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Example commands using the off_align program. This program
aligns one polyhedron with another. One polyhedron
is a brick and is aligned with the other, the base, by matching
vertices or faces. When aligning with a face the brick may be
bonded to the base, while removing the bond faces,
producing an augmentation or excavation of the base polyhedron.
Any of the alignments may be repeated symmetrically.
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Align v2
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Med
Lrg
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Description :
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The -v option with two numbers matches a vertex on the brick
(second index number) with one on the base (first index number)
by a translation. In this example a pentagonal
pyramid is turned on its side and has its apex aligned with a
square pyramid. Notice that the brick was specified as '-' to
indicate that it should be read from standard input.
View this model with the command
off_trans pyr5 -R 0,90,0| off_align -v -,4,5 pyr4 -M 2 | antiview
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Align v4
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Med
Lrg
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Description :
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The -v option with four numbers matches two vertices on
the brick (second set of two index numbers) with two on the base
(first set of two index numbers) by a translation to align
the first pair of vertices, then a rotation to align the second pair.
In this example a pentagonal pyramid has a slanting edge aligned
with a slanting edge on a squre pyramid, but in the opposit direction.
View this model with the command
off_align -v pyr5,4,0,0,5 pyr4 -M 2 | antiview
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Align v6
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Med
Lrg
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Description :
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The -v option with six numbers matches three vertices on
the brick (second set of three index numbers) with three on the base
(first set of three index numbers) by a translation to align
the first pair of vertices, then a rotation to align the second pair,
then a rotation about the line joining these two vertices to align
the third pair of vertices.
In this example a square pyramid has three verices on its face aligned
with those of an ictagonal pyramid. Notice that the base polyhedron in
the off_align command is read from standard input.
View this model with the command
polygon pyr 8 | off_trans -R 0,0,10 -R 110,0,0 | off_align -v pyr4,0,2,3,2,1,0 -M 2 | antiview
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Align f
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Med
Lrg
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Description :
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The -f option aligns a face on the brick with a face on the base.
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example the base polygon of a pentagonal
pyramid is aligned with a face of a dodecahedron. Default
values are used: dodecahedron face 0 is used, the pyramid base has
index number 0, it is aligned in the first of the possibilities.
View this model with the command
off_align -f pyr5 dodecahedron -M 2 | antiview
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Align f
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Med
Lrg
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Description :
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The -f option aligns a face on the brick with a face on the base.
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example the base polygon of a pentagonal
pyramid is aligned with a pentagonal face (index 1) of a dodecahedron.
Default values are used for the pyramid base (index 0) and the
alignment number (0). The brick is is repeated with the symmetry
of the base model by specifying -y full and the bricks are
output without the base model (default for -M).
View this model with the command
off_align -f pyr5,20 -y full icosidodecahedron | antiview
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Align F
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Med
Lrg
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Description :
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The -F option aligns a face on the brick with a face on the base
and then uses it to augment or excavate the base model (the polyhedra
are joined and the bonding faces removed)
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example the base polygon of a pentagonal
pyramid is aligned with a face of a dodecahedron. An alignment
number is chosen that causes the pyramid to lie inside the dodecahedron,
producing an excavation. As the result is a single polyhedron
the whole polyhedron will be output.
View this model with the command
off_align -F pyr5,3,0,5 dodecahedron | antiview
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Align F
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Med
Lrg
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Description :
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The -F option aligns a face on the brick with a face on the base
and then uses it to augment or excavate the base model (the polyhedra
are joined and the bonding faces removed)
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example the base polygon of a pentagonal
pyramid is aligned with a face of a dodecahedron. An alignment
number is chosen that causes the pyramid to lie inside the dodecahedron,
producing an excavation. The bonding operation is repeated with the
symmetry of the base model be specifying -y full.
View this model with the command
off_align -F pyr5,0,0,5 -y full dodecahedron | antiview
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Align F
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Med
Lrg
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Description :
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The -F option aligns a face on the brick with a face on the base
and then uses it to augment or excavate the base model (the polyhedra
are joined and the bonding faces removed)
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example a base polygon of a pentagonal
antiprism is aligned with a face of a dodecahedron. The default
alignment causes the antiprism to lie outside the dodecahedron,
producing an augmentation. The bonding operation is repeated with the
symmetry of the base model by specifying -y full.
View this model with the command
off_align -F ant5 -y full dodecahedron | antiview
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Align F
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Med
Lrg
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Description :
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The -F option aligns a face on the brick with a face on the base
and then uses it to augment or excavate the base model (the polyhedra
are joined and the bonding faces removed)
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example a face of a tetrahedron is bonded to
a face of an icosahedron, and the bond is repeated with
tetrahedral symmetry by specifying -y T.
View this model with the command
off_align -F tet -y T ico | antiview
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Align F
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Med
Lrg
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Description :
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The -F option aligns a face on the brick with a face on the base
and then uses it to augment or excavate the base model (the polyhedra
are joined and the bonding faces removed)
It may be possible to align the face in various ways, the third
number selects from these possibilities, with the first possibility
being 0. In this example the upper polygon of a square cupola is
bonded with itself. The base is read from standard input, the
brick is specied as a copy of the base by not providing a name
for it.
View this model with the command
off_trans -R 110,0,0 cup4 | off_align -F ,1,1 | antiview
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