This paper aims to extend the investigation of the fundamentals of isovists grids to encompass a wider range of possible grids and hence determine whether there is an optimal grid type and, if so, what would it be. We initially discuss the problem of the selection of grid-spacing (or the interval between isovist generating locations) and will then show, with worked examples, how both the grid size, the orientation of the grid and the selection of its origin can produce variance in any resultant space syntax, i.e., relational, measures, when applied to real world spatial systems. We then go on to show how orthogonal grids can exhibit particular problems when the building or urban area contains curved walls, since the orthogonal grid often does not conform well to arbitrary curves. Another problem we discuss is that of small openings or narrow corridor-like spaces (often missed by larger grids) where there is a mis-match between the grid-spacing and aperture size. In the second half of this paper, we will explore alternative options to the cartesian, orthogonal grid, suggesting a number of alternative grid-types and then introduce a new form of visibility graph analysis that we are terming Restricted Randomised Visibility Graph Analysis, or R-VGA. By applying R-VGA analysis to some test cases, we demonstrate how this method of analysis has considerable advantages over the more commonly used, square-based grid of VGA analysis. Finally, we will present a new, proposed taxonomy, as an entire family of VGA and VGA-derived analyses.