Three methods are described for transforming grids in bounded two- and three- dimensional physical domains into a uniform grid in a rectangular computational domain. The methods are based on mathematical interpolation functions and do not require the solution of differential equations or the use of complex variables. They are simply referred to as algebraic methods and are called transfinite interpolation, the multisurface method, and the two-boundary technique. The primary advantage of the methods is that they provide explicit control of physical grid shape and physical grid spacing. Secondly, they require relatively few computations. Consequently, the application of inter-active computer graphics in conjunction with the methods is advocated for rapid generation of grids. The basic mathematical structure of each method is described, and particular attention is given to surface representation, parameter variable generation, and control function generation. Physical boundary topology and grid derivative requirements are presented.