An Efficient Motion Planning Algorithm for a Convex Polygonal Object in 2 Dimens
An Efficient Motion Planning Algorithm for a Convex Polygonal Object in 2 Dimens
K Kedem
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3. 4. Constructing the edge-graph EG By now we have calculated a set T of size OiknX^ikn)) that contains all the critical orientations of all three types. Suppose that T is sorted in ascend- ing order, and assume without loss of generality that = is not an orienta- tion in T. -27- As in Section 2, we represent each node i of the graph EG by a pair (u, L^), where L„ = (61, 82) is the angular life span of 4, and where u is the (discrete labeling of the) comer of VGq, for C; L„, that lies on the e...dge of FP represented by ^. The calculation of EG will be accomplished in a manner similar to that of [LSI]. That is, we process critical orientations in increasing order, maintain- ing the "cross-section" graph VGq and use it to update EG at each critical orientation. At each such orientation 6 we determine those nodes of EG whose life-span terminates at 6 (these are nodes whose corresponding comers have to be deleted from VGe), and the new nodes whose life span starts at 9. Nodes of the first kind will already have been stored in EG, and we update their life span by adding 6 as its terminal orientation.
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