triangle -S

Specifies the maximum number of Steiner points (vertices that are not in the input, but are added to meet the constraints on minimum angle and maximum area). The default is to allow an unlimited number. If you specify this switch with no number after it, the limit is set to zero. Triangle always adds vertices at segment intersections, even if it needs to use more vertices than the limit you set. When Triangle inserts segments by splitting (-s), it always adds enough vertices to ensure that all the segments of the PLSG are recovered, ignoring the limit if necessary.