On the Non-Termination of Ruppert's Algorithm

A planar straight-line graph which causes the non-termination Ruppert’s algorithm for a minimum angle threshold larger than about 29.5 degrees is given. The minimum input angle of this example is about 74.5 degrees meaning that failure is not due to small input angles. Additionally, a similar non-acute input is given for which Chew’s second algorithm does not terminate for a minimum angle threshold larger than about 30.7 degrees.