# Calculating sawn edge length for repeating irregular Polygon tiling

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I'm asking if there is a way to script calculation of minimum sawn edge for a repeat tiling pattern given a known set of rules.

If there's a way of solvng this mathematically without CAD I'd be very interested in that solution (it feels like there would be).

A client asked me if I could find a way to utilise an area of old concrete as he likes my approach to reusing old materials. I suggested sawing the concrete into pavers in the shape of Cairo-type irregular polygon tiles – specifically type 4 (link below). This is the most blocky of the Cairo tiles, hence most suitable for this kind of work as least likely to break during processing, handling and laying.

Rao 2018 Exhaustive search of convex pentagons which tile the plane. Page 15, Type 4 (second from right) in graphic. J Mathematics > Combinatorics. https://doi.org/10.48550/arXiv.1708.00274 [arxiv.org 200Kb .pdf] I've put page 15 into the vw file. (I have no idea why this very simple file is 13Mb!)

I've now designed the surface using this form (image above - and .vwx encl). Due to rounding of angles tiles are not mathematically perfect i.e. if you zoom in you will see some slight overlaps across the surface - at this point I have not taken paver gaps into account (probably about 10mm at laying time).

If it makes it eaier I would explode the symbols back to polygons - I image a script could traverse that more straight-forwardly.

Rules for thinking about minimum edge length

Paver edges within planters do not need to have a sawn edge and can utilise an existing broken/ existing edge.

(red organic shapes will be raised planters that will sit over the edge of pavers - there will be no pavers under the planters as I want connection to the soil below). Where there are small white areas outside of the shapes, or where a tile edge nearly follows the planter edge I intend to use off-cuts to support the planter.

Outer edge pavers do not need a sawn edge and can utilise an existing broken/ existing edge.

The light-weight red closed polygon at the right of the area is a future brick path. Pavers crossing this line do not need a sawn edge and can utilise an existing broken/ existing edge.

As shown pavers are a symbol, held by the class:
5 HS surface_-paver_Type4_Holder
with the paver p 2ndolygon itself in another class:
5 HS surface_-paver_Type4

the brick surface polygon and the planter polygons are in their own separate classes:
5 HS_-court brick
5 HS_-court planters v3 dimensionable

So … is this a problem that can be solved with vectorworks scripting, or is it an impossible ask?

If there is an algorithm for what you want, then Vectorscript can probably do it, and Python can almost certainly do it. So the short answer to your question is Yes, VW scripting can give you the answer you want. The hard part is figuring out what that is.

Can you restate your question in simpler term?  It may be that I don't have the correct background to understand the problem as you have stated it.

Are you looking to have the concrete area cut into pavers and then re-layed?  Or do you want to leave the concrete in place and just cut the paver score marks part way or completely through the concrete? For your parts around the outside edge, you state they can stay uncut, but won't at least some need to be cut to prevent overlap and interference?

Are you looking for exact or close enough?

My first thought would be to break a copy into lines. Sum the length of all the lines and you have the maximum cut length.

Name the objects that make up the outlines of the planting areas and path and then find the lines that are completely within those areas. Those are the internal edges that don't need to be cut.

For the outer edge do something similar and make a polygon the encloses only the outside lines and sum those length to get the external edges that don't need to be cut.

You should be able to do all of this in a worksheet. No real scripting required.

HTH. Ask again if I have not been clear enough.

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