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I'm designing a big door -- a rectangle sized 3*2.6 meters. (7.8 square meters).

Given that the material I'm going with is OSB, which comes in 2.5*1.25 m. (3.125 sq.m.) sheets. Is there a tool/method to devise a cutting plan that'd use the least number of polygons to cover the rectangle?
UPD: Inspired by the answer: The smallest I've got to is with 5 rectangles cut out from 3 pieces of OSB: enter image description here

Gleb
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  • Did you have a reason for using the term "concave" in your title? I don't think that word applies to your problem. – A. I. Breveleri May 04 '17 at 15:24
  • Five is the minimum number of tiles you will need. – A. I. Breveleri May 04 '17 at 15:27
  • @A.I.Breveleri. Yes, of course, it's convex polygons, not concave. Can you elaborate why 5 is the minimum number of tiles? – Gleb May 04 '17 at 15:33
  • I think I have a good solution to your problem but you'll need to change your question. The goal to minimize the number of polygons doesn't really make sense to me. I think what you are looking for is (1) to avoid consuming 4 sheets of OSB when 3 will do it, (2) to assemble the OSB in such a way that is structurally sound (avoid very small or narrow pieces, perhaps avoid lining up all the seams), and (3) to reduce the number of cuts you need to make, and (4) to avoid complex cuts. This is a classic tiling problem but with very large tiles and you should look to brick bonds for inspiration. – Stanwood May 04 '17 at 16:01
  • I suggest dividing the 3 m length into three even 1 m lengths. Then divide the 2.6 m width into two uneven lengths. If you want to minimize cuts I suggest 1.25 m and 1.35 m. These add up to 2.5 m. Out of a single 1.25 x 2.5 board you can cut out one 1.00 x 1.25 piece and one 1.00 x 1.35 piece. It will require 3 straight cuts. Repeat three times and assemble. Change your question and I will post you a picture. – Stanwood May 04 '17 at 16:04
  • @isherwood a [convex polygon](https://en.wikipedia.org/wiki/Convex_polygon) is a shape with no interior angles over 180 degrees; i.e., it doesn't have anything "cut out" of it. My first thought here would be to use triangles rather than squares, if you really want to save material, but squares would be easier to cut and possibly look better. – Robert Nubel May 04 '17 at 16:05
  • The question in your title does not match the question in your text. The title asks for the least number of sheets consumed, and the text asks for the least number of polygons on the finished door. These are not the same. @Stanwood is on the right track. – A. I. Breveleri May 04 '17 at 16:48
  • @Stanwood I think that I'll be handling seams between OSB pieces by covering them with straight strips, so I'm looking to minimise both length and number of seams. – Gleb May 04 '17 at 18:29
  • @Stanwood, your proposal wouldn't work practically, as OSB sheets available to me can deviate in size +-5 mm. And to get exact side with unfrayed edges I need cuts on all sides. And the cut has to be no closer than 1 cm from the edge – Gleb May 04 '17 at 19:31
  • @isherwood the pieces need to be convex, the circular saw wouldn't make nice incut – Gleb May 04 '17 at 19:33
  • You can adjust the two lengths to suit your additional requirement for finish cuts on all four sides. For example, adjust the uneven lengths to 1.20 and 1.30 and center the piece away from the edges. This lets you run a saw along all four lengths of each piece with at least 25 mm of kerf. If you want to maximize the kerf use 1.175 and 1.425 and push the two pieces together for a kerf of 37.5 mm on all sides. It will take 5 straight cuts to make the two pieces. – Stanwood May 04 '17 at 19:57

1 Answers1

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I suggest dividing the 3 m length into three even 1 m lengths. Then divide the 2.6 m width into two uneven lengths. If you want to minimize cuts I suggest 1.25 m and 1.35 m. These add up to 2.6 m.

Out of a single 1.25 x 2.5 board you can cut out one 1.00 x 1.25 piece and one 1.00 x 1.35 piece. It will require 3 straight cuts (labeled in order below).

Cut 2 pieces from each board

Repeat three times and assemble. I've drawn two versions of the assembly. Which one you prefer may depend on the framing that the OSB is attached to and what you intend to cover it with, if anything.

Assembly aligning the vertical seams Assembly alternating the vertical seams

A. I. Breveleri
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Stanwood
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  • The idea is useful, thanks, I just make the 1.35 piece longer, and 1.25 pice a bit shorter. – Gleb May 04 '17 at 19:38
  • I've included my current idea in the question https://i.stack.imgur.com/C2gGP.png. Same 3 sheets raw material., 5% longer overall seam length. I'm going to order banding of the outer edges, and in my design the advantage is that it'd be 8 strips of banding, vs 12. – Gleb May 06 '17 at 19:44