We use projective clustering to design and implement a fast surface reconstruction algorithm for point clouds that also works well for sharp edges and corners. Our method relies on two new approximation algorithms developed and implemented for the first time, namely, fast projective clustering and parallel dynamic nearest neighbor searching based on shifted quad-trees. Also, our implementation is one of the first for this problem with any kind of guarantees (for a very restricted type of manifolds). Our algorithm is easy to parallelize and is external-memory friendly. Finally we provide a method for combining increasingly more complex fitters in a cascade which allows planar regions of the point cloud to be quickly processed while spending more time on high curvature areas including sharp features. In the domain of normal estimation, our method is faster and more accurate than previous systems on a large number of point clouds.