Each governing board shall provide, as part of the zoning ordinance, for the processing of applications for variance permits. A variance is a modification of the bulk and placement requirements of the ordinance as to lot size, lot coverage, width, depth, front yard, side yard, rear yard, setbacks, parking space, height of buildings, or other ordinance provision affecting the size or shape of a structure or the placement of the structure upon lots, or the size of lots. A variance shall not be considered a right or special privilege, but may be granted to an applicant only upon a showing of undue hardship because of characteristics of the site and that the variance is not in conflict with the public interest. Prior to granting a variance, notice and an opportunity to be heard shall be provided to property owners adjoining the parcel under consideration and the manager or person in charge of the local airport if the variance could create an aviation hazard as defined in section 21-501, Idaho Code. Denial of a variance permit or approval of a variance permit with conditions unacceptable to the landowner may be subject to the regulatory taking analysis provided for by section 67-8003, Idaho Code, consistent with the requirements established thereby.