Firstly, apologies for using this (UK)terminology (setting-out), as I'm from a joinery background: we think this way.

However, a few or more years ago I built a Japanese teahouse with the help of a Japanese carpenter from Tokyo, who actually was a finishing carpenter who had worked in the Imperial Palace
(sic) and worked for the main Tokyo building carpentry company.

One thing I must say before I go on, is that this carpenter who didn't speak English, and I got on very well: we had a common language: our craft. He gave me his tools (chisels, saws, square,
hammers,etc: but not his ink-line which was inherited from an architect forbear) when he left our job.

The hammer is the best tool I have, bar none. I think of him most times I use it, and the planes he gave me too. The little wooden finishing plane (burnishing) beat a Mathieson on a bench test with a friend, for finishing.

But what I want to get down to is the method of marking out, based on centre-lines.

I have used this since on all my oak-framing, using "nodes" crossing centre lines with trigonometry. (I establish a line in the "beam" then square off it) Then I use offsets/scribes. It's damned accurate.
I take it others must do this, but I don't hear of it: do you guys use trig? I guess you must do but there's not much information here.

I hear ya, mr. lignator(were'd you get that handle??) I love this method, it is how I was taught. So simple, in particular for shop plans, but there is prep time to set out the centerlines accurately. So I also work in square rule for small buildings to save time. I learned from an ex-pat american named Joe Erikson, who had been in the museums....

Thanks mr Davidson, I am not alone!: as I'm out on a limb where I live, no framers about here (good for business!), I had to develop my own methods, using the Japanese practice I experienced as a base. (Centrelining).

The English framers I have worked with since say the method I have worked out is OK for what I do (mainly roof framing) but not so good, for something like a cruck frame x 6 for example.

However, .. mostly I don't have to lay out the frames before cutting, which in a one-man outfit is important timesaving and back-saving. I think that is more onerous than the lengthy process of lining out, but which is also a useful selection process.

I don't know how other people do it, but I establish, from the initial centre line, chosen for various reasons on a particular facet at a particular orientation, a vertical plane transferred to the opposite face, then this is squared to an horizontal plane, ditto. In all the calcs, I am envisioning these planes then imposing the sides/section of the timber on them, offsetting etc.

I only use the sashigane (metric, though I have the Japanese one) + a calculator, and a scribe. Not much in the toolbox: (and you can stick the sashigane in your belt: I don't own a western roofing square:too big) something which originally impressed me by my Japanese carpenter friend: not much to carry, but so much to utilise.

I use the trig to transfer back to numerical settings on the square, in metric it's so easy to multiply up etc.

I can't understand why more carpenters don't use such an easy method which is only dependent on a few formulae, and a basic understanding of triangles.

"However, .. mostly I don't have to lay out the frames before cutting, which in a one-man outfit is important timesaving and back-saving. I think that is more onerous than the lengthy process of lining out, but which is also a useful selection process."

I'm not sure what you mean by the above?

I think we line out in the same way, I set the vertical first with a plumb line, the set the horizontal with the square. Alternately I will set the vertical line first with the square, then transfer that line to the other end with a level.
The last guy i worked with helped me build an octagon frame and we were setting housed braces into a 7.5in/12ft slope(sod roof) and he had a great "I get it moment" with the lines.
Something I like is just the fact that the line is in the middle of the timber, and usually very accessible to the square. I use a regular carpenter's square for layout, though I have some Japanese squares... I think I'm addicted to the number 12.
Watch out for out of square faces when working in angles other than 90, though, makes me realize why the Japanese square things up nicely.
This method is not for everybody, and not every building, IMO

I guess it's horses for courses. I make a lot of biggish oak truss roof frames so the system suits me. Of course I use other methods when required, though since I have no hardstanding outside my workshop, just about a foot of oak chippings, I can't chalk on the floor..

I just looked at the index for "Timber Framing" and could find only one reference to trig: "Trig for the perplexed"! However, found some refs about trig in the "Joiners Quarterly". Can't recall anything in UK journals, but since I'm working across the range of woodworking, can't read 'em all!

Anyway, you guys have impressive and almost intimidating knowledge beyond my experience of framing at any rate. I just wondered if anyone had stumbled on the same system as me, by whatever route.

Lignator, I generally work with log builders and don't know anything about Japanese framing and joinery. Given the nature of logs or dressed timbers the method you are describing is the only way to go.
The roof dimensions and their intersections (the "nodes") are determined using trigonometry. Joints at the intersecting members are built about these datum lines and points. Quick, easy and accurate.

Center lines are used in French Scribe methods. On the end make two lines corner to corner. Plumb through the intersection and level through the intersection, then chalk the four lines. Make sure your stick is level first (with level mark).

Some of us also use centerlines during hip roof framing (especially when two different pitches intersect). All jacks and purlins are given centerlines on their top faces (the faces in the roof surface). From there all lengths are measured from where these centerlines meet the offset line of your hip. Then through different scaled drawings and a calculator measurements can be found regarding jack and purlin lengths.

Regarding centre lines: I brought this subject up for these reasons:
1) because I came to this from an Asian route, centre lines
2) I worked from this to a mathematical easier route than many conventional solutions:ie using trig.
It's worked for me: why not for other craftsmen?
All my setting out is based on centres/trig.
My own solution to working with a japanese craftsman was to abandon our own ideas......

(...of course I mean all my framing setting-out with big and/or rough timbers.

My comment re the Japanese craftsman is really about mind-set, referred to elsewhere.)

Very interesting to hear how other people do things their own ways.

I suppose I'll have to say something about the mindset, though I don't really want to. I think there's some out there think it's
*******

I spent some time with a Japanese artist who my client engaged to keep some company, culture-wise, with the Japanese carpenter working on the project we made, since this man didn't speak English and I only knew a few words in Japanese.

A lot of what we talked about wasn't carpentry, some of it was
about poetry, film, paintings, architecture etc.

However, because this artist started off in his life as an architectural student, and then moved over into "art" he was well attuned to what we do.

He did some brilliant drawings for me which I have, and understood the building properly, which he tried to convey to me.

I realised, at a point, that I was bending my understanding into a different mode:it was quite painful, but positive.

I can only say you need to experience this to know it: it's not a religious experience, it's an opening into another mode of thought.

By the way, I've built a few boats! No money in it!