I have been doing a fair amount of 3D printing with my Prusa i3 MK3s printer. I have graduated from downloading and printing stl files from thingiverse to creating my own. There are multiple different 3D design programs out there and I have tried several. For complicated things, I use Fusion 360, which has a Free for Hobbyist page. Hurray!
For most things, however, I use TinkerCad. It’s a great web-based tool that will cover most of your needs. The one glaring flaw that I have found with TinkerCad is that there is no ‘Intersection’ tool. If you have two objects, like the short box and cylinder below:
and you want to produce their intersection:
then you are out of luck with the built-in tools.
However, not all is lost! What TinkerCad does provide are 2 things that we will use to produce and intersection: Group and Holes. A Group joins together two objects into a single object. A Hole turns an object into a negative version of itself. Here is how we use these to do an Intersection.
Step 1: Select one of the objects and turn it into a Hole.
Note, if you were to Group this with box, then you would end up with the following (You Group them by shift-clicking on the box, so the hole-cylinder and box would both be selected and then clicking on the Group button ):
This is not what we want, so don’t do this yet!
Step 2: Duplicate the other piece. You do that by selecting it (left-clicking) and doing Cntl-D:
Step 3: Group the Hole and the Duplicate. Shift-click on the Hole and click on the Group button. Here the Duplicate and Hole are selected:
And this is what it looks like after the Grouping. Note that there is a line showing where the duplicate is now missing a piece:
Step 4: Turn the Grouped-Duplicate-Hole into a Hole. Without unselecting the Grouped object you just created, click on Hole, turning it into a hole:
It’s a good idea to do this immediately, because the original box and the Grouped-Duplicate-Hole objects are on top of each other and it can be difficult to select the right one.
Step 5: Group the Grouped-Duplicate-Hole-Hole object with the original box. So, shift-click the original box (the red part above) and Group:
and after you have Group-ed them:
And this is the Intersection, which is what we wanted.
Why does this work? Because of set theory. What we want is the Intersection, but that is not a function that is available to us. We do have Union, since that is what Group does. We don’t have Set Difference exactly, but we have a ‘Hole’ function. So, what we are doing above is:
You may think to yourself that A – (A – B) = A, but this is not arithmetic. This is set theory and set differences are not associative. How do we get A – B? We turn B into a hole and group it, so:
We want to do the difference again, so we have to turn the above into a hole and group again. So, the final equation is:
where is a duplicate of A. In terms of TinkerCad, do it starting in the middle and work your way out. The steps are:
- Turn B into a Hole, call it Bh
- Duplicate A, call it Ad
- Group Ad and Bh, call this Ad-Bh
- Turn Ad-Bh into a hole, call it (Ad-Bh)h
- Group A and (Ad-Bh)h
And then you have your intersection.