Fast safe spline surrogates for large point clouds

To support real-time computation with large, possibly evolving point clouds and range data, we fit a trimmed uniform tensor-product spline function from one direction. The graph of this spline serves as a surrogate for the cloud, closely following the data safely in that, according to user choice, the data are always ´below´ or ´above´ when viewed in the fitting direction. That is, the point cloud is guaranteed to be completely covered from that direction and can be sandwiched between two matching spline surfaces if required. This yields both a data reduction since only the spline control points need to be further processed and defines a continuous surface in lieu of the isolated measurement points. For example, using a 20 times 20 spline, clouds of 300 K points are safely approximated in less than 1/2 second.