Question

I am a beginner in CAD development & want to know some things about OpenGL.
My main objective is to represent conics, cycloid, epicycloid, hypocycloid, involutes, etc
Can i directly represent them using some trigonometry, or do i need to convert these curves into B-Spline?
Actually i am currently developing the kernel & want to develop the kernel so that i cant display the above mentioned curves.(there is no use in supporting these curves in kernel if i cant graphically represent them!)
I dont know much about OpenGL, so please pardon me if my question is really stupid!
I tried searching over here but could not find anything useful.

Answer 1

OpenGL can directly render Bezier curves and surfaces using evaluators and even NURBS using the GLU API. See the OpenGL Programming Guide for more information. So you could transform those curves and surfaces into this form.

But I highly recommend you not to use these features, as they are deprecated (dropped from the core of newer OpenGL versions) and nowadays likely to be implemented in software and not in hardware.

Instead you should rather implement your own evaluation routines for such curves and surfaces, that evaluate the corresponding equations at a specified sampling rate and generate a simple vertex array (and maybe and index array). This way you stay future-ready as these can be rendered as standard line strips or triangular meshes using VBOs (the only way to render something in modern OpenGL).

And you even stay API agnostic, as a general vertex array can also be rendered using Direct3D or whatever. So this way you don’t pollute your CAD kernel with draw calls. All it needs is a function to transform parametric curves and surfaces into arrays of vertices (and maybe indices) and the client/user of the kernel is responsible for drawing these with whatever API he likes.