Sculptured surfaces are used in several applications. The manufacture of sculptured surfaces is carried out using numerically-controlled machines, and automatically-generated tool paths. This process is affected by several error sources, which result in geometric deviation between the machined surface, and the design intent. Coordinate measuring machines, CMMs, are used to assess the quality of the machined surfaces.

A new perspective on the geometric inspection of sculptured surfaces is presented in this thesis. This perspective is based on three concepts:​ 1) construction of a substitute geometry for the physical object, 2) scanning the model surface along its isoparametric curves, and 3) using surface complexity measures to calculate the scanning curve locations. This work is twofolds:​ 1) a CAD-based module for sculptured surface sampling, and 2) a framework for CMM measurement analysis.

The CAD-based sampling module is used to generate a sampling plan which ensures a substitute geometry that lies within a satisfactory tolerance band around the CAD model. New methodologies for sampling sculptured surfaces are presented in this module which use the surface complexity measures to calculate the locations for the sample curves. These surface complexity measures are:​ the surface curvature, the accuracy of the substitute geometry, and the shape topology, namely, the model trimmed regions. A hybrid approach for sampling a single trimmed surface is developed, and used as a basis for sampling more generalized models. The substitute geometry is constructed using surface skinning of cross section curves. The CAD-based sampling module is implemented, and demonstrated in this thesis.

The framework for the analysis of CMM measurement is composed of three modules:​ 1) a module for automatic generation of the CMM probe scanning path(s) using the output of the sampling module, 2) a two-step CMM data localization module to align the CMM measurement with the CAD model, and 3) a new method to construct the substitute geometry for the physical object using the CMM measurement data. This work is demonstrated using two case studies.

This thesis is divided into five chapters. Chapter One presents the background, and motivation for this work. Chapter Two includes a survey of the previous literature. The CAD-based sampling module is presented in chapter Three. Chapter Four includes the framework for the implementation of the sampling plan, and the analysis of the CMM data. The conclusions of this work are included in Chapter Five.