Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See page_maxonapi_getting_started_foundations_cinema_parameters.
Parameter: Curve
BASEGROUP_SUBFACTOR_CURVE_SLIDER
Parameter: Surface U
BASEGROUP_SUBFACTOR_SURFACE_U_SLIDER
Parameter: Surface V
BASEGROUP_SUBFACTOR_SURFACE_V_SLIDER
Parameter: Apply
BASEGROUP_SUBFACTOR_BUTTON
Parameter: Type
BASEGROUP_SELECT_TYPE
Parameter: Subtype
BASEGROUP_SELECT_SUBTYPE
Parameter: Deselect
BASEGROUP_DESELECT_BUTTON
Parameter: Select Additionally
BASEGROUP_SELECT_BUTTON
Parameter: Select Only
BASEGROUP_SELECTONLY_BUTTON
Parameter: Convert to Polygons
BASEGROUP_CONVERT_TOPOLYS
Parameter: Convert to Arranged Polygons
BASEGROUP_CONVERT_TOGROUPS
Parameter: Convert to one Object
BASEGROUP_CONVERT_TOONE