The complete algorithm and the implementation are described in:
1. Nina Amenta, Sunghee Choi and Ravi Kolluri
The power crust (pdf)
Sixth ACM Symposium on Solid Modeling and Applications 2001, pages 249-260.
All of the theory is in:2. Nina Amenta, Sunghee Choi and Ravi Kolluri.
The power crust, unions of balls, and the medial axis transform (ps.gz) (pdf)
Computational Geometry: Theory and Applications, 2001, 19:(2-3), pages 127-153, (special issue on surface reconstruction).
Some of this appeared earlier in a conferece:3. Nina Amenta and Ravi Kolluri.
Accurate and efficient unions of balls (ps.gz)
ACM Symposium on Computational Geometry, 2000, pages 119-128.
Some key lemmas came from a previous paper:4. Nina Amenta and Marshall Bern
Surface reconstruction by Voronoi filtering (ps.gz)
Discrete and Computational Geometry, 22, pages 481-504, (1999).
An earlier version appeared in the
14th Annual ACM Symposium on Computational Geometry, pages 39-48, (1998).