Open Access
December 2008 Visibility of point clouds and exploratory path planning in unkown environments
Y. Landa, R. Tsai
Commun. Math. Sci. 6(4): 881-913 (December 2008).


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.


Download Citation

Y. Landa. R. Tsai. "Visibility of point clouds and exploratory path planning in unkown environments." Commun. Math. Sci. 6 (4) 881 - 913, December 2008.


Published: December 2008
First available in Project Euclid: 18 December 2008

zbMATH: 1162.65318
MathSciNet: MR2511698

Primary: 65D18 , 68T40 , 68T45 , 68W05

Keywords: interpolation , path planning , point louds , visibility

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 4 • December 2008
Back to Top