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.

UAV任务常需要满足地面位置与飞行器位置之间的特定几何约束。本文描述了一种能够快速计算包围所有三维坐标的三维体积的系统的理论与实现；并将其称为可见性体积。该方法通过使用GPU加速的深度图计算和几何布尔运算来计算可见性体积。这种算法提供了感知和导航敏感性的解决方案，产生了一个满足任务路径和感知需求的三维坐标体积。

GPU加速的3D多边形可见性区块以促进感知和导航