**CAPCPO.COM**

Published the 04.04.2017

## RELIER |
2.1 | CONTACT |

Relier is a software that enable to link points for the drafting of network.

From a set of points to be linked (points, circles, or blocks) and a polygonale boarder (2d or 3d polyline) surounding the dots , the software can compute four kind of networks, and the associated minimum spanning trees.

Relier has eight main commands for drawing the following networks:

- DELAU-NET to link a set of points with the network associated to the Delaunay triangulation;
- L1-SPAN-TREE for linking a set of points by the L1 norm (|x|+|y|) minimum spanning tree;
- L2-SPAN-TREE for linking a set of points by the L2 norm (√(x²+y²)) minimum spanning tree;
- QUARTER-DELAU-NET for quartering the Delaunay's net;
- QUARTER-NET for quartering a set of points by a rectangular network;
- LINF-SPAN-TREE for linking a set of points by the Linf norm max(|x|,|y|) minimum spanning tree;
- RECT-STEINER-NET to link a set of of points with the rectilinear Steiner network;
- RECT-STEINER-SPAN-TREE for linking a set of points by the minimum rectilinear Steiner spanning tree;

The generation of the network can be constraint inside concave polygons.

For every kind of network, one can link a set of point entities, the centers of a set of circles, and the insertion points relative to a set of blocks; by simple lines or by polylines formed of two consecutive arcs (randomized a little bit). The entites to be linked can also been filtered by their belonging to a specific layer.

*The software runs in 2D.**In the case of concave boarder the reach of an optimum is not guaranted.*

The performances of execution (magnitude of time on a 1.6Ghz processor) are for normal spanning trees in the case of a convex boarder of about 300 secondes for 1000 dots, and same time but only for 100 dots in cas of the rectilinear spanning tree. in the case of concave boarders and normal spanning trees, the execution time can be much more long with a presumably factor of 100, depending on the complexity of the boarder and the number of points to be linked.

Delaunay's network constrained by a concave boarder.

Rectangularised Delaunay's network constrained by a concave boarder.

Rectangular network constrained by a concave boarder.

Rectilinear Steiner network constrained by a concave boarder.

L1-norm arborescent network (or spanning tree), constrained by a concave boarder.

L2-norm arborescent network (or spanning tree), constrained by a concave boarder.

Linf-norm arborescent network (or spanning tree), constrained by a concave boarder.

Steiner rectilinear arborescent network (or spanning tree), constrained by a concave boarder.

No opinion til today. |