Linear-Size Meshes

Most modern meshing algorithms produce asymptoti- cally optimal size output. However, the size of the opti- mal mesh may not be bounded by any function of n. In this paper, we introduce well-paced point sets and prove that these will produce linear size outputs when meshed with any "size-optimal" meshing algorithm. This work generalizes all previous work on the linear cost of bal- ancing quadtrees. We also present an algorithm that uses well-paced points to produce a linear size Delau- nay mesh of a point set in Rd.