Parametric Curves Curves and surfaces can have explicit, implicit, and parametric representations.
Parametric representations are the most common in computer graphics.
Reparameterization Parameterizations are in general not unique. Parametric Cubic Curves Cubic curves are commonly used in graphics because curves of lower order commonly have too little flexibility, while curves of higher order are usually considered unnecessarily complex and make it easy to introduce undesired wiggles. Each dimension is treated independently, so we can deal with curves in any number of dimensions. It is often convenient to think of the parameter t as being time in order to visualize some of the properties of the curve. A First Example Suppose we wish to define a cubic curve such that the user specifies the position of two endpoints and a midpoint, as well as the tangent at the midpoint.