How can I make a hexagonal grill?

How can I make a hexagonal grill?

How can I make a hexagonal grill?

EDIT : I simply realised that I hadn’t included the .mix file for this (I had supposed to… why did no person point out it 😉 ) making it a complete lot of effort to duplicate it to make use of in your individual initiatives!

Anyway, right here it’s :

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I realise that there are already 4 solutions to this query however all of them tackle it by creating it as new geometry. I wished to supply a unique method through the use of a procedural texture to provide the looks of the grill. On this approach we solely want so as to add a single airplane – somewhat than geometry for every particular person cell of the grill.

Right here’s the ultimate end result :

Node Group external

Node Group internalsimple grid material

By utilizing the Edge Distance to combine between a Clear and Diffuse shader we are able to produce the next easy impact :

simple gridedge view ray passing through

For a extra convincing grid we have to add depth. For a ray to cross by the grill it will must cross by the ‘gap’ on the floor and out the corresponding gap on the opposite aspect. The depth of the grill will decide how perpendicular the ray should be to have the ability to cross by the floor. To realize this we are able to use two similar hexagonal grids – one to symbolize the ‘high’ floor of the grid and the second to symbolize the underside floor of the grid. The trail of every ray can then be decided by contemplating the way it interacts with every of these grids.

bottom grid offset calculation

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By ‘sliding’ the second grid to the aspect primarily based on the angle of the ray and the depth of the grill we are able to simulate the place it will be when the ray reaches the ‘backside’ of the grid. In a ‘actual’ grill the ray will solely cross by whether it is at a steep sufficient angle to cross by the highest and backside surfaces. The calculation of the place of the second grid will be performed as proven beneath :

colored regions

There are two components to this calculation. The primary half (high row) determines the route of the offset parallel to the floor. That is achieved with a pair of Cross Product nodes. The primary combines the Incoming ray with the Regular to generate a ray parallel with the floor however at right-angles to the incoming ray. The second Cross Product flips it across the Regular once more – by 90 levels – so it’s alongside the road of the incoming ray (however nonetheless parallel to the floor). The underside row of the calculation determines the magnitude of the required offset primarily based on the incoming angle (determines by way of the Dot Product with the Regular) and the set Thickness of the grill. The outcomes of those branches are Multiplied collectively to provide the required offset.

The next picture exhibits the attention-grabbing areas primarily based on the place it strikes the highest and backside grids.

simple hex grid with depth

The colours symbolize the next :

  1. White – The ray is near a high cell ‘edge’ and so has hit the highest floor of the grill
  2. Crimson – The passes by one cell on the floor however can be ‘out’ of a unique cell – ie, it will need to have hit the aspect of a cell.
  3. Inexperienced – The ray is near the cell ‘edge’ on exiting the grill and so has nonetheless hit the aspect of the cell (however virtually acquired by)
  4. Blue – The ray enters by one cell and exits by the corresponding cell within the different grid – ie, it’s handed during.

Shading the White area with one materials for the floor of the grill, Crimson and Inexperienced with one other for the perimeters of every ‘gap’, and Blue as Clear we get the next end result :

final material

The above materials does produce extra convincing outcomes – particularly in the way in which extra indirect angles lead to much less gentle passing by the grill – however the surfaces are nonetheless ‘flat’. To enhance this additional we are able to generate Normals primarily based on the place the grill is struck – ie, on an inside edge it is going to be angled parallel to the floor (perpendicular to the aspect of the ‘cell’) whereas on the highest floor (the sting of a cell) it is going to be nearer to the floor Regular. As well as, we are able to add a curve or bevel to the highest floor of the cells.

To realize this we are able to use the next materials :

final results

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Be aware the calculation of the Regular utilizing a mixture of the Cell Vector and 2nd Cell Vector to find out the route of the Regular of the corresponding cell wall. The Vector Rework node is used to remodel the calculated Regular (which will probably be in Object area) into World area as required for the Regular handed to the Shader.

And this produces the next outcomes :

suzanne_animated

The fabric can be utilized on extra difficult shapes – though, because it stands, care must be taken for the reason that calculated Regular for the internal edges and higher floor of the cells doesn’t take the precise floor regular under consideration (I’m certain this may very well be improved by tweaking the calculation however haven’t but had the possibility to look into it in a lot depth). Nevertheless, it nonetheless produces affordable outcomes as proven with this ‘wireframe’ Suzanne.

bad edges

Limitations

Be aware that the shading on the perimeters of the cells isn’t excellent – it may well produce odd outcomes with thick grills when seen at an indirect angle – the place the calculated regular is miscalculated because the unsuitable edge. That is as a result of ‘second nearest’ being the inaccurate cell to make use of for the angle of the ray and is tough to appropriate for as it’s depending on the ‘depth’ by the grill the place the ray hits the aspect. The issue is illustrated by this picture :

How can I make a hexagonal grill?

The result’s ample for this slight discrepancy to not be usually noticable but when anybody has any recommendations on a approach to tackle this then please do let me know! One potential answer is to calculate the depth on the level the ray hit the cell and to place a 3rd hex grid at that depth to find out which cell boundary is most related. Nevertheless, this may have an effect on effectivity because the hex grid is already fairly computationally intensive.

One other limitation is that at the moment the Regular calculation assumes that the floor is oriented within the X/Y airplane. For extra difficult surfaces (similar to Suzanne), this isn’t at all times the case and the calculated normals might produce odd outcomes (similar to when seen from behind). That is usually not noticable however can lead to incorrect lighting and/or incorrect reflections – particularly on the ‘inside’ surfaces of the cells. Additionally, this implies it’s not appropriate to UV unwrapped meshes (keep on with Generated or displaced Object coordinates).

Be aware additionally that nodes that generate the hexagon sample require constructive X/Y coordinates solely. When utilizing Object coordinates (or some other coordinates that might lead to adverse values), use a Mapping node to shift the coordinates an acceptable quantity to ensure they’re at all times constructive.

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