Design Small Bathroom Layout

I am designing a small bathroom in my new workshop and need a bit of plumbing help.?
The room will have a single toilet and sink. I have an existing slab and the guys who poured it already placed the initial plumbing (although I am not sure it is sufficient. I am planning on teeing into the bottom of clean-out on the back of my main house (about 20 feet away. It’s a clean-out for my master bath and the bottom of the clean-out is about 20″ below grade).
I have the sewage pipe entering the workshop, teeing in for the toilet and up to catch the line from the sink and continuing up for the vent. I would like to know how to layout continuing up for the venting. I do need to angle over about 2 feet to avoid a window directly behind the toilet and then a tie in for the sink. I am not sure of the size the vent pipe needs to be to include both the toilet and sink.
I would be happy to include a diagram and any further details needed.
Any help would be greatly appreciated.
bmg
In our location, if the vent for the sink (2″ pvc) is within 6′ of the stool flange, you’ll still fall within code. Of course you’ll have to verify that with your local code officials (if you are covered by such).
3D Bath Tub Design (Using Chief Architect)