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How can I divide a convex polygon into quadrilaterals considering the hatched polygons (holes) already in place. Any suggestions will be greatly helpful.

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What am I actually trying to do is to find quadrilateral strips as two of them are shown below. I thought may be dividing the whole polygon into quadrilaterals would help achieving this.

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Vahid
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  • Your result has some triangles in it. Also, why are some rectangles split into smaller rectangles wherever there is a line extending from any hole but in other areas they are joined into one? – Ian Mercer May 12 '16 at 20:51
  • @IanMercer Thanks for your interest in this. What am I actually trying to do is to find quadrilateral strips as shown in the updated question. I thought may be dividing the whole polygon into quadrilaterals would help achieving this. – Vahid May 12 '16 at 21:11
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    Could you simply smash the large polygon into smaller polygons by bisecting it using the (extended) edge of every internal polygon, then take any that have more than four sides and split them into quadrilaterals, and then join those small polygons back together starting with any triangles and favoring joins that create 'strips'? – Ian Mercer May 12 '16 at 22:59
  • @IanMercer Thanks Ian, seems a good idea. I'll work on that. – Vahid May 13 '16 at 06:15
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    The polygon isn't convex. –  May 13 '16 at 08:59
  • Do you want to find all strips or some strips? If all, do you need all possible strips or minimal number of strips to cover region? What is a strip? Does it have to have at least two parallel edges or not (just simple quadrilateral)? – Ante May 14 '16 at 18:38
  • @Ante Strips are quadrilaterals. In the drawing above 13 strips can be identified. – Vahid May 14 '16 at 23:35

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