The input encoding algorithm of the polarization-encoded optical shadow-casting (POSC) scheme is modified to include the design of trinary combinational logic units. For illustration, the modified algorithm is deterministically employed in the design of trinary adders. Two design approaches are examined for identifying the constraints and flexibilities that are encountered depending on whether the zero-output conditions are considered. The more complicated POSC overlap equations are handled by incorporating LED source encoding to the input encoding process.