TABLE OF CONTENTS While B zier curves are a powerful tool, they are not very convenient when it comes to modeling complex curves. For these, composite curves are typically used also known as splines. A composite curve is composed of pieces, and thus the term piecewise curve is also used.
In this chapter, we will examine B zier curves that are linked together, and we will outline the conditions for various kinds of smoothness at the transition from one curve segment to the next.
Local and global parameters are discussed in Section 4.7. Composite B zier curves provide an application of these concepts. As illustrated in Sketch 81, each B zier curve is defined over an interval. The intervals are defined by two successive knots [ u i, u i+1]. All knots are referred to as the knot sequence. We will use the notation ? i = u i+1 ? u i. Piecewise curves defined over a common knot sequence are called spline curves.
When examining a property of a spline curve s, we will refer to the global parameter u within the knot vector. When examining a property of the i th B zier curve s i, defined over [ u i, u i+1], we will refer to its local parameter t ? [0, 1]. Recall from Section 2.1 that
We will also use the term junction...
