FAT TRIANGLES DETERMINE LINEARLY MANY HOLES

The authors show that for every fixed delta > 0 the following holds: I f F is a union of n triangles, all of whose angles are at least delta, then the complement of F has O(n) connected components and the bounda ry of F consists of O(n log n) straight segments (where the constants of proportionality depend on delta). This latter complexity becomes li near if all triangles are of roughly the same size or if they are all infinite wedges.