How is the scale of ParametricPlot3D determined?

Question

I define a couple ParametricPlot3D planes like so;

xyPlane = ParametricPlot3D[{0, y, z}, {y, -5, 5}, {z, -5, 5}];
yzPlane = ParametricPlot3D[{x, 0, z}, {x, -5, 5}, {z, -5, 5}];

Calling Show without BoxRatios returns

Whereas BoxRatios -> {10, 10, 10}

returns

Note the difference in gridlines. Is there some way to make them uniform? More generally, is it known what is going on under the hood of ParametricPlot3d that causes this?

You want AspectRatio as true BoxRatio for all three axes, right? — Narasimham, Mar 31 '18 at 17:33
I'm not sure. I am about to try messing with Mesh, but fundamentally I want to understand howParametricPlot3d decides this stuff. — jamesson, Mar 31 '18 at 17:43
I had long felt that an option for automatic proportional scaling was lacking in the Plot menu. — Narasimham, Mar 31 '18 at 17:52
@Narasimham So, what setting should I use to get correct output? — jamesson, Mar 31 '18 at 17:58
@Narasimham, besides, why the hell doesn't BoxRatios do this correctly? In other words, why doesn't it produce 10 divisions form -5 to 5 instead of 10 divisions from -1 to 1? — jamesson, Mar 31 '18 at 18:01
@BobHanlon no. To clarify,I am putting aspectratio on plane definitions and boxratio on the show statement — jamesson, Mar 31 '18 at 18:06
@BobHanlon I just want the same exact number of gridlines on both planes, and the same numebrs on both axes — jamesson, Mar 31 '18 at 18:07
@BobHanlon, interestingly enough sticking aspectratio into show throws the error The specified setting for the option Graphics3DBoxOptions, AspectRatio cannot be used. — jamesson, Mar 31 '18 at 18:11
If you want to faithfully plot a box $3 ^{'}X ,2 ^{'}X,1 ^{'} $ then BoxRatios-> {3,2,1} has it plotted proportionally. — Narasimham, Mar 31 '18 at 18:12
Before we all get hung up on BoxRatios: have you tried evaluating Show[xyPlane, yzPlane, PlotRange -> All]? — J. M.'s missing motivation, Mar 31 '18 at 18:12
@J.M. Yes. That's it exactly.Thanks so much. But, why does ParametricPlot3d decide to chop things off like that? — jamesson, Mar 31 '18 at 18:15
Because of option inheritance (in this specific case, the setting for PlotRange). Try evaluating Show[yzPlane, xyPlane], and then try adding PlotRange -> All again. — J. M.'s missing motivation, Mar 31 '18 at 18:17
@J.M. I would like to take a second to offer my best wishes and moral support (whatever that's worth) for your health problems. I would love to help you out, but sadly I am a poor undergraduate with health drama of my own. I really hope you get better. — jamesson, Mar 31 '18 at 18:23
The well-wishes are very much appreciated, and I hope you get well, too. — J. M.'s missing motivation, Mar 31 '18 at 18:25

How is the scale of ParametricPlot3D determined?

0 Answers0