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Element Pairs

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:

We interpolate the local coordinate systemsgif and scaling factors of elements and to produce an interpolated element . This element encodes the spatial configuration of the feature in .

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.

Inverse mapping:
For every point in of , we find the corresponding point in in two simple steps (see figure 3): (i) We find the coordinates of in the scaled local system of element by

(ii) is the point with coordinates , and in the scaled local system of element , i.e. the point .gif

Last update: 11 May 1995 by Apostolos "Toli" Lerios