pol_recip - polar reciprocals (duals)

Usage | Examples | Notes

Usage

Description

Read a file in OFF format and make a polar reciprocal from the face planes.

Options

input_file: input file in OFF format, or if not given the program reads from stdin

-h

program help

-c <cent>

centre of reciprocal sphere, in form "x_val,y_val,z_val" (default: "0,0,0")

-r <rad>

radius of reciprocal sphere (default: 1)

-R <elms>

radius of reciprocal sphere using elements

v - nearest vertex distance
V - furthest vertex distance
e - nearest edge distance
E - furthest edge distance
f - nearest face distance
F - furthest face distance

or a comma separated list of vertex indices (starting from 0) and the distance is to the space containing those vertices

-I <dist>

maximum distance to project any normal or infinite dual vertex (default: 1e15), if 0 then use actual distances and delete infinite points

-o <file>

write output to file, if this option is not used the program writes to standard output

Examples

Make a reciprocal pair. Make the dual of a cuboctahedron, a rhombic dodecahedron, and then make the dual of that. The final output is the same as the original cuboctahedron.

   pol_recip -o rh_dodec.off -R e cuboct.off

   pol_recip -o orig_cuboct.off -R e rh_dodec

Make a cube whose vertices are the mid-points of an octahedron's faces

   pol_recip -o cube.off -R f octahedron.off

A polyhedron has a face made of vertices with indexes 0, 2, 4. Make a dual which has a vertex in the plane of this face

   pol_recip -o dual.off -R 0,2,4 poly.off

Notes

A dual of a convex polyhedron is normally made with the centre of reciprocation at the polyhedron centre and the radius to just touch the edges.

Some polyhedra have faces passing through their natural centre. This causes a problem when making a dual because the vertex which is dual to this face should be infinitely far away. pol_recip allows these vertices to be included by placing them at a specified (probably very large) distance normal to the face. Any programs dealing with these distant vertices (e.g. povray) can interpret these distant vertices accordingly.

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Packinon Documentation 16.12.2005 - http://packinon.sourceforge.net/