Parameters are accessed with C4DAtom::GetParameter()/ C4DAtom::SetParameter(). See Parameter IDs.
Parameter: Object
JOINT_OBJECTParameter: Connect Selection
JOINT_MOGRAPH_SELECTION_CONNECTParameter: Reference Axis
JOINT_REFERENCEParameter: Attachment
JOINT_APPLICATIONParameter: Index
JOINT_POINTParameter: Map
JOINT_POINT_SELECTIONParameter: Region Of Influence
JOINT_REGIONParameter: Shape Conservation
JOINT_POINT_SELECTION_SHAPE_CONSERVATIONParameter: Damping
JOINT_POINT_SELECTION_SHAPE_CONSERVATION_DAMPINGParameter: Pin to World
JOINT_PIN_TO_WORLDParameter: Selection
JOINT_MOGRAPH_SELECTION_PIN