Randomize Curve handles (position and rotation) on Mesh Faces

Question

I'm looking for a way to generate a 3D jigsaw puzzle with random pieces using only nodes. It should be scalable and accept various mesh as input: Grid, plane, cube, spheres, cones, custom mesh. Pieces should be able to be created for quads, triangles, or ngons.

The workflow would be as follows:

1. Instance mesh
2. Convert faces to curves
3. Subdivide curves (to 2 control points with handles)
4. Move/Adjust only the non corner curve points /handles towards face center.
5. Rotate individual curve handles to randomly create a unique piece shape on each face.

I have started putting together a node tree for this task, but so far I haven't been able to figure out to move individual control points and rotate handle on the face geometry (polygon) underneath.

See images for details.

Here the blender file for those who are wondering what I have done so far. Slide the scale on the curve handle values. I wanted to have the scale change the handles following the face normals or lines.

the lines help randomize the puzzle pieces since it uses a nearest node and the algorithm has to decide randomly which face is the nearest.

The results should look like the following:

Scalable and flexible.

Answer 1

To be honest, the task is not quite trivial to solve and requires a relatively high number of nodes.

However, the result is quite respectable:

Here I use the following node tree:

The difficulty here lies in the selection of the right points, and in the topology of the mesh.

Briefly explained I do the following:

1. First I subdivide the cube with Subdivide Mesh into the desired number of subdivisions and capture with Capture Attribute the position and index of the resulting edges. These values will be needed later.

2. Then I instantiate simple curves at the edge centers, which consist of two points each, and move these curve points with Set Position to the endpoints of the edges.

   This step is crucial, because none of the other methods, e.g. with Split Edges or similar, gives the possibility to select the single points later comfortably. In addition, this way I avoid duplicate edges.

3. By instantiating curves here, I then have the possibility to select the middle point as well as the inner points with Endpoint Selection. This is especially helpful, because the curve points should be moved individually for each spline/edge.

4. But instead of dividing the curves with two intermediate points as in your example, I divide them three times here. This gives me a better selection possibility and I don't have to move the curve handles complicatedly in any directions, but I can reach the biggest part directly by moving the curve points.

   The points are moved here according to the following principle:

   • The position of the center point of each curve is randomly shifted a little, and then the closest face center point of the original mesh is used as the direction and scaled.
   • The intermediate points of the curve are shifted a little in the direction of the edge center. Just change the Seed value of the node Random Value to get different results.

   This way I get a good basic shape.

5. In the last step these curves are converted into Bezier curves and the handles are smoothed.

   Finally, the handles of the center curve point are scaled out a little more, so that a teardrop-like shape is created.

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I have no idea what you want to do with this thing, but I hope this suggested solution helps you a bit.

The funny thing about this setup is that you can actually apply it to any mesh, even a simple Ico Sphere for example:

Here is the blend file, have fun!

_{(Blender 3.2+)}