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We present Delaunay refinement algorithms for estimating local feature on the 0-skeleton of a 2D piecewise linear complex (2D) and on the 1-skeleton of a 3D PLC. These algorithms are designed to eliminate the need for a local feature size oracle in quality mesh generation of domains containing acute input angles. In keeping with Ruppert's algorithm, encroachment in these algorithms can be determined through only local information in the current Delaunay triangulation. The algorithms are simpledoi:10.1142/s0218195911003780 fatcat:lrorbfnsijb2zjx35w3duu4jqq