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Journals ACM SIGGRAPH Computer Graphics Volume 24 Issue 4

A polyhedral solid modeler that operates on boundary representations of objects must infer topological information from numerical data. Unavoidable errors (due to limited precision) affect these calculations so that their use may produce ambiguous or contradictory results. These effects cause existing polyhedral modelers to fail when presented with objects that nearly align or barely intersect107.An object description associating a tolerance with each of its topological features (vertices, edges, and faces) is introduced. The use of tolerances leads to a definition of topological consistency that is readily applied to boundary representations. The implications of using tolerances to aid in making consistent topological determinations from imprecise geometric data are explored and applied to the calculations of a polyhedral solid modeler. The resulting modeler produces a consistent polyhedral boundary when given consistent boundaries as input.

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Using tolerances to guarantee valid polyhedral modeling results

Segal, Mark
ACM SIGGRAPH Computer Graphics , Volume 24 (4)
Association for Computing Machinery – Sep 1, 1990

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