Most facies maps are designed to show the approach of the stratigraphic section toward one or another of the end members used in the map design. In certain applications of facies maps it is observed that some optimum combination of end members is associated with particular environmental, tectonic, or other conditions, some of which may have practical significance in oil occurrence. A "distance function" based on transformation of trilinear to Cartesian coordinates permits selection of any point within a facies triangle as a center of optimum combination of end members, with contour lines indicating the "facies distance" of any other section from the selected point. The distance function provides a single system of contours which serve as an evaluation map for more detailed studies of lithologic variations. The relation of the distance function to other contouring systems in facies map design is developed by several illustrations.