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One use of graph theory in geometric modeling is to abstract a given model's cells into a graph. Each cell of the geometric model becomes a point of the graph. Points of the graph are connected with lines (or edges) only if the cells of the geometric model are adjacent with faces.
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Another use of graph theory is to abstract a given model's faces into a graph. Each face of the geometric model becomes a point of the graph. Points of the graph are connected with lines (or edges) only if the faces of the geometric model are adjacent.
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In either case, once a graph has been obtained, the graph subsystem can be used to find the shortest path, the shortest cycle, the cut edges and vertices, etc.
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An example of using graph theory in
ACIS is in selective Booleans and sweeping. Cells used as part of sweeping are passed into the graph subsystem. Using graph theory, the shortest path is calculated and used to trim the trees of the graph. Mapping this result back to the original cells (and entities) determines which portions of the resulting swept model to keep and which to throw away.
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