(1) Except as otherwise provided in this section, any vehicle stopped or parked upon a two-way roadway where parking is permitted shall be so stopped or parked with the right-hand wheels parallel to and within twelve inches of the right-hand curb or edge of such roadway. No vehicle shall be parked upon a roadway when there is a shoulder adjacent to the roadway which is available for parking.
(2) Except when otherwise provided by a local authority, every vehicle stopped or parked upon a one-way roadway shall be so stopped or parked parallel to the curb or edge of such roadway, in the direction of authorized traffic movement, with its right-hand wheels within twelve inches of the right-hand curb or edge of the roadway or its left-hand wheels within twelve inches of the left-hand curb or edge of such roadway.
(3) A local authority may permit angle or center parking on any roadway, except that angle or center parking shall not be permitted on any federal-aid highway or on any part of the state highway system unless the Director-State Engineer has determined that such roadway is of sufficient width to permit angle or center parking without interfering with the free movement of traffic.
(4) The Department of Transportation or a local authority may prohibit or restrict stopping, standing, or parking on highways under its respective jurisdiction outside the corporate limits of any city or village and erect and maintain proper and adequate signs thereon. No person shall stop, stand, or park any vehicle in violation of the restrictions stated on such signs.