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A Voronoi diagram is an approach to the tessellation of medium. In this diagram, there are many points in a plane that divide the medium to many specific regions by their bisector. Any region is convex and has a circumscribed rectangle. the circumscribed rectangle of convex shape that has the smallest area (We have an algorithm to imagine any edge on the direction of a specific edge and perpendicular to edge and find a rectangle with the smallest area.). I want to place the points in a way that creat random convex polygons (Random means have different numbers of edges.). But I want to control the size of the width and length of their circumscribed rectangle. So I want to know is there any algorithm (as math or computer) for the locating points with the above property? Voronoi tessellation with known cell areas and unknown seeds Same class solution and there are still some people that say "Please clarify". I don't edit the question. You can close the question. I will go and find the answer and come back and write it here.

ALIN
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  • What exactly do you call a circumscribed rectangle ? –  Jun 22 '20 at 08:01
  • @YvesDaoust For any convex shape, there is a rectangle with the shortest width and longest length. I mean the circumscribed rectangle of convex shape that has the smallest area. – ALIN Jun 22 '20 at 08:06
  • "Smallest area" is ok. "Shortest width and longest length" is not necessarily possible. –  Jun 22 '20 at 08:11
  • @YvesDaoust I think both are the same. We have an algorithm to imagine any edge on the direction of a specific edge and perpendicular to edge and find a rectangle with smallest area. – ALIN Jun 22 '20 at 08:18
  • No, they are not the same. There is no bounding rectangle with "shortest width and longest length" that circumscribes a square. –  Jun 22 '20 at 08:20
  • @YvesDaoust OK. Circumscribed rectangle has a specific length and width. These variables are specific. – ALIN Jun 22 '20 at 08:26
  • Let us continue this discussion in chat. – ALIN Jun 22 '20 at 08:42
  • Learn punctuation, grammar, and other writing skills before making ill-informed guesses about other people's knowledge of English. Rudeness doesn't help. What might help is if you show an example of a Voronoi diagram that satisfies your conditions. – David K Jun 22 '20 at 12:48
  • @DavidK beautiful "ill-informed"!!! I don't know the mean of "example" (and really if there is an example I don't ask). I just want to tesselate the plane with polygons that have a random number of edges and can control the polygons by the size of their circumscribed rectangle. – ALIN Jun 22 '20 at 13:16
  • Your examples don't have to be correctly calculated, they just need to illustrate what you mean by what you're trying to say. "I mean something like this: ... but not like this: ... ." – David K Jun 22 '20 at 13:40
  • @DavidK This is an example of regular random Voronoi diagram. Here We don't have any control over the size (that I described above) of the shapes. I want to locate the point of sites in a way that can control the size of polygons. For example, I can say the size of the site that on (x,y) is W and L. – ALIN Jun 22 '20 at 14:05
  • I don’t see anything labeled W, L, x, or y in that figure. I think you will have to draw your own figure or at least modify one to show what you mean. – David K Jun 22 '20 at 14:47

1 Answers1

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Five points arranged in a cross define an arbitrary rectangular Voronoi cell.

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Then you can modify the shape without modifying the bounding rectangle by adding well-chosen points.

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  • That is exactly not I want. I want to locate points in space in a way that creat polygon that has a circumscribed rectangle with smallest area. That rectangle has a specific long edge (length) and short edge (width). – ALIN Jun 22 '20 at 08:22
  • @ALIN: in what way does my solution not allow specific side lengths ?? –  Jun 22 '20 at 08:24
  • I want to tesselate plane with random polygons. These polygons have a circumscribed rectangle with the smallest area. That rectangle has a specific long edge (length) and short edge (width). So at first, there is no one region, second, this shape must random, and third, specific circumscribed rectangle. – ALIN Jun 22 '20 at 08:32
  • @ALIN: what do you call random ? –  Jun 22 '20 at 08:34
  • @ALIN: "there is no one region": what ? –  Jun 22 '20 at 08:35
  • Random means have different numbers of edges. But I want to control the size of the width and length. the region I mean there is no one shapes but we have many shapes. – ALIN Jun 22 '20 at 08:59
  • man this is wrong solution your solution is just OK for the first shape if we go beyond that one the process is very difficult. – ALIN Jun 22 '20 at 09:14
  • @ALIN: I regret to have tried to help you. –  Jun 22 '20 at 09:25
  • Completely clear – ALIN Jun 22 '20 at 10:37