How a can know details about parabolic grid generation while I haven't any equation?

Question

How a can know details about parabolic grid generation?

I am working on a project and need urgent help and more details about parabolic grid generation

i haven't any equation about that

and I need it for my final project to receive B.Sc degree

ty

Answer 1

For cylindrical co-ordinates your equation is

z = ar^2

A 2-dimensional wireframe can be generated using the equation(s)

x = rcosθ

z = a(rcosθ)^2

Step θ from 0 to 90 to generate a family of parabolas.  Three equal steps should be more than adequate.

The z-coordinate steps can be drawn as horizontal lines using the outer z = ax^2 for boundaries.

Transforming to "3-d" requires translation and rotation exercises which can become quite interesting, and depend on whether you want an isometric view or perspective view.

Cartesian coordinates require two orthoganal families of parabolae.