I have tried to explain this project in as few words as possible. Please read the description below and message me if you need more details or clarification etc.
I will give you an equation of a closed curve. Step 1: You will produce/plot that curve in Matlab or MathCAD or anyother software in x-y plane. Step 2: You will drag that curve in Z-direction while revolving it at the same time. (Step 2 is called sweep and twist along a path in SolidWorks). Step 3: (This is where the real work starts) You will have to find out the gradient of the surface (which we created in Step 2) in multiple directions (not necessarily along x,y or z direction). Based on the gradients, we will modify our equation and do the whole process again. It will probably involve programming and doing iterations etc. I am not sure which branch of calculus will be most relevant to it, therefore I am just uploading it in Maths and Mechanical Engineering section.
Waiting to hear from Mathematicians.