We recently proposed a new and efficient next-best-view algorithm for 3D reconstruction of indoor scenes using active range sensing. We overcome the computation difficulty of evaluating the view metric function by using an adaptive hierarchical approach to exploit the various spatial coherences inherent in the acquisition constraints and quality requirements. The impressive speedups have allowed our NBV algorithm to become the first to be able to exhaustively evaluate a large set of 3D views with respect to a large set of surfaces, and to include many practical acquisition constraints and quality requirements. The success of the algorithm is greatly dependent on the implementation efficiency of the constraint and quality evaluations. In this paper, we describe the algorithmic details of the hierarchical view evaluation, and present efficient algorithms that evaluate sensing constraints and surface sampling densities between a view volume and a surface patch instead of simply between a single view point and a surface point. The presentation here provides examples for the design of efficient algorithms for new sensing constraints.