Not a pressing issue, just something from the back of my mind.
Has anyone managed to create a proper hexagonal tile grid with just the Tile Pattern COP? What I mean by "proper", is a pattern consisting of regular hexagons with gaps of equal width inbetween. Something like this [external-content.duckduckgo.com].
Loosely related thread from the past: https://www.sidefx.com/forum/topic/49509/ [www.sidefx.com]
Tile pattern COP: hex grid with regular hexes/gaps
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- ajz3d
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- Satoru
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- ajz3d
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- ajz3d
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I stumbled upon an old textbook from 1894 titled "The Anatomy of Pattern" by Lewis F. Day. There's a hint on page 85 that to properly tile a hexagonal pattern inside a square, the minimum number of hexagons should be equal to 7 in a row and 8 in a column (in a pointy-top orientation).
Let's take your Tile Pattern COP configuration and set:
We now have a tileable hexagonal grid with a minimum number of hexagons.
It can be extended with:
Where
We made it. Problem solved.
Let's take your Tile Pattern COP configuration and set:
headerbond_tilewidth = 1 / 3.5
headerbond_tileheight = 1 / 4
It can be extended with:
headerbond_tilewidth = 1 / (3.5 * ch("multiply"))
headerbond_tileheight = 1 / (4 * ch("multiply"))multiplyis an integer >= 1. This way we get a nice slider for increasing the density of the grid.We made it. Problem solved.
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- Mike_A
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- ajz3d
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I was too hasty to declare full success, because I've noticed an issue which I'm still unsure how to resolve. The pattern looks good when gaps between the hexagons are set to a modest value (Uniform Scale <= ca. 1.26). Once I get past this point, it becomes clearer to the eye that the gaps are uneven - diagonal ones are slightly thicker than vertical. At a
scaleof about 1.32 vertical gaps begin to fuse, while diagonal still remain visible.
Edited by ajz3d - 2025年3月24日 11:40:22
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- Aizatulin
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- ajz3d
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Interesting modification, Aizatulin. Gap widths are equal, and they can be modified with shape's "Radius" instead of the "Uniform Scale", which is a big improvement. Sadly, the pattern is not tileable. Or, should I rather say - while it can be tiled with arbitrary "Tile Width" values, it doesn't output regular hexagonal grid.
For instance, please enable the "Tile Vis: 3" and set "Tile Width" to 1.1667 (it is as close as I could get to seamlessly tile this modified pattern). Some rows will now contain irregular hexes. Depending on the "Tile Width", hexagons in these rows will be either squashed or stretched vertically.
With high enough hexgrid resolution and some additional math, this modified pattern could probably be cropped to a 7x8 area and resampled back to size_ref. This however would come with a quality loss and it would involve nodes other than just "Tile Pattern COP".
Hence, our ultimate quest for finding a way to create a seamlessly tiling hexagonal grid built from regular hexagons, using just the "Tile Pattern COP", continues.
For instance, please enable the "Tile Vis: 3" and set "Tile Width" to 1.1667 (it is as close as I could get to seamlessly tile this modified pattern). Some rows will now contain irregular hexes. Depending on the "Tile Width", hexagons in these rows will be either squashed or stretched vertically.
With high enough hexgrid resolution and some additional math, this modified pattern could probably be cropped to a 7x8 area and resampled back to size_ref. This however would come with a quality loss and it would involve nodes other than just "Tile Pattern COP".
Hence, our ultimate quest for finding a way to create a seamlessly tiling hexagonal grid built from regular hexagons, using just the "Tile Pattern COP", continues.
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- Mike_A
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- Aizatulin
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I had no succes without changing the resolution. If you change it to the sqrt(3) / 2 - ratio it seems to work, if you use the same ratio for tile_height / tile_width. I had to increase the scale to 16/9 and the radius needs to be smaller (between 0 and 0.75).
Edited by Aizatulin - 2025年3月25日 03:31:21
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- ajz3d
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Mike_AWell done, Mike! If there are minor distortions, I don't see them.
I think the best compromise - for me - is ajz3d's solution above with:
Shape > Stretch Shape = enabled
Size > Horizontal scale = cos (30)
Some minor distortion perhaps, but equal line widths I think - and it tiles.
It will make a great recipe.
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