The city engineer, in cooperation with the street department and the police department, is authorized to mark off such individual parking spaces as needed in the opinion of the city engineer on public streets and other parking areas under the control of the city, the parking spaces to be suitably designated by lines or other markers. At each space so designated or marked off, it is an infraction to park any vehicle in such a way that such vehicle shall not be entirely within the limits of the space so designated and marked off.