creating non overlaping triangles?

hello,

I have been tryin hard to create triangles from given vertices( that are taken from mouse input) but the thing is the triangles “shouldn’t have any of its edges overlapped”.
Can any1 help me…

regards
Sid

Please continue here :
http://www.opengl.org/discussion_boards/ubbthreads.php?ubb=showflat&Number=264944