As in the 2D morphing system of [2], the animator
identifies two corresponding features in and
, by
defining a pair of elements
. These features
should be transformed to one another during the morph. Such a
transformation requires that the feature of
be moved,
turned, and stretched to match respectively the position, orientation,
and size of the corresponding feature of
. Consequently, for
each frame of the morph, our warp should generate a volume
from
with the following property: the feature of
should possess an intermediate position, orientation and size in
. This is achieved by computing the warp in two steps:
Figure 3: Single element warp. In order to find the point in
volume
that corresponds to
in
, we
first find the coordinates
of
in the scaled
local system of element
;
is then the point with
coordinates
in the scaled local system of element
. To simplify the figure, we have assumed unity scaling
factors for all elements.
(ii) is the point with coordinates
,
and
in
the scaled local system of element
, i.e. the point
.