Melding two 3D objects by matching vertices

I have two 3D objects in my Sketchup file, which I would like to merge into one. Here’s a simple example of what I’m trying to do - if you can explain how, I can apply the process to my more complicated shapes:

  • Imagine I have a cube, defined by 8 vertices (P1-P8). P1-P4 are on the X-Y (flat) plane, P5-P8 are directly above P1-P4 - also in an X-Y plane, but displaced vertically in the Z plane, making a cube.
  • Imagine I have a second cube, with the same dimensions as the first cube, defined by vertices P9-P16. This cube is offset somewhere in the file - in X, Y, and Z directions. P9-12 are the vertices directly below P13-P16.
  • I would like to merge the cubes, so that they form a rectangular prism, by essentially sitting one cube on top of the other (so the prism’s height is twice its length or width). I would like this prism to be one object, not just two objects that happen to be on top of one another.
  • Essentially, P5 and P9 become the same vertex, P6 and P10 become the same vertex, P7 and P11 become the same vertex, and P8 and P12 become the same vertex. In the end, I should only be left with P1-P8 and P13-P16 as vertices - that is, 12 total vertices, not 16.

How can I do this?

(Please note that my actual objects - more complicated than cubes - still have vertices that can be correlated between the two objects, as in the cube example, so I don’t have to worry about the complication of joining two arbitrary objects that weren’t designed to eventually be merged).

Thank you.

Depending on the exact shapes, you might need to manually stitch between the vertices assuming they don’t touch. If you can move one object so its vertices correspond to the vertices on the other boject you could use Outer Shell. Or it might be that you could use an extension like Curviloft.

The two cubes are easy enough but with your actual model we’d need to see it to give you an exact workflow.

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Here’s a slightly more complex one than a cube.
As long as the objects are solids just about any shapes can be joined into one using Outershell.
You can see in this one that the relevant vertices join making a shape that is exactly double the original. But the shapes could overlap and still work with outershell.

You could also explode both groups and just delete the face that joins them.

Once the two cubes are joined, you can select the edges that compose the junction and delete them.

Of course, to get a prism that has one of its dimension double of the original cube. you can scale it along the required direction (X or Y or Z) and use 2 as the scale factor.

I like your mathematical way of thinking!

You speak about more complex shapes than cubes. I suppose the prequisite is that their z projection is identical. In that case, I would cut both objects in the middle, keep top part of the top object and bottom part of the bottom object, close the holes and use push-pull to join them.