How can I fill this gap by resizing the two parts the least amount possible?
What is the mathematical formula to do this?
No, I do not want to use any plugin.
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Odd but okay.
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Easiest way is to just set the snap to grid to something really small (.2, .1) and make it smaller (.01 probably) until it overlaps. Just slowly pull each one forward, one at a time.
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Don’t fill it, use ResizeAlign to overlap the parts: ResizeAlign v1.3 - Rounded Join + Dragger Mode
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I approve of the idea, but apparently he needs the non-plugin solution which I respect.
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Rather than to think inside the box, how about outside?
Try replicating the solution using unions, it should be easier.
- Cut the first side of the line you’re making.
- Cut it
- Duplicate the same object and line it properly for the appropriate width.
- Cut it and done
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normally I would had said to use ResizeAlign
But theres also a way to do this without it, and you don’t need to do math for it.
when you want to create such a bend, duplicate the part, resize it in such a way that its pivot point is at the edge of the previous part, around which you want to rotate/create a bend.
Then rotate it, and resize accordingly.
for example is theres a 5×1×1 stud block, and you want to create a bend at it, first duplicate it (Ctrl+D), then resize it into 2×2×1 studs, such that its centre coincides with the edge of the first part, then you may rotate it, and resize it accordingly.
Hope this helped (I’m sorry, I cannot use roblox studio now since I use a 32 bit device, otherwise I could had recorded doing that)
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I have a strong desire to know why OP doesn’t want to use plugins. 
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I have already easily filled that gap using blender
the secondary goal of this post is to find out what the logic/mathematical formula is for determining how much to resize the two parts such that the edges then meet for the case of if I did not have blender.
No plugins
No unions
No third parts
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You may look at the source code for the ResizeAlign plugin by inserting it in your game.
local obj = game:GetObjects("rbxassetid://165534573")[1]
obj.Parent = workspace
game.Selection:Set({obj})
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