  UAV missions often require specific geometric constraints to be satisfied
between ground locations and the vehicle location. Such requirements are
typical for contexts where line-of-sight must be maintained between the vehicle
location and the ground control location and are also important in surveillance
applications where the UAV wishes to be able to sense, e.g., with a camera
sensor, a specific region within a complex geometric environment. This problem
is further complicated when the ground location is generalized to a convex 2D
polygonal region. This article describes the theory and implementation of a
system which can quickly calculate the 3D volume that encloses all 3D
coordinates from which a 2D convex planar region can be entirely viewed;
referred to as a visibility volume. The proposed approach computes visibility
volumes using a combination of depth map computation using GPU-acceleration and
geometric boolean operations. Solutions to this problem require complex 3D
geometric analysis techniques that must execute using arbitrary precision
arithmetic on a collection of discontinuous and non-analytic surfaces.
Post-processing steps incorporate navigational constraints to further restrict
the enclosed coordinates to include both visibility and navigation constraints.
Integration of sensing visibility constraints with navigational constraints
yields a range of navigable space where a vehicle will satisfy both perceptual
sensing and navigational needs of the mission. This algorithm then provides a
synergistic perception and navigation sensitive solution yielding a volume of
coordinates in 3D that satisfy both the mission path and sensing needs.
