Graphics Reference
In-Depth Information
Q ( v )
P ( u )
Frame f 1
Frame f 2
FIGURE 4.4
Two key frames showing a curve to be interpolated.
Reeves [ 29 ] proposes a method of computing intermediate curves using moving point constraints ,
which allows the user to specify more information concerning the correspondence of points along the
curve and the speed of interpolation of those points. The basic approach is to use surface patch tech-
nology (two spatial dimensions) to solve the problem of interpolating a line in time (one spatial dimen-
sion, one temporal dimension).
The curve to be interpolated is defined in several key frames. Interpolation information, such as the
path and speed of interpolation defined over two or more of the keys for one or more points, is also
given. See Figure 4.5 .
The first step is to define a segment of the curve to interpolate, bounded on top and bottom by inter-
polation constraints. Linear interpolation of the very top and very bottom of the curve, if not specified
by a moving point constraint, is used to bind the top and bottom segments. Once a bounded segment has
been formed, the task is to define an intermediate curve based on the constraints (see Figure 4.6 ) . Var-
ious strategies can be used to define the intermediate curve segment, C t ( u )in Figure 4.6 , and are typ-
ically applications of surface patch techniques. For example, tangent information along the curves can
be extracted from the curve definitions. The endpoint and tangent information can then be interpolated
along the top and bottom interpolation boundaries. These can then be used to define an intermediate
curve,
C t ( u ), using Hermite interpolation.
C 1 (u)
C 2 (u)
C 3 (u)
P 11
P 12
P 13
P 21
P 22
P 23
P 32
P 31
FIGURE 4.5
Moving point constraints showing the key points specified on the key curves as well as the intermediate points.
 
Search WWH ::




Custom Search