Communications in Mathematical Sciences

Volume 6 (2008)

Number 4

Visibility of point clouds and exploratory path planning in unkown environments

Pages: 881 – 913



Y. Landa

R. Tsai


We present an algorithm for interpolating the visible portions of a point loud that are sampled from opaque objects in the environment. Our algorithm projects point clouds onto a sphere entered at the observing location and performs essentially non-oscillatory (ENO) interpolation of the projected data. Curvatures of the occluding objects can be approximated and used in many ways. We demonstrate how our visibility formulation can be incorporated into novel algorithms for mapping unknown environments with single or multiple observers, and target finding problems. A convergence proof is provided indicating suitability of our algorithm for some canonical types of environments. Various postprocessing optimization techniques are considered to obtain a more uniform exposure of the region along the path.


Visibility, interpolation, point louds, path planning

2010 Mathematics Subject Classification

65D18, 68T40, 68T45, 68W05

Published 1 January 2008