TABLE OF CONTENTS Surface models are a special type of solid models and are widely used in automotive, aerospace, and mechtronics industries. They are normally created by surface profiles (surface profile curves). According to the usage of surface profiles in engineering practice, various surface models are created. In design modeling, surface profiles are based on: (1) experiments, (2) mathematical calculations, and (3) visual observations. When the creation of the surface profile is based on experimental results, i.e. aircraft wing and automotive body profiles, the given conditions are often in the forms of data sets. Because of the nature of experiments and visualization, these data may exhibit degrees of error and "noise." The influences of these errors on modeling need to be minimized. The tactic is to derive the profile curves that represent the general trend of the data. Thus, whether surface profile curves intersect each and every experimental data point is less important than following the intrinsic pattern of the point set as a group. An approach to this kind of surface profile is called least-square regression.
When the creation of surface profiles is based on mathematical equations, such as for gear tooth profiles, the profiles are already in the form of theoretical curves, or they are digitized into discrete data sets. There are generally no errors (except mathematical truncation errors). In other words, the absolute errors of these curves/data are zero, and are negligible in comparison to the previous case. In this case, the proper approach is to fit...
