Trying to explain things again. The sketch is of the item in the photo (resting on its front in the photo). Scale wise, once again the tenons are 15cm wide, so measure up from there.
As a younger chap most of my woodworking efforts were add ons to existing structures. Working in this way one becomes accustomed to measure from surfaces so that the things being made will fit with what is already there. This is a nightmare when working on a house, as all the timber is of different dimension, you need to switch your brain around to work out from planes that run through the center of all the timbers.
Making a structure of an irregular nature requires this centered approach. I have written a bit about the center lines on all the work pieces in my structure. The most difficult joints are those at the head of the pillars where they mate into the shape of the rounded underside of the top beam. Because I don't yet have a fixed height for all the pillars I can let that remain unknown and simply push the pillar into the beam as far as I need to, cutting it to the correct contour and leaving the tenon as true as possible. When I know the floor level at the center of the pillar I will measure from the level line on the beam to cut the pillar to length. Well actually I will measure from the center of the tenon that passes right through the pillar as that is 60cm from the level line on the beam. That marker means I don't have to have the beam on the pillar when I measure. If I had to make a similar joint at the other end I would have to make a measurement from the center to figure out how much to chop back and hope not to mess up the joint and cut off too much. A more difficult proposition.
This is why I opted for the other type of joint here, the actual Japanese gateway structures this is based on only have a plank that passes right through both beams, I wanted something more solid, but with the same through tenon. Here the beam has a square shoulder on the tenon that is housed in a recess in the pillar. This is a more feasible solution where the width between the two pillars is decided. I measure out from the center where it is marked A on the right hand sketchbook page, then I subtract that amount from the width so that I know where to cut the shoulder on the through tenon. This distance, something like 6cm in this case (which means the squared pillar I need to keep in mind while working is 12cm square in section) tells me how deep to cut the recess in the pillar to house the end of the beam. The photo and drawing are of the south west corner of my structure, so there is a recess cut in the pillar to house the corresponding beam that will connect to the north west corner pillar.
The truck tie down ratchet mechanism with red belt (resting on the through tenon beam) was very useful to tug on the beam and pull the tenon home as I planed off scraps of material here and there. Applying tension with that and then nudging with some taps from a maul I made ages ago (Just checked, that was made on September 22 2007, a more regular posterson back then).