Comment on Central Design by pillemaster
yea a tiny overlap remaining. I stretched the triangle a bit into shape, using Julian n=1, distance >1.
Yes, julian gives a slightly different shape (same as smartcrop and smartshape). I wanted to "fix" this in smartcrop2/smartshape2 but proper implementation of smartshape2 is tricky.
has poincare/hypershift any advantage? ... I have no clue how to use it...
Hypertile is basically a poincare with pre-calculated offsets, and hypershift is a simplified poincare. So all three mathematically do the same thing.
Try this:
1. Make a vertical line. for example, square with post transformation x:0, y:2.
2. Add a chained hypershift to this line. With default shift value 0.1 you will get a curve like this: (
3. Add a chained hypertile2 to hypershift, and link it back to itself to get a hypertile pattern. Set p:4, q: 6 in parameters.
4. Try changing shift value on hypershift. You will see that the lines align at some values. For example, for p:4, q: 6 hypertile these values are ~0.318, ~0.577, ~0.757 and so on.
Hypertile (plain hypertile, not hypertile2) with p:4, q:6, n:0 will give you the same result as 0.577 hypershift.
So, these hypershift offsets are the coordinates at which hyperbolic tiles align. Knowing this you can tile anything without overlapping.
Here's an example: Hyper. First example just tiles the squares using single hypershift. Second example uses hypershift > crop > hypershift trick to crop the triangle in a hyperbolic way.
There is a way to calculate the exact hypershift offset values, but I don't remember how it's done, and don't really want to investigate it now. You can try to calculate it yourself, or ask Zueuk. He will know for sure.
Try this:
1. Make a vertical line. for example, square with post transformation x:0, y:2.
2. Add a chained hypershift to this line. With default shift value 0.1 you will get a curve like this: (
3. Add a chained hypertile2 to hypershift, and link it back to itself to get a hypertile pattern. Set p:4, q: 6 in parameters.
4. Try changing shift value on hypershift. You will see that the lines align at some values. For example, for p:4, q: 6 hypertile these values are ~0.318, ~0.577, ~0.757 and so on.
Hypertile (plain hypertile, not hypertile2) with p:4, q:6, n:0 will give you the same result as 0.577 hypershift.
So, these hypershift offsets are the coordinates at which hyperbolic tiles align. Knowing this you can tile anything without overlapping.
Here's an example: Hyper. First example just tiles the squares using single hypershift. Second example uses hypershift > crop > hypershift trick to crop the triangle in a hyperbolic way.
There is a way to calculate the exact hypershift offset values, but I don't remember how it's done, and don't really want to investigate it now. You can try to calculate it yourself, or ask Zueuk. He will know for sure.
Thank you very much for the detailled discribtion... wad a little bit difficult to understand but the examples were very enlightening! Unfortunately one still needs to crop off some overlap... but there should be a way to make a plugin that could do the job for us.... and fit a planar ngon into hyperbolic geometry...
You don't need to crop anything if you align the tiles in hyperbolic plane from the beginning. Like in the first example.
Spidron in The Simple One is done this way, and there's no cropping. Parameters are available in Polled flamepack v2 if yo want to have a look.
As for the transformation that will "do the job for us", smartshape2 is the one. There are some issues with it though that cannot be solved in apophysis/chaotica approach, so I will release it only in my editor.
Spidron in The Simple One is done this way, and there's no cropping. Parameters are available in Polled flamepack v2 if yo want to have a look.
As for the transformation that will "do the job for us", smartshape2 is the one. There are some issues with it though that cannot be solved in apophysis/chaotica approach, so I will release it only in my editor.