How to expand/inflate shapes with collision?

[Imonobor]

Hello!

 I have this grid of dots that I want to expand, so they take up all the white space between them, while not colliding into eachother (which means they won't be circles anymore, but weird hexagon-ish shapes, depending on how many neighbors they have, except the outermost circles that would still be circles on the outside, albeit bigger ones). Kinda similar to what Substance Painter does with unused parts of the texture, so there are no seams around the edges, but in vector.

Basically divide the white space to the objects evenly, while keeping them separate objects, so I can color them differently and make a mosaic.

Does anyone know what this "technique" is called so I can search it better or know a way to achieve it in Designer?

 

Thanks in advance!

[GarryP]

I would be pleasantly surprised if you can do this with the Affinity applications.

It’s the “while not colliding into each other” part which is the most difficult bit, meaning that the software will need to do geometrical calculations on each shape, taking the geometries of the surrounding shapes into consideration, and modify each shape accordingly.

This may be possible with a combination of functionalities, probably with rasterisation (not vector), but I’m fairly sure that it can’t be done without a lot of manual effort.

[Imonobor]

@GarryP Well, it doesn't have to be calculated in such a caveman way. It could be an algorithm that calculates where the "seams" between these objects (or even just the centerpoints of the objects, they don't have to be seen as circles, just points) are and split a larger circle shape by these seams. I just don't know if such an algorithm exists or is possible to do in the program.

[GarryP]

I’m not quite sure what you mean by “caveman way” but, if I have understood your requirements correctly, lots of very specific complex vector calculations will need to be made and I don’t think the Affinity software can do what you want it to do. (I’d be happy to learn otherwise.)

There may be other software out there that will do it but I don’t know what you could search for to find it.

[NotMyFault]

Maybe this pattern?

Only bitmap, may use an tracing app to vectorize.

Recipe:

1. add Gaussian blur, radius px size of circles as starting point
2. add Gaussian blur, set blend mode to difference, 0.1px radius
3.  Add levels adjustment, set white level to about 1%
4. add threshold adjustment, adjust to taste

circle pattern.afphoto

[NotMyFault]

Honest question: how did you create the circle pattern? Can you share the .afphoto file?

 

[MEB]

Hi @Imonobor,
No, there's no way to do this in Affinity dinamically. Actually as far as I'm aware no 2d illustration vector software is able to do what you want. You have more chances to find this type of function on a 3d based software then on a vector based illustration app. You can however draw an hexagonal grid from scratch in Designer and eventually use a custom grid to help you snap the hexagons in place as you see fit.

[Imonobor]

@NotMyFault Sorry, I need it to be this precise pattern. I did it mostly with geometry and maths - made a line of dots, spaced them evenly and started duplicating and rotating some of them, ended up with this. I've attached the file if you want it.

@MEB Thanks for the answer, I'll look into doing this kind of thing in blender. Is it possible to import the vertex "vectors" from planes in blender back to curves in Affinity Designer?

 

Also, the thing I'm trying to do is called Voronoi Diagram apparently - https://en.wikipedia.org/wiki/Voronoi_diagram

Circle.afdesign

[Pšenda]

22 minutes ago, Imonobor said:

Also, the thing I'm trying to do is called Voronoi Diagram apparently

https://affinity.help/photo/English.lproj/pages/Filters/filter_voronoi.html

[Imonobor]

34 minutes ago, Pšenda said:

https://affinity.help/photo/English.lproj/pages/Filters/filter_voronoi.html

Sadly, that's just a filter that generates cells at random, not a real Voronoi generator. This is how it's supposed to be generated, from points, not a raster image:

[Old Bruce]

9 hours ago, Imonobor said:

Does anyone know what this "technique" is called so I can search it better or know a way to achieve it in Designer?

I think what you are after is a packing problem. My math/geometry skills have atrophied to the point of uselessness. The centre dot would be a hexagon because of the six surrounding dots. The six would be ... this is where I fail, there are ten dots outside ... so maybe pentagons for the six dots or 3 + 4 or 3 + 2? I just can't recall how to do this. 

Each larger radius would be composed of polygons which fit side by side for the circles and inner radius and outer radius number of sides would need to fit with the number of dots in those circles. I think it is easy once you understand the packing.

[Alfred]

2 hours ago, Old Bruce said:

I think what you are after is a packing problem. My math/geometry skills have atrophied to the point of uselessness. The centre dot would be a hexagon because of the six surrounding dots. The six would be ... this is where I fail, there are ten dots outside ... so maybe pentagons for the six dots or 3 + 4 or 3 + 2? I just can't recall how to do this.

Why would you switch from hexagons to pentagons, instead of using hexagons throughout (like bees do for their honeycombs)? One hexagon is surrounded by a ring of six hexagons, a ring of six is surrounded by a ring of twelve, and so one on.

Edited July 27, 2022 by Alfred
Corrected typo.

[Imonobor]

I found a couple of videos and scripts that generate real Voronoi patterns from points, but they are all for Adobe Illustrator. Guess I'll use that then.

@Old Bruce @Alfred The pattern I have is not "regular" at all - the points are placed seemingly randomly (athough I did follow certain mathematical calculations), so the end result won't have any regular hexagons or pentagons, besides the central one. I'll post it here once (and if I'm able to) I make it. But doing this manually is just not something a sane person would try to do.

[Old Bruce]

17 minutes ago, Alfred said:

Why would you switch from hexagons to pentagons, instead of using hexagons throughout (like bees do for their honeycombs)? One hexagon is surrounded by a ring of six hexagons, a ring of six is surrounded by a ring of twelve, and so one.

Because of the drawing in the first post, centre, then a ring of six then a ring of 10.

[Pšenda]

26 minutes ago, Old Bruce said:

Because of the drawing in the first post, centre, then a ring of six then a ring of 10.

 

??? I see 12 of them!

[Old Bruce]

24 minutes ago, Pšenda said:

??? I see 12 of them!

Right. I was wrong. But we cannot have a series of dots in circles that match a Hexagonal grid. Distance across the flats versus across the points. This is tiling the plain  or packing problem.

[v_kyr]

14 hours ago, Imonobor said:

Does anyone know what this "technique" is called so I can search it better or know a way to achieve it in Designer?

I think it's called Circle Packing !

• Circle packing theorem

See related:

• Circular Packing
• Basic Circle Packing Chart
• Packing circles in a circle
• Position N circles of different radii inside a larger circle without overlapping
• Circle Packing Using Stochastic Search
• circlepacking (GitHub)
• ... etc.
  
   
• Controlled circle packing with Python

[Imonobor]

Okay of all the places, I found a perfectly-working Voronoi Diagram Generator that was built into Inkscape. Open source software never ceases to amaze me.

This is exactly the result I was looking for. Thanks for all the input everyone!