# The Roller Coaster Effect

Imagine that you are sitting on a roller coaster box following the track. The track can be considered as a curve. Thus, the box moves in the direction of the tangent vector at the current position, the binormal vector points where your head points, and the normal vector points to the turning direction. More precisely, if you have a left (resp., right) turn, the normal vector points to the left (resp., right). As your box follows the track, you are sitting at the tracing point of a curve and have a ``local'' view of the world. This system can provide you with such vivid effect.

Before activate this effect, make sure that Tangent, Binormal & Normal has been activated. If you want to see the curvature sphere, you can also activate Curvature Sphere. Then, click on Roller Coaster to activate the roller coaster effect.

In the following, we still use file space-curve-1.dat as our working example. Click here to download a copy. After clicking on Roller Coaster, the Roller Coaster Window appears. It shows the curve, the tracing point, and the moving triad. The eye position can be modified to obtain a better view. We shall return to this later on. The left figure below shows the tracing point at the beginning of the curve. The roller coaster window also depicts the same. We can actually see control point 0 behind the tracing point.

Let us move the tracing point further entering a sharp turn. Now we can see control point 3 in front of the tracing point; but our position is somewhat up-side-down because the binormal vector (the green one) points downward. However, since the binormal vector points to where our head is pointing, even though the curve goes up, the roller coaster window shows a down turn. This matches our roller coaster experience.

Let us move forward to a place just before entering an inflection point as mentioned in the Curvature Sphere page. From the roller coaster window, it is clear that the curve is about to change its turning direction.

The following figures show the result after passing the inflection point. Please notice that the curvature sphere changes sides as well.

It may be difficult for you to extrapolate your roller coaster experience on a screen. But, going around the curve a few more times and, if it is necessary, do some scene rotations, you will be able to see and learn more about the effect of moving triad and curvature, and gain some visual experience of how curve turns!