in reply to Placeing Tiles in a Circle

There are only four positions to consider. If you view this image, you see that there are 4 circles drawn over a grid of squares:

  1. The green circle, is centered at the green dot, which aligns with a crossover point of the grid.

    It contains 4 full tiles.

  2. The blue circle, is centered at the blue dot, which is aligned with the grid in the y-axis and misaligned by half a tile in the x-axis.

    It encompasses 6 full tiles in a 3 x 2 arrangement.

  3. The yellow circle, is centered at the yellow dot, which is aligned with the grid in the x-axis and misaligned by half a tile in the y-axis.

    It also encompases 6 full tiles, this time in a 2 x 3 arrangement.

  4. And the magenta circle, is centered at the magenta dot, which is the center of a tile.

    It encompasses 5 full times.

Whether you need full tetrameric (quadrilateral) symmetry (green or magenta) or will settle for bilateral symmetry (blue or yellow), those really are the only 4 points to consider regardless the proportions of the tiles.

How you choose between them is really just a case of deciding upon your criteria and a little math.

With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

Replies are listed 'Best First'.
Re^2: Placeing Tiles in a Circle
by janDD (Acolyte) on Nov 29, 2013 at 19:17 UTC
    Hi BrowserUK, your analysis is perfectly true and you are describing the algorithm I just implemented. The magenta circle is essentially picture 1 of my post.

    But lets consider again this picture: http://www.myimg.de/?img=tile2a1863.png - how would you achieve that the distance of the uppermost green tile has the same distance to the circle as the lower left green tile? I don't think that this can be achieved by placing the center of the circle to any of the four points you mention ...

    The tricky think is to move the center of the circle such that the beholder "thinks", the tiles are centered. Please look at my last pic (http://www.myimg.de/?img=tile417dd5.png) where the optical glitch of a nonsymmetric tile array becomes obvious ...

    Best regards Jan
[reply]
      I don't think that this can be achieved by placing the center of the circle to any of the four points you mention ...

      Let me re-state this. If you want symmetry, then positioning the circle at one of those 4 points will ensure that. No other point will give you symmetry. Full stop.

      The problem with this (please learn to use the links), is that you are comparing eggs with oranges. That is to say why are you comparing the 'gap' of the bottom square in column 1 with a 'gap' of the top square in column 2? It doesn't make any sense at all.

      If you fill in the rest of the tiles, you'll see that once you compare like with like (ie. caps top and bottom of the same columns), that "problem" goes away.

      And you'll also see that once like for like gaps are equalised, the circle is centered at the half-tile offset in both x-axis and y-axis (the magenta circle on my plot). And for a full grid, it will always be one of those 4 positions.

      Only now, having typed that last sentence does the word "irregular" from your OP ring alarms in my head....

      What you real want is an algorithm to evenly encircle any pattern of tiles on a grid, partial or full. Yes?

      (Assuming so, I'll let my brain mull that completely different problem to the one I was solving and get back to you if I come up with anything :)

      With the rise and rise of 'Social' network sites: 'Computers are making people easier to use everyday'
      Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
      "Science is about questioning the status quo. Questioning authority".
      In the absence of evidence, opinion is indistinguishable from prejudice.
[reply]
        Dear BrowserUK,

        I am sorry if I expressed myself a bit clumsyly. Your last statement is exactly what I want:

        "What you real want is an algorithm to evenly encircle any pattern of tiles on a grid, partial or full."

        Best regards Jan

        P.S.: I know about the links but I had a strange error "permission denied" and I found a post in here that sourced this to the usage of links ... So I removed them ;)
[reply]

In Section Seekers of Perl Wisdom