1. A texture mapping method for applying a texel value to a pixel on a computer screen comprising the steps of: (a) converting a screen pixel address to a fractional coordinate in a texture map, said fractional coordinate including an integer portion and a fractional portion and said texture map including integer texel values; (b) performing a four-texel averaging texture mapping technique if said fractional coordinate is outside a first predetermined range from all integer texel values in said texture map; (c) performing a two-texel averaging texture mapping technique if said fractional coordinate is within a second predetermined range of two texels in said texture map and outside a third predetermined range from all other texels; and (d) selecting a nearest texel to said fractional coordinate if said fractional coordinate is within a fourth predetermined range of said nearest texel.