Models of the magnetospheric and magnetosheath magnetic fields are used to determine the relative orientations of these fields at the dayside magnetopause in order to locate potential merging sites. Areas on the magnetopause with different fractional antiparallel components are displayed by contour diagrams for a variety of interplanetary field orientations. For interplantary fields oriented perpendicular to the solar wind velocity the areas of nearly antiparall field agree with those obtained by Crooker using simplified representations for the magnetic field geometry. Here, the application of more realistic models gives the locations of areas where any antiparallel component occurs. Potential merging sites for interplanetary fields with radial components are also illustrated. The results suggest that the topology of the magnetosheath and magnetospheric fields provides antiparallel components over a substantial fraction of the magnetopause for most orientations.