Introducing the Curve Application

Joining Bezier Curves

Joining multiple Bezier curves is very easy because the curve always begins and ends at the end control points. You can achieve C continuity by using the same control point for both the end of one curve and the start of the next . Depending on your implementation, you may actually use two points that have the same location, but the bottom line is that collocated control points at the end of the curve ensure that the curve itself is C continuous.

You can join two curves with C ¹ continuity almost as easily. The slope at the endpoint of a Bezier curve is equal to the slope of the last line segment in the control polygon. Therefore, curves can maintain C ¹ continuity if the last and first line segments are collinear. For the most part, these first two levels of continuity are all that you will need to worry about when you want to smoothly join two curves. Figure 3.7 shows examples of curves with different levels of continuity. The upper curves are joined, but there is a kink at the join. The lower curves are joined with matching slopes, producing a smooth transition.

Figure 3.7: Joining Bezier curves.