ABSTRACT
This chapter discusses in detail the polynomial and parametric representation of curves on a plane and surface in space for geometric modeling. In contrast to the other books that usually start from the classical fundamental theories behind the equations, this chapter leads us directly to the method of finding equations or functions from a given set of data points. These techniques are used in the following chapters to represent the surfaces of plate and shell geometric and structural modeling. The main purpose of this chapter is to lead the reader to understand the concept of the nonuniform rational B-spline surface, which is the basis for the construction of plate and shell element formulations in the isogeometric approach. All the numerical examples are accompanied by their relevant and complete MATLAB® codes.
