlucas suggestion:

Graphics3D[
 	{Cuboid[{2, 2, 2}], Sphere[{2, 2, 2}]},
 	Boxed -> False, Axes -> True, AxesOrigin -> {0, 0, 0}, Ticks -> None,
 	PlotRange -> 4
 ]

10543Sphere.png
10543Sphere.png256×227 6.3 KB

4

Thanks a lot guys it´s been of great help.

5

Axes can easily be distinguished by color:

Graphics3D[
 	{Cuboid[{2, 2, 2}], Sphere[{2, 2, 2}]},
 	Boxed -> False, Axes -> True, AxesOrigin -> {0, 0, 0}, Ticks -> None,
 	AxesStyle -> {Red, Darker@Green, Blue}, PlotRange -> 4
 ]

Axes.png
Axes.png266×242 6.4 KB

But I can not find a way to add arrowheads to the axes by setting an option to Graphics3D

6

Beware that if you go the AxesOrigin -> {0, 0, 0} way, the axes will be rendered on top of everything else, which in 3D can be very confusing. I think that the design choices of Wolfram regarding the axes in 3D have good reasons behind. The three axes as arrows make sense only in some cases, and you are advised to draw them manually as appropriate in each situation.