Mathematical model of the curve vs curve parameters in blender

Good day!

I have a little bit unusual tasks. It is not about how to do something in Blender and / or why something is not working. I need to match the curve in Blender with the mathematical description of the curve. Ie to understand what are the formula for each type of curve. Eg, it is clear that when I change the Order in the field of Active Spline (Object Data) I change the order of the spline. But what other options in the Object Data are key? What parametrs does it change in formulas when I change it in Blender? Are formulas changed, if I change the type of interpolation (Tilt / Radius)? What algorithm is used in Blender to avoid loops in the construction curves within splines?

I would be glad for any links related to topic as well as for straight answers. I apologize if this issue was raised somewhere before - just happy to read any of previous discussions.

what do u want to do with the math model ?

in any case math model is inside bl code

in Bl curves re made with Nurbs spline
but can be converted to Bezier or simple curve.
you can also make scripts using curves

happy bl

The main task is to pass programmers implementation description of the curve, made in Blender. I’m not able to read bl code, so that’s why I wonder if there are any documentation or articles written by anyone which can help to match math parametrs with blender one.

but can u use scripting to get the values and transfer these to whatever other math model you have ?

you can always go to IRC blendercoder and ask questions to developer and see if some one can help
but this is rather heavy from a math point of view

I know that curves use the B spline Nurb type
but have never look at the C model for it only with script

or ask questions on

let us know if you find some info
it is an interesting subject !

happy bl