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We present a sketching interface for modeling shapes defined by large sets of points. Our system supports powerful modeling operations that are applied directly to the points defining the surface. These operations are based on sketch input to allow directly creating objects using simple strokes. Objects may be edited by either by boundary over-sketching, or by cutting, relief drawing on surfaces, merging and cloning. By combining these operations we can create complex shapes, including objects with sharp features. Our work uses the Multi-level Partition of Unity Implicits (MPU) technique to convert point clouds into implicit surfaces. Furthermore, we have devised a fast adaptive incremental polygonization algorithm which takes advantage of the MPU structure. This makes local re-polygonization possible and allows real-time modifications to large point sets since it avoids re-calculating the whole polygonal representation from scratch after each modification.