The city shall have the power to designate and establish controlled-access facilities, and may design, construct, maintain, improve, alter, and vacate such facilities and may by ordinance regulate, restrict, or prohibit access to such facilities so as best to serve the traffic for which such facilities are intended. The city may provide for the elimination of intersections at grade with existing roads, streets, highways, or alleys if it finds the public interest shall be served thereby. An existing road, street, alley, or other traffic facility may be included within such facilities or such facilities may include new or additional roads, streets, highways, or the like. In order to carry out the purposes of this section, in addition to any other powers it may have, the city may acquire in public or private property such rights of access as are deemed necessary, including but not necessarily limited to air, light, view, ingress, and egress. Such acquisitions may be by gift, devise, purchase, agreement, adverse possession, prescription, condemnation, or otherwise as provided by law and may be in fee simple absolute or in any lesser estate or interest. The city may make provision to mitigate damages caused by such acquisitions, terms and conditions regarding the abandonment or reverter of such acquisitions, and any other provisions or conditions that are desirable for the needs of the city and the general welfare of the public. The city is further authorized to designate, establish, design and construct, maintain, vacate, alter, improve, and regulate frontage roads within the boundaries of any present or hereafter acquired right-of-way and exercise the same powers over such frontage roads as is exercised over controlled-access facilities. Such frontage roads may be connected to or separated from the controlled-access facilities at such places as the city shall determine to be consistent with public safety. Upon the construction of any frontage road, any right of access between the controlled-access facility and property abutting or adjacent to such frontage roads shall terminate and ingress and egress shall be provided to the frontage road at such places as will afford reasonable and safe connections. If the construction or reconstruction of any controlled-access facility results in the abutment of property on such facility that did not theretofore have direct egress from or ingress to it, no rights of direct access shall accrue because of such abutment, but the city may prescribe and define the location of the privilege of access, if any, of properties that then, but not theretofore, abut on such facility.