Returns a list of
- a Matrix A with the vertices of the convex hull of L in its rows
- a Matrix Adual with the vertices of the dual in its rows
- a list of lists with the faces of the convex hull sorted by increasing dimension.
Each face is a list with two elements. The first is a list of the vertices of the face, the second a list of the vertices of the dual face.
The vertices of the faces are represented by the indices of the rows of A.
This requires that the convex hull of L contains 0 in its interior.
This uses the Convex functions convHull and faces.
i1 : L={vector {1,0,0},vector {-1,0,0},vector {0,1,0},vector {0,-1,0},vector {0,0,1},vector {0,0,-1}}
o1 = {| 1 |, | -1 |, | 0 |, | 0 |, | 0 |, | 0 |}
| 0 | | 0 | | 1 | | -1 | | 0 | | 0 |
| 0 | | 0 | | 0 | | 0 | | 1 | | -1 |
o1 : List
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i2 : P=mConvexHullFacesAndDuals(L)
o2 = {| 1 0 0 |, | 1 -1 -1 |, {{{{}, {1, 2, 3, 4, 5, 6, 7, 8}}}, {{{1},
| -1 0 0 | | -1 -1 -1 |
| 0 1 0 | | 1 1 -1 |
| 0 -1 0 | | -1 1 -1 |
| 0 0 1 | | 1 -1 1 |
| 0 0 -1 | | -1 -1 1 |
| 1 1 1 |
| -1 1 1 |
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{2, 4, 6, 8}}, {{2}, {1, 3, 5, 7}}, {{3}, {1, 2, 5, 6}}, {{4}, {3, 4, 7,
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8}}, {{5}, {1, 2, 3, 4}}, {{6}, {5, 6, 7, 8}}}, {{{2, 5}, {1, 3}}, {{3,
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5}, {1, 2}}, {{1, 5}, {2, 4}}, {{4, 5}, {3, 4}}, {{3, 6}, {5, 6}}, {{2,
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3}, {1, 5}}, {{1, 3}, {2, 6}}, {{2, 4}, {3, 7}}, {{1, 4}, {4, 8}}, {{2,
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6}, {5, 7}}, {{1, 6}, {6, 8}}, {{4, 6}, {7, 8}}}, {{{2, 3, 5}, {1}},
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{{1, 3, 5}, {2}}, {{2, 4, 5}, {3}}, {{1, 4, 5}, {4}}, {{2, 3, 6}, {5}},
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{{1, 3, 6}, {6}}, {{2, 4, 6}, {7}}, {{1, 4, 6}, {8}}}, {{{1, 2, 3, 4, 5,
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6}, {}}}}}
o2 : List
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