Cubic Bezier Spline Construction

When Bezier Curves are used in computer graphics, it is often useful to create figures that consist of multiple curves connected together. By constructing Bezier Splines, we can create more complex shapes without resorting to higher-order curves. This example features a Bezier Spline composed of three Cubic Bezier Curves, along with the parametric construction. The individual curves are combined into a single smooth curve by enforcing that the lines connecting the shared and adjacent control points are parallel. As a result, however, not all of the control points can be draggable in this diagram (the dark gray ones aren't).