Animation Nodes Rubik's Cube

Question

I am trying to create a Rubik's Cube using the Animation Nodes addon. The aim is to be able to make a specific sequence based on a custum group node system.

They could be a node for each individual action, like turn the top. (you are going to have the option to turn it left or right with a boolean option).

The main problem to solve is how do you know which cubes to move when you make an action? I solved this problem with no errors by making a custom group recognizing the layers depending on the positions of each cube.

This does work really well but the problem I currently have is I am not really used to use the an matrices. I tried to make a prototype in order to make the layer rotate around the center, but the problem is the animation seems to cumulate on each frame and you can't go back by returning to the first frame.

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If you could help me to find a solution for my non knowledge of the matrix system this would be really helpful.

Maybe the approach I am using to create this is not the most efficient one...

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Edit

I tried my best to fix the matrix problem and found an other approach which is parenting every cube of a face / layer to the center cube of the layer (unlike the real Rubik's, there is still a center cube in order to control mid layers).

I created this custom node group, and when I animate the rotation of a center cube after linking the correct cubes to it, it works well!

But if I try to make it a group and then put two one after the other, the animations get cumulated, and you have both of the rotation occuring at once. Also this make the rotation of the linked cubes happen a strange way, and I didn't figure out why.

I provided some text help in the blend file to help you understand the project without going through each individual node because the project is a little bit complex now.

Answer 1

Here is my solution:

(updated to v3.5)

How to Use:

-First, download and install Animation Nodes v1.6 from here.

-Open the file, DIY your own sramble and solution notation list in Text Editor.

-Tweak parameters on Settings node if needed, then play animation.

Advantages:

1. Use standard move notations to control moves.
2. Allow playback.
3. Solvable (any move is pre-calculated).
4. The whole cube is parented to a root object for additional transformation control.
5. With a few more additional features for convenience.

Basic Idea:

First, generate a sequenced euler list by the notations read from textblock(s) for each move.

Second, generate bool list for each unit to decide whether it should be rotated according to the notation during each move (e.g. when notation is U, it means only the top layer will be moved, while the mid layer and bottom layer will keep still).

For the unit objects, a custom property called Position ID is implemented, which indicates the exact position of each unit right before next move starts. After moving(rotating), the Position ID will be overwritten by a new one according to the new position.

[TBC..]

Answer 2

The principle I used here is the following:

• Filtering the cube list considering the frame range they need to move and the axis they correspond to
• Rotating this filtered list around this axis

The input

All cubes belong to an object group.

This group is used as input for the string of nodes which define each rotation.

A rotation is itself defined by:

• An axis: the axis is either (1,0,0), (0,1,0), (0,0,1) to indicate the corresponding positive faces, or (-1,0,0), (0,-1,0), (0,0,-1) for opposite faces
• A rotation orientation
• A frame which indicate the starting time for the rotation
• A duration

!Don't overlap the nodes triggering frame!

(note that this node corresponds to a loop subprogram but is not used as a loop as the objects are given as a list input)

Animation

• The animation begins with a filtering of the object list so that only the needed cubes are kept once the list is mask (it uses a 'mask list' node which is accessible with the search function)
• Then the corresponding rotation matrix is calculated and given as input to a 'rotate' subprogram

The rotation is calculated this way:

• We get either 90 or -90 degrees depending on the rotation orientation
• Then divide by the amount of frames for the movement
• This give a value "r" in degrees to be applied at each step/frame
• This value is used to multiply the input rotation vector, so that we have an equivalent to an Euler rotation (considering that this vector have to be one of the six indicated above). So the result can only be (r, 0, 0), (0, r, 0), (0, 0, r) or (-r, 0, 0), (0, -r, 0), (0, 0, -r).
• Once this calculation done, it is injected into a 'real' Euler rotation node

Filtering

• The filter calculates if the current frame is inside the correct range (bottom part)
• And calculates if the cubes are along the good axis (top part). This is done using a dot product which is positive if the wanted cubes locations are in the same side as the rotation axis
• The result is a list of boolean values which is used above to filter the overall cubes list

About the dot product node:

• This calculation assumes that the whole cube is centered and little cubes are separated at least by one unit

Rotation

The rotation itself is a simple matrix product.

Issues

The rotations are not always stable. Depending on the rotation speed, some cube may 'miss' (? I think) some rotation values.

I don't exactly know why: that may be some rounding issue (I don't really believe it) or other. I tried to avoid it using 'update object matrix' node (see above) but it is still not perfect... sometimes.

That could also be a bug because of the way I did it (a bug in my setting, I mean).

Using it easily

• Assign the group named 'group.002' in the input node
• AltA to trigger the animation
• Esc to stop it
• CtrlZ to come back to the initial state (and the group will come back to 'group.001' so that the cubes won't move on any change)

Note: the version of AN I'm using here is this one, which is not released yet. I've been reported that 'Mask list' node was not available in the last official release for now.