The Precise Measurement of Free-Form Surfaces1

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.