The book says triangulation algorithm takes quadratic time in worst case. but why? The book says - take leftmost vertex and try to connect its neighbors. If you succeed - you get triangle and polygon
and therefore as the consequence you get quadratic time algo. But why?
I made this procedure and for a polygon of 7 vertices I performed 4 divisions...
In general I do not see how quadratic time is possible... cannot come up with an instance.
Your diagrams are of convex polygons. The algorithm is for a polygon which may be decidedly concave, with hundreds of edges crossing the $uw$ line.