I have wondered about this since I began sewing the panels together.
Say I have a curve. Shouldn't I be able to measure that curve and then use math to compute how much pleat I need?
Using a French curve or something else?
Furniture is not that precise. Especially used furniture.
Ah, math geek here. In fact, I'm doing a presentation on compass and straightedge constructions at the woodworker's club tomorrow. I can probably help you, but I don't quite understand your problem.
But like above, you don't often need to be that precise.
And there's an article I did a while back at Carr's Corner.
http://www.cincinnatiwoodworkingclub.org/LinkClick.aspx?fileticket=_wjx0Ex24H0%3d&tabid=105&portalid=0&mid=481
I'm starting to understand. I just thought if there was a way to know how much of an angle you could then understand how much of a pleat, angle etc that you need.
But I just went and laid out the fabric and played with it until I got pretty close.
When and if you build a piece of furniture from scratch and do it very precisely then you could use geometry to figure most everything. But the variables in furniture are to much to really rely of math. Even filling is not precise. Check it sometime. Measure a piece of foam in several places sometime. Sometimes it is OK to use but more often it is just better to fit a pattern to the piece.
I follow a couple different shops on instagram that make frames all the way to upholster.
I wonder what sort of measuring they use? Basically the designer comes to them and says, make me a custom banquet. Here are the dimensions. The results are incredible.
There is a local place that you can learn CNC machining for a nominal fee, but I don't really have the desire or energy for all that. The shop I consigned (and now sold) one of my pieces does all kinds of woodworking. Maybe down the road I could use him as a source to build custom stuff from the ground up.
I just look at like the back legs and armrests and realize that someone put in some good time figuring out just the right arc to make something comfortable. Barrel chairs come to mind.
Building onezes is what I do on occasion. Someone has a design idea, they may have a space to fill with a sofa or sectional and it is unique. I take the build on and from there I use my own knowledge to build it from the ground up. No CNC No CAD. It is just doing it. My furniture without trying to brag should be around for a long time. And I do use math at some points but I figured you were talking about ReUpholstery and using math for figuring curves. That is totally different ball game.
I cut my teeth in the factories. They have the luxury of fitting and patterning. As many time as it takes. They have full time workers and that's all they do. And they have plenty of fabric to mess around with.
Us down in the trenches don't have that luxury. We need to get it right the first time every time. If we're lucky the piece is a virgin and we can use the original pattern for all of our cuts. More often than not we have to deal with furniture that was recovered by someone who just didn't care. In this case your method, "But I just went and laid out the fabric and played with it until I got pretty close" is the right method. In this case padding and a regulator is your best friend.