Mathematica help union/intersection of 3d plots

In summary, the individual has 4 RegionPlot3D plots, A1, A2, B1, and B2, each representing a region in a 3d space. The goal is to first find the union of A1 and A2, called A, and the union of B1 and B2, called B, and then find the intersection of A and B. The individual has tried using the Show function for the unions, but is having trouble finding the intersection. They have also discovered the || operator for unions and the && operator for intersections in the RegionPlot3D function.
  • #1
yzhang33
2
0
I want to do the following:

Say I have 4 RegionPlot3D plots, namely A1 A2 B1 and B2. Each of those four plots are region plots so they occupies some kind of region inside the same 3d space.

First I want to find and display union of A1 and A2, call it A. Then find and display union of B1 and B2, call it B. Lastly, I want to find and display intersection of A and B.

Somethings that I have tried:
1. I can use Show[A1,A2] to graphically find the union of A1 and A2, but after I got A and B. I can't use the Show function to find intersection.

2. I can directly use RegionPlot3D to find intersections of two plots by naming the regions region1 and region2. I can use do RegionPlot3D[region1 && region2...] to do it. But I can't find unions using this method.

3. If my goal is first do intersection, then do union, I can use above two method to do it. But my goal is first do union. So if I use, it doesn't really tell me what region does the union results in, it just displays it.
 
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  • #2
yzhang33 said:
I can use do RegionPlot3D[region1 && region2...] to do it. But I can't find unions using this method.
If you can do RegionPlot3D[region1 && region2...] for intersection
then why can't you do RegionPlot3D[region1 || region2...] for union?

http://reference.wolfram.com/mathematica/ref/RegionPlot3D.html
 
  • #3
right right. I just found it out there is a || operator as well. Thank for the reply.
 

Related to Mathematica help union/intersection of 3d plots

1. How do I plot the union of two 3D plots in Mathematica?

To plot the union of two 3D plots in Mathematica, you can use the "RegionPlot3D" function with the "RegionUnion" option. For example, if you have two 3D plots defined as "plot1" and "plot2", you can use the code "RegionPlot3D[RegionUnion[plot1, plot2], PlotRange -> All]" to plot their union. This will create a new 3D plot with the combined regions from both plots.

2. Can I plot the intersection of two 3D plots in Mathematica?

Yes, you can plot the intersection of two 3D plots in Mathematica using the "RegionPlot3D" function with the "RegionIntersection" option. Similar to plotting the union, you can use the code "RegionPlot3D[RegionIntersection[plot1, plot2], PlotRange -> All]" to plot the shared region between the two plots.

3. How can I change the color or style of the union/intersection plot?

You can change the color or style of the union/intersection plot by adding additional options to the "RegionPlot3D" function. For example, you can use the "MeshStyle" option to change the color of the mesh lines, or the "PlotStyle" option to change the color of the surface. You can also use the "Mesh" option to adjust the density of the mesh lines.

4. Is it possible to plot the union/intersection of more than two 3D plots?

Yes, it is possible to plot the union/intersection of more than two 3D plots in Mathematica. You can use the same syntax as mentioned in the first two questions, but instead of two plots, you can include as many as you need. For example, "RegionPlot3D[RegionUnion[plot1, plot2, plot3], PlotRange -> All]" will plot the union of three 3D plots.

5. Can I use Mathematica to find the volume of the union/intersection of 3D plots?

Yes, you can use Mathematica to find the volume of the union/intersection of 3D plots. After plotting the union/intersection using the "RegionPlot3D" function, you can use the "Volume" function to calculate the volume of the region. For example, "Volume[RegionUnion[plot1, plot2]]" will give you the volume of the union of two 3D plots.

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