Author 
Comment/Response 
Bill Simpson

05/21/13 00:08am
In Response To 'Re: Re: How do I merge 3D graphics?'  You wrote
"Why don't I see all three points in the output of
Show[elips,pBeg, pMin, pMax]?"
I can't see what you see, but when I scrape that code off the screen, paste it in my notebook and evaluate it I see all three of your points in the plot with one just at the upper corner. If you can't see that then perhaps opening a fresh notebook, pasting the code, evaluating the cell and doing a screen capture showing the code and the plot with the missing point might provide supporting evidence. (Usually a screen shot is a terrible way to ask for help because others just need to type it back in, but maybe in this particular case it might be OK)
I suspect the bounding box is just large enough to contain the points. I purposely made the points huge, so that you couldn't miss them, and that can make part of the big black dot be outside the box, but I think the point is on the edge of the box.
You can change the plot range to make it as large or small as you like.
You wrote
"Why does Opacity work in
surf = Plot3D[Sin[x + y^2], {x, 3, 3}, {y, 2, 2}, PlotStyle > Opacity[0.5]]
but not in
elips = ContourPlot3D[ x^2 + 2 y^2 + 6 z^2 == 1, {x, 1, 1}, {y, 1, 1}, {z, 0.5, 0.5},
PlotStyle > Opacity[0.5]]"
Options[Plot3D] tells you all the options Plot3D will accept. PlotStyle is one of those.
Options[CountorPlot3D] tells you all the options ContourPlot3D will accept. PlotStyle is not one of them.
Always checking that you are using valid options is an excellent idea.
If you aren't getting bright red warning about "Unknown option PlotStyle" in your ContourPlot3D then something is very wrong with the error system.
You wrote
"It's frustrating that Mathematica plotting is so inconsistent. Something that does just what I want in one place doesn't work in another. I expect there's a workaround, but I need advice to find it"
I do not mean anything rude by this, but you may not have even begun to see the magnitude of frustration waiting to be found.
I highly recommend getting yourself some good books and read them carefully. "Mathematica Navigator" is still good, but it is somewhat dated. "Mathematica Cookbook" is good and newer. "Mathematica Graphics Guidebook" was excellent, but it is deeply unfortunate that it is now very very old and there has not been an up to date edition published. "The Mathematica Book" 5th edition is very old and heavy to ship, but it is the last one that will ever be published. Getting at least a couple of those and reading them over and over will probably be helpful.
You are attempting to learn "the Mathematica way of thinking." That is not nearly as simple learning many other far simpler and more mechanical languages with fewer surprises in hiding. You are trying to learn how to, by the third or fourth guess, find what the answer to a problem is or at least what to look at which will lead you to the answer.
I have a general rule that seems to be verified again and again: If getting just the math sort of working and maybe some kind of plot takes about X time and effort then getting the math really exactly correct often takes between two and ten times longer than that. Getting everything "desktop published" and the graphics exactly the way you want them done and the fonts and the superscripts and subscripts pretty consistently takes between two and ten times, and possibly infinitely, longer than all that, depending on your personal standards.
Again and again I see "I got the math typed in in five minutes and well yes it did take me an hour to find and fix my mistakes in that, but I don't want to think about that. But what do you mean it is going to take me between two and twenty four hours of intense effort and repeated failures and lots of experience before I have five minutes of math that looks close to how I imagine I want it to look?!?!?!"
Well that is because it is often just the way it is. Even more annoying, often the better someone gets at Mathematica, the higher their standards are for desktop publishing, so the "two to ten" factor doesn't go away and might even get worse.
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