How to break up 2d art into triangles using OpenGL

Question

I have 2d character art that will be mapped to a Box2d skeleton. The character's arm, for example, may be 2 physics rectangles connected with a joint at the elbow. Each rectangle will have its own corresponding art sprite. The art for the lower arm will not be completely rectangular. It may be a rectangular png source, but there will be a lot of negative space where the arm isn't necessarily drawn.

My question is what is the best way to break up the 2d art into triangles? Should I treat all flat sprites as a simple rectangle made up of 2 triangles, leaving a lot of alpha space? Or is it best to break up the shape into multiple triangles and try to match the actual shape (possibly with a triangle fan)? What might be some of the advantages/disadvantages of each approach? I will be updating the textures as various things happen to the character.

Here's an illustration of what I'm talking about:

(the red square is the physics shape, and the blue lines are possible triangle configurations)

Answer 1

Less geometry is usually better for performance (3rd from the left).

The "exact" triangulation (4th from the left) would be useful for high-fidelity collision-detection (lasers reflecting off a shiny asteroid?).

Be careful with frequent texture updates. glTexSubImage2d() is the way to go.

If your GL implementation supports it you can do asynchronous uploads using PBOs.