Differences in 3 Dimensional objects?

Questions
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1

I’m am subtracting a 3D shape form another 3d shape.

This code works nicely;

    tray = Cuboid[-1.0 {714.35, 130.66,  0}, {714.35, 130.66, 153.94}]; 
	trayCutout = Cuboid[-1.0 {699.21, 115.52, 15.14}, {699.21, 115.52, 138.79}]; 
	reg = Fold[RegionDifference, tray, {trayCutout}];

This code fails …

    object = RegionPlot3D[0.012537762251 (x^2 + y^2) - z <= 0, {x, -101.60, 101.60}, {y, -101.60, 101.60}, {z, 0, 129.43}]
    cutout = RegionPlot3D[0.023816076541 (x^2 + y^2) - z <= 0, {x, -54.88, 54.88}, {y, -54.88, 54.88}, {z, 0, 71.72}] 
    region = Fold[RegionDifference, object, {cutout}];

Any thoughts on why the RegionPlot3D fails & the Cuboid works nicely. And how can I make the RegionPlot3D work ?

2

RegionPlot3D generates a Graphics3D object, not a region.

3

Thanks Frank , My goal with this code is ‘to subtract 1 shape from another shape’ , so I added these lines …

        (*     RegionPlot3D generates a Graphics3D object,  not a region !     *)
        objMesh = DiscretizeGraphics[object];
        cutoutMesh = DiscretizeGraphics[cutout];
        region = Fold[RegionDifference, objMesh, {cutoutMesh}];

        (*     Use RegionMember to turn this into inequalities:     *)
        ineqs = RegionMember[region, {x, y, z}];

All is good till here and this last line fails …

        contourRegionPlot3D[ineqs, {x, -101.60, 101.60}, {y, -101.60, 101.60}, {z, 0, 129.43}, Mesh -> NoneBoxRatios -> Automatic,         PlotRange -> All, Boxed -> False, Axes -> False]

        results : Mesh::ilevels    NoneBoxRatios -> Automatic is not a valid mesh specifications.

Any ideas why ‘contourRegionPlot3D’ fails here ?

4

RegionPlot(3D) can handle And Not Or Xor et cetera:

RegionPlot3D[
 0.012537762251 (x^2 + y^2) - z <= 0 \[And] 
  Not[0.023816076541 (x^2 + y^2) - z <= 0], {x, -101.60, 
  101.60}, {y, -101.60, 101.60}, {z, 0, 129.43}]
5

Sander , I like this!
A single line, not so many coercive lines of code.

I’ve read about ‘And Not Or Xor’ & about RegionPlot3D.

I Think this says, a larger paraboloid solid at the origin, minus a smaller paraboloid solid also at the origin.

RegionPlot3D.png
RegionPlot3D.png842×477 17 KB

I am guessing that this does not say what I think it says.

Ideas ?

6

If you do a straight copy from my above post, in a clean Mathematica 11 you should get:

ScreenShot2016-09-26at20.54.14.jpg
ScreenShot2016-09-26at20.54.14.jpg740×832 134 KB

7

I have a Home version, purchased & registered a few days ago. Clean ?.. I think it has to be.

Can you send a screen shot of ‘the line of code’. I suspect, copy and paste may be the problem.

This solves a big problem for me. I’ve been using Applescript to do the math, logic & write the Mathematica code . I do the same, writing Python code to drive Blender. I’m hoping to do everything with Mathematica , alone.

Greatly appreciate your input !

On a side note; I have a picture of Machu Picchu, shot from the exact same spot as yours. Went there in the 1980’s on a Shirley MacLaine film. In fact we climbed to the top of Huana Picchu the mountain in the background.

8

Again, it is just a copy from above:

ScreenShot2016-09-26at21.34.26.png
ScreenShot2016-09-26at21.34.26.png770×194 14.7 KB

9

Here, even better, the file.

10

GOT IT !

I quit Mathematica 11 and restarted it.
I think there were too many spurious variables floating around.

Near the origin, it fell apart …

11

that’s what I meant with clean (restart, fresh kernel, no prior definitions et cetera).

At the origin the two surfaces touch so that will be very tricky to plot using RegionPlot. If you plot it as two surface (ContourPlot3D) you won’t have such a problem. But might not be easy for other region/surfaces…

12

Awe, surfaces touching..

I can fix that, In a previous version I did in python, I had the outer paraboloid’s height & radius larger, affording an even thickness.
I neglected that in this sample, trying to make Mathematica code work.

Sander, you’ve been a great help,
Thanks.