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- W2499850100 abstract "An algorithm is presented for set operations on a wide and easily characterized class of decomposition models, including some of immediate potential interest.Recent extensions to point-set and boundary models allow the representation of general objects, including those with internal structure (composite objects). In set operations on these new models, the subdivision step is definitely the most time-complex, and is usually quadratic in the number of elements. We restrict our attention to composite objects, and propose an efficient algorithm to accomplish the subdivision step. In 2-D, the analogous problem is map overlay, for which an optimal algorithm exists. Unfortunately, it does not extend to 3-D, and there is an optimal algorithm in 3-D for plane arrangements only. Our research was motivated by the lack of an efficient algorithm for a wider class of applications.We model each composite object with an exhaustive space decomposition into cellular volumes, called cells. Each cell is equivalent to an r-set, and each face is accessible from every other face through face-edge adjacencies. We utilize these properties in a topological subdivision algorithm that guarantees that faces in the interior of one decomposition, with respect to viewpoints on the boundary of the other decomposition, will never be tested for intersection.We require that when positioning the two decompositions the user must specify a pair of elements, edges or faces, such that the set intersection of the specified pair produces at least one line segment. Using this as a starting point, the subdivision algorithm finds a pair of overlapping faces or of partially-overlapping cells, and intersects them. The search then resumes, encompassing the newly determined output elements. Since interior faces can never be adjacent to partially-overlapping cells, these faces are never considered for intersection.The algorithm has been analyzed, its correctness has been proved, and it has been implemented and tested on various objects. As expected, the improvement in computational efficiency over the conventional approach depends on the number of interior faces in the objects being combined.The applications of this algorithm are in 3-D VLSI, in finite element meshing, and in modeling with composite objects." @default.
- W2499850100 created "2016-08-23" @default.
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- W2499850100 date "1992-01-01" @default.
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- W2499850100 title "Efficient subdivision of two polyhedral composite objects" @default.
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