I'm working with OpenGL ES 2.0 on iOS. Not using GLKit or an engine. I've tried several approaches but they seem flawed from the start because, unfortunately, my knowledge and experience with trigonometry is quite limited. Here's the problem I'm facing.

I have two vertices that represent points on a sphere. I'd like to draw an arc in between those points. This arc would have dimension and as it becomes higher, it widens. Basically, it is at it's thinnest at each coordinate and thickest at the tallest point of the arc.

I'm not expecting any specific code, just a good discussion on how you would approach this problem. I'd talk about this with other developers, however, none around me know OpenGL ES or have an understanding of 3D concepts/programming. Having a lone dialogue with myself the past few months has been a bit maddening and I've finally turned to seeking some help. Let me know if I can provide any more information. Thank you for taking the time to read this post.