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!

There are two buttons for choosing the up direction. It is either based on
the binormal vector or the negative normal vector. Normally, since
the binormal vector points to the head direction, the up direction, by
default, is the binormal direction. For interesting effect, one can choose
the negative direction so that you would get an interesting viewing effect.
Click on button **Binormal**
(*resp.*, **Negative Normal**) to
use the binormal (*resp.*, the negative normal) direction as the up
direction. The left figure blow is the normal case, the up direction being
the binormal direction, while the right one uses the negative normal direction
as the up direction.

There are three sliders for modifying the eye position. Please note that
**wherever the position, the passenger always look at
the tracing point.** In the following, we use the binormal vector
as the up direction. We can move closer to or farther away from the
tracing point with the **Near/Far**
slider. The default value is 0.2. The left figure below shows moving
closer to the tracing point (0.25), while the right one shows moving away
from the tracing point (1.0).

We can also use the **Left/Right** slider to
move to the left or right. The default value is that
the view position is slightly shift to the right side at a value of 0.1.
If we move to the left to -0.1, we are in the ``left'' side of the curve.
This is shown in the left figure below. The right one shows the effect of
moving to the right side of the curve at 0.25.

Use the **Low/High** slider to move up and
down. The default value is 0.2, meaning that the viewing position is
slightly above the floor of the roller coaster box. The left figure below
shows a value of 0.05, which is near to the floor of the roller coaster
box and as a result the tangent vector can barely be seen. The right figure
shows the effect of moving up to 0.5, which is high above the floor.