1. A computer-implemented process for constructing implicit surfaces from point clouds, comprising using a computing device to perform process actions for: receiving an oriented point cloud, each point in the cloud having a normal direction; for each point in the cloud, identifying a set of closest neighboring points within a radius around each point; defining a set of oriented disks, such that for each point in the cloud, a corresponding one of the oriented disks is delimited by the position, normal and radius of the corresponding point; for each node in a volumetric grid, identifying a corresponding set of neighboring oriented disks as any oriented disk that is closer to the node than the radius of that oriented disk; for each node having a set of neighboring oriented disks, computing a signed distance as a weighted average of a signed distance to each neighboring oriented disk; and delimiting an implicit surface corresponding to the oriented point cloud by using the signed distances of each node to construct a signed distance function on the volumetric grid.