Graphics Reference
In-Depth Information
1
3
(
P
1
−
(b) Show that if we apply the rule
v
0
=
P
−
1
)
, then the formula from
part (a) lets us simplify this to
v
0
=
3
(
P
1
−
P
0
)
.
Exercise 22.4:
In the Catmull-Rom spline, we placed a fictitious control point
at each end, placing it so that the last three control points at each end were sym-
metrical. What would happen if we set
P
−
1
=
P
0
and
P
n
+
1
=
P
n
instead? The
resultant spline will still interpolate all the original control points, but thinking
of the spline as describing the position of a moving point at time
t
, we'll see its
motion change at the ends. How will it change?
Exercise 22.5:
Show that the Catmull-Rom spline is in general
not C
2
.On
each segment, the second derivative is a linear function (as it is for any cubic
spline). Show that this function need not be continuous between segments.
