Today, I did some research about Generalized Helicoid. I will try to draw Mobius Strip by this tech in OpenGL.
The Key Theory
- Create a profile curve
- Create a sweep curve
- Sweep the profile curve along the sweep curve, the swept area is the generated surface.
Some Try
First, I created a rect prfile curve.
Then, I try to create the whole Mobius Strip sweep curve by a group of bezier curves.
However, the result is not satisfying.
If I need to create a smooth Mobius Strip, I should create a more accuracy mobius bezier curve group.
The Final Solution
Finally, I just created a circle profile curve by bezier curve group, and rotate the profile curve during the sweep stage by interplating. Then I got a better Mobius Strip.
More Mobius Strips
By modifying profile curve rotating interplating function, I can get more interesting Mobius Strips.
