Visibility of point clouds and mapping of unknown environments

We present an algorithm for interpolating the visible portions of a point cloud that are sampled from opaque objects in the environment. Our algorithm projects point clouds onto a sphere centered at the observing locations and performs essentially non-oscillatory (ENO) interpolation to the projected data. Curvatures of the occluding objects can be approximated and used in many ways. We show how this algorithm can be incorporated into novel algorithms for mapping an unknown environment.