The precise measurement of free-form surfaces

We outline a new procedure for measuring free-form curves and surfaces using implicit polynomial equations. Such equations have long been known to offer certain advantages over the more traditional parametric methods. However; the lack of general procedures for obtaining implicit polynomial models of higher degree, which precisely represent arbitrary 3-D shapes, have prevented their general use in many practical applications, including rapid and precise metrology. Recent mathematical advances obtained at Brown University, experimentally verified using a state-of-the-art Chameleon coordinate measuring machine, have demonstrated potential advantages of implicit methods for modeling and measuring a variety of manufactured objects.