Rotate and scale instances on points from instanced curves based on float curve. AKA Instanception

Question

I have a shape that is popping up in my dreams :) And I've decided to model it. Of course it does not consist of some cones as in the image attached. However, I found this describes my problem better than the original geometry itself.

Now I have a primitive cone to instance on the points.

And I would like to create vertex in the geometry node, that will be positioned to shape like a rugby ball with diamond meshes lets say like the example that I modelled by hand in Image-1.

I would like to do this instancing work on geometry nodes and god I am trying that for the last two days.

I can create it as a cylinder. I do that by adding a curve circle primitive which is instanced on vertex of a mesh line primitive. I rotate curve circles on each step with a value according to the resolution of the circle, to get the result you see in the Image-2. I do that by using the geometry nodes in Image-3.

Then I realize these intances which I will use as points for the second instancing, which will instance ico-cones like in this example. I do that by nodes in Image-4.

I get the result in Image-5.

Image1-5:

At this point to go on further for the desired result, I tried several ways to scale both the circles and instanced ico-cones together. Because in the end, I want circles to be wider, and instances to be scaled up to fill that wider circles.

However, only way I have managed to do so was to instance ico-cones on the circle first, then instance the ico-cone rings on mesh line vertex. And manage the scale on the second instancing by scaling individual rings. Here I do the scaling controlled by a float curve, because I would like to expand the posibilities to different shapes than a rugby ball as well. Geometry nodes on Image-6

Result on Image-7

I seem successful until this step.

Now is the step to rotate these instanced cones, to align on the imaginative normals that are going outwards from this imaginative rugby balls vertex, so that they will face outwards. However, whatever I try, I could not manage to do so. The result I desire is in Image-8 made in modelling.

Also, since I already mentioned that I would like to extend the possibilities of a shape other than a rugby ball, I also desire the result in Image-9 (Embedded in Image-8 Above) -->All instanced ico-cones pointing outwards from pot shape created based on float curve. Done in modelling

However, while I can see that a scale is possible to control with float curve, I doubt I can convert this data and use for rotation for a float curve like in the Image-9.

I appreciate a lot even if you only read it :) Sorry for the long post.

Second Part of the question: First of all thank you very much for your efforts guys.

Now I would like to change how I require to build the shape as "non-manifold". Because, it is hard to work with 4 vertex base, and it causes my instanced geometry to be scaled unevenly.

I would like to instance heads on the diamond mesh. And all of the heads should look in the direction of the normal of their instanced diamond surface. After the instancing done, I am going to realize and boolean instances.

Hence, I tried: Diamond mesh nodes from answer, and followed by nodes below: Getting the result:

Tweaking the "Align Euler to Vector" node I get the result below:

As you see, when I select the pivot as "auto" I get the alignment of y axis of heads with the normals of diaamond faces. However, it also rotates the heads around face normal.

I infer, Blender constructs local coordinate system for each point created from diamond faces. However while Z axis of coordinate systems aligns with diamond face's normal going outwards from face, there is no limitation for X and Y axes.

So how do i make it so that the head's do not rotate around its Y axis, which is also aligned with diamond face's normal?

In other words, geometrically the YZ plane of the head should be defined with center line(Global z axis) and the instance point on the diamond face.

Answer 1

Diamond tube

• To make a diamond-lattice mesh in XY, you can instance a 4-sided Mesh-Circle on the edges of a Mesh Grid.
• You can deform the mesh in XY to a tube, Z-up, as shown in the lower illustration, below:

Once the fiddly arithmetic is done to make everything fit, it can be merged to a contiguous mesh.

Map instances to quads

• A Tile object is imported , which occupies the XY unit square in its own object space, with its origin at (min X, min Y)
• A small subgroup collects the ordered face-corner positions per-face of the substrate.
• The corner-positions are each transferred by face-index to duplicated instances of the tile-object. (Substrate Face Index <-> Duplicate Index)
• Once the realized tile instances know where the corners (P0-P3) of their containing quad-faces are, they can be mapped in XY to their faces, by bilinear interpolation, using the original XY locations in the unit square as factors along the edges of the faces:

(above, the original XYs come in on the Vector input)

We now have instances deformed to their quads, squashed flat in Z. They also know the Normal and Face Area of the quads they occupy.

• The instance-vertices are un-flattened, by being offset along the normals of their underlying quads, scaled by their original Z.
• The offset is further scaled by the square-root of the underlying face-area, to keep the tile depths in linear proportion to their widths and heights.

The tree below groups that up in 'Tile Quads'. The rest of the tree creates the diamond tube substrate, and provides for its deformation in Z, using a Float Curve node:

With this sort of result:

_{(Blender 3.4.1+)}