Getting precise measurement of a complex rod I'm trying to build a headrest for my Sayl office chair. For that, I'm designing a 3d-printed part that's going to fit on one of the existing rods of the chair.

Check out this picture:



How would you go about in getting the exact measurements of that white rod? I tried a caliper, and I'm able to get the width and depth, and I can just assume that the rod's profile is a perfect ellipse, which is probably a close estimate. But say that I want to get a more precise measurement. Is there any technique to do that?
You need to disasemble the part and measure it with special equipment, a caliper can help but only as reference since the part has an angled shape.

I recommend to use an optical comparator (base shadows) with this you can have X and Y data to calculate the angle and curves. If you want more precise measurements you can try an Optical Measurement Device (based camera), this also can give you Z but X and Y will help you a lot. Both equipments use a system called Quadra Chek many industries has at least one of this to assure his quality due meets all requirements for Ford GDT guides (geometric dimensional tolerances). no matter the manufacturer brand.

I´ve tried to measure with the phone or table application but is hardly to calibrate on each required dimension. I had to buy an optical comparator.