Many siting and other terrain analysis problems require the determination of the visibility from large numbers of observer locations over their surrounding terrain. The computational costs of existing visibility algorithms often require serious compromises on the fidelity, accuracy, or scope of analysis in real world settings. A highly accurate viewshed determination Algorithm, R2, is presented that executes in O(R2) time (where R is proportional to the number of points along the radius of the potential viewshed) and does not suffer from numerical problems, complex special cases, or high constant factors. Since the size of the output in viewshed determination is also O(R2), that time complexity of R2 is within a constant factor of optimality. The R2 algorithm is used to verify a fast and effective visibility index estimation procedure, WeightF. WeightF has time complexity O(R) and produces visibility index estimates with a correlated variation to R2 in excess of 0.9 on a variety of terrain datasets and problem settings. These visibility indexes can be used to select points with best aggregate visibility in an area. On real terrain, analysis using WeightF shows that points with significantly above average visibility index values are only a very small number of the total observer points. This property and the fast execution time of WeightF makes it useful for identifying high visibility points for use in siting algorithms, and to produce a viewable visibility index image that can display a large amount of visibility information in an intuitive fashion.