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.