SAIF considers abstract mathematical objects, like points, arcs, polygons, and tetrahedra to be members of a class of objects known as GeometricObject. An arbitrary collection of such geometric objects may also be considered a geometric object in its own right. SAIF provides an extensive type hierarchy of zero through four dimensional geometric objects. It includes zero, one, two and three dimensional vector structures, as well as two, three, and four dimensional grids with rectangular, hexagonal, or triangular structures.
Members of the class GeometricObject are specified ultimately through one or more points, each of which is given a one to four dimensional (x,y,z,t) coordinate. For example, a polygon may have a series of arcs defining its boundary, with each arc defined by a list of points. In three dimensional space the coordinate for one of the points might be (12.5, 3.9, 46.8). So long as the necessary geometric constructs are available, any shape may be specified through appropriate values of the coordinates. However, without additional information the coordinates are purely abstract in nature.