Described is a technology by which a user interacts with a surface representative of a point cloud data to correct for imperfect scan data. The surface is reconstructed based on the interaction. Real time viewing of the image is facilitated by parallel surface reconstruction. For example, the user may draw strokes to reduce topological ambiguities in poorly-sampled areas. An algorithm automatically adds new oriented sample points to the original point cloud based on the user interaction. Then a new isosurface is generated for the augmented point cloud. The user also may specify the geometry of missing areas of the surface. The user copies a set of points from another point cloud, and places the points around the target area. A new isosurface is then generated.