We describe and demonstrate an algorithm that takes as input anunorganized set of points fx1􀀀


􀀀 xng 􀀀 IR3 on or near an unknownmanifold M, and produces as output a simplicial surface thatapproximates M. Neither the topology, the presence of boundaries,nor the geometry of M are assumed to be known in advance — allare inferred automatically from the data. This problem naturallyarises in a variety of practical situations such as range scanningan object from multiple view points, recovery of biological shapesfrom two-dimensional slices, and interactive surface sketching.