Abstract 
The power crust is a construction which takes a sample of points from the surface of a threedimensional object and produces a surface mesh and an approximate medial axis. The approach is to first approximate the medial axis transform (MAT) of the object. We then use an inverse transform to produce the surface representation
from the MAT. This idea leads to a simple algorithm with theoretical guarantees comparable to those of other surface reconstruction and medial axis approximation algorithms. It also comes with a guarantee that does
not depend in any way on the quality of the input point sample. Any input gives an output surface which is the ‘watertight’ boundary of a threedimensional polyhedral solid: the solid described by the approximate MAT. This unconditional guarantee makes the algorithm
quite robust and eliminates the polygonalization, holefilling or manifold extraction postprocessing steps required in previous surface reconstruction algorithms.
In this paper, we use the theory to develop a power crust implementation which is indeed robust for realistic and even difficult samples. We describe the careful design of a key subroutine which labels parts of the MAT as inside or outside of the object, easy in
theory but nontrivial in practice. We find that we can handle areas in which the input sampling is scanty or noisy by simply discarding the unreliable parts of the MAT approximation. We demonstrate good empirical results on inputs including models with sharp corners, sparse and unevenly distributed point samples, holes, and
noise, both natural and synthetic. We also demonstrate some simple extensions: intentionally leaving holes where there is no data, producing approximate offset surfaces, and simplifying the approximate MAT in a principled way to preserve stable features.
