## ABSTRACT

A curve is an infinitely large set of points. The points in a curve have the property that any point has two neighbors, except for a small number of points that have one neighbor. Some curves have no endpoints, either because they are infinite or they are closed. Different representations of curves have advantages and disadvantages. Different representations of curves have advantages and disadvantages. Some properties of curves are attributed to only a single location on the curve, while other properties require knowledge of the whole curve. For an intuition of the difference, imagine that the curve is a train track. Bézier curves are one of the most common representations for free-form curves in computer graphics. The curves are named for Pierre Bézier, one of the people who were instrumental in their development. Bézier curves have an interesting history where they were concurrently developed by several independent groups.