ABSTRACT
The features of the convolution are obtained by con volving pairs of matching features of B and R. A pair of features is said to match if the whisker sets of the two features have a non-empty intersection. In order to keep the notation simple, we assume that the in tersection of the whisker sets of any two features is simply connected (and thus defines only one feature, whose whisker set is the intersection of the two orig inal sets). In two dimensions, a forward move com bined with a right turn becomes a backward move in the convolution. Likewise, in three dimensions, we ex pect that some faces will change sign in the convolu tion. A face / ' in the convolution can arise when a face / of one tracing is convolved with a matching vertex v in the other. As / and / ' have the same whisker, a change of sign requires a reversal of the edge ring (Figure 4). A face in the convolution is also obtained when a blue and a red whisker arc intersect on the sphere; their corresponding edges generate a parallel ogram (the Minkowski sum of the two edges). The whisker of this new face is well defined, but its sign has to be determined.
