The goal is to produce tiles resembling natural stone paving, with parameters adjusted to allow quality CNC production, which means no sharp angles, no short edges, no 4-way intersections, consistent adjustable seams, ability to create varistions.
Standard out of the box Voronoi Diagram does not satisfy these constraints as it generates unacceptable issues with not much control over them. You can see a 4-way intersection as well as micro edges appear at random places with Voronoi generation on surface.
Instead, I developed a multi-step workflow using Kangaroo. The process began with a TriRemesh-based mesh to establish clean topology and eliminate 4-way intersections by design.
Voronoi cells were then introduced as soft attractors rather than direct geometry, allowing controlled irregularity by influencing vertex positions through collision goals.
The simulation was executed in two stages. An initial relaxation phase stabilized the mesh using averaged target values for area and constrained angle limits. This was followed by a secondary relaxation phase, where additional goals were applied to meet precise fabrication constraints while maintaining the desired level of non-uniformity.
The result is a production-ready tiling system that balances natural variation with strict fabrication requirements and is proven stable on the set of different boundary conditions.
Very nice!
If I had to nitpick, real crazed paving has more tile and joint size variation, and less concavity. Avoiding this would probably break your “no 4-ways” rule though, so it’s a matter of taste really.
A cheeky question, which people in the trade might be better suited than me to answer:
Is this cheaper than the traditional method?
A pile of random stones, already flat-faced but jagged, which are then chiselled and cut to fit on site.
vs:
A pile of larger flat-faced slabs, which a packing algorithm fills with calculated shapes to be cut by CNC, marked with an ID# and then fit together on site.
My intuition is that an experienced flooring mason will generate less wastage but take longer, while the computer version will be quicker with more wastage (and also include capital costs for the CNC machine, and processing overheads). Putting figures to that is tricky.
From a grasshopper perspective it is an interesting project.
I assume this is a wall finish. If this is a real world project I can see a few hurdles:
There are products on the market following this idea, but most use a cheaper material to save costs. Some of these products do not require the skills of a mason to install, so the benefit is they go up quicker with one less trade. None of them look anywhere near as nice as what a skilled stone mason can create.
If you are trying to compete with a stone mason using the same materials I am not sure you have not saved a lot when you go thru all the steps to produce parts you can sell.
Waste will be a major factor in the cost here.
I am not sure how you plan to create the blanks for each tile. Maybe you hope to find someone to send you flat blanks to start. If not, the reality of cutting the raw product into something that can be cut into the shapes you show will be difficult. Fixturing irregular materials is not easy, and will really reduce the production of your CNC. Even with robots you will find it difficult with small parts. Human hands work much better since you have two that are controlled by a brain.
Most find the stone finish appealing because of the natural look when it is done. If your product ends up looking like a tile after install I am not sure it will appeal to most in this market.
I see you can customize the shapes, but that will slow down CNC production a lot and lead to a packaging nightmare.
Your joints are likely going to stand out like a sore thumb to a trained eye. If you made them more like a basket weave pattern they will look better, but that will lead to a huge production problem.
Thinking about it, if you’re using CNC to cut the tiles from a large slab, why bother cutting all the way through? Just rout out the “joints” and fill them back in with mortar afterwards. Add in some jitter to the outlines to make it look more handmade and nobody will ever know…
Partial cuts will be very slow. The most likely machine to use for this would be a water jet. That cuts thru. Partial cuts are possible with a diamond bit router, but they could become a problem for fixtures as well if you have any small parts. A CNC like that applies a force to the part when it cuts, and as a result you must hold the part much better. This type of cut will expose any of those fine cracks, and can make you end product brittle and prone to break.
Large pieces like this create some other problems. They are far more expensive, and very costly to install. We had one client putting in 48” square stone floor tiles. In Canada, it cost $400 to install each tile. Your average stone mason is going to want parts to be no more than 100lb or so.
Probably the best examples of this type of machine used in practice will be those cutting kitchen counter tops. The glass cutting industry uses a lot of CNC as well, and it will be very similar.
