The use of bounding structures in the form of orthogonal polygons (also known as rectilinear polygons) with a varying number of vertices in contrast with a minimum bounding rectangle (an orthogonal polygon with just 4 vertices in two dimensions) as an object approximation method is presented. Orthogonal polygons can be used to improve the performance of the refine step in the filter-refine query processing strategy employed in spatial databases. The orthogonal polygons are represented using the vertex representation implemented as a vertex list. The advantage of the vertex representation implemented as a vertex list is that it can be used to represent orthogonal polygons in arbitrary dimensions using just their vertices. This is in contrast to conventional methods such as the chain code which only work in two dimensions and cannot be extended to deal with higher dimensional data. Algorithms are given for varying the number of vertices used to represent the objects. It is shown that the use of non-trivial orthogonal polygons (i.e., with more than four vertices) is of benefit when a spatial index is used in the filter step for processing spatial queries such as point-in-object and windowing. If no spatial index is used, then all objects must be examined. In this case, many of the objects are small thereby not benefiting from the variation in the number of vertices that they have as the simple bounding box is adequate.