> User's Guide > Geometry |
Parallel
Hyperplanes Files |
A hyperplane can be represented mathematically as: |
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A pair of parallel hyperplanes can, therefore, be represented as: |
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A pair of parallel hyperplanes can be used to define a space |
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where the hyperplanes |
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define its boundaries. |
A parallel hyperplanes file is a type of single-vector file used to store pairs of bounding parallel hyperplanes. The variables in these files are linear combinations, and the values are intervals. The linear combinations are used to represent the hyperplanes, and the intervals are used to represent the lower and upper values the hyperplanes can assume (βlower and βupper). Taken together, these elements form pairs of parallel bounding hyperplanes. For example, the space formed by the inequality 0 ≤ x + y + z ≤ 1 is bounded by the pair of parallel hyperplanes x + y + z = 0 and x + y + z = 1. This could be represented in a parallel hyperplanes file as: See the Text Formatting Rules for additional information. |