Analysis of three dimensional measurement data and CAD models

This thesis presents several new mathematical derivations and analysis procedures for extracting compact, meaningful information from the combination of unstructured point clouds and three-dimensional CAD models. This useful information includes optimal transformations of the data to align the cloud with the design model, the deviation of each point from the model, identification of which points go with which model faces and the optimal geometric parameters of model features. The new formulations and computational methods facilitate realization of faster and more accurate results in computational analysis of three-dimensional measurement data.; New methods for combining elements such as point to surface deviation calculations, point set transformations, multivariate non-linear minimizations, point to surface assignment and surface assignment trust regions are proposed. First order information for deviation computations and point set transformations are developed in a framework that facilitates analysis of three-dimensional coordinate measurement data. That is, information describing how the overall separation of the point cloud from the model changes with respect to both the point set transformation parameters and geometric parameters is provided. A trust region for point to surface assignments is introduced to further reduce the assignment burden.; The formulations and methods developed provide an extensible foundation for three dimensional metrology analyses.