As in the 2D morphing system of , 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 .