The purpose of this project is to develop an algorithm to manipulate and solve a 3x3 Rubiks cube as quickly and efficiently as possible using javascript. The p5.js library is being used to display the cube.
* create cube as an object
* permutate cube given input
* represent cube in two dimensions
* check state of cube
* reset cube
* scramble cube
* setup html site with inputs, outputs, formatting
* efficiency and speed not goal here
* given any random scramble, find permuation sequence which will return cube to solved state
* modify basic case to emulate Friedrich's Method (CFOP)
* maybe implement Reduction Method
* maybe implement Petrus Method
At least for the inital implementation of this case, each cube is an object so multiple variations can be followed in future steps. Each cube is simply represented as a one-dimensional 54 element array in the format:
[ U1, U2, U3... U8, L1,... F1,... R1,... B1, ..., D1,...]
Here, the faces are represented by
- U = upper face
- L = left face
- F = front face
- R = right face
- B = back face
- D = lower face (down)
The cube visualized as follows, where each values represents the cube object's corresponding array indice:
| - | U | - | - |
|---|---|---|---|
| L | F | R | B |
| - | D | - | - |
| - | - | - | 0 | 1 | 2 | - | - | - | - | - | - |
|---|---|---|---|---|---|---|---|---|---|---|---|
| - | - | - | 3 | 4 | 5 | - | - | - | - | - | - |
| - | - | - | 6 | 7 | 8 | - | - | - | - | - | - |
| 9 | 10 | 11 | 18 | 19 | 20 | 27 | 28 | 29 | 36 | 37 | 38 |
| 12 | 13 | 14 | 21 | 22 | 23 | 30 | 31 | 32 | 39 | 40 | 41 |
| 15 | 16 | 17 | 24 | 25 | 26 | 33 | 34 | 35 | 42 | 43 | 44 |
| - | - | - | 45 | 46 | 47 | - | - | - | - | - | - |
| - | - | - | 48 | 49 | 50 | - | - | - | - | - | - |
| - | - | - | 51 | 52 | 53 | - | - | - | - | - | - |
A canonical cycle notations is used to define each clockwise permutation.
To turn a face counter-clockwise, the permutation cycle is simply reversed.
Therefore, each face turn can be described by five four-mode cycle permutations of the cube elements:
- u: [[0,2,8,6], [1,5,7,3], [38,29,20,11], [37,28,19,10], [36,27,18,9]]
- l: [[9,11,17,15], [10,14,16,12], [0,18,45,44], [3,21,48,41], [6,24,51,38]]
- f: [[18,20,26,24], [19,23,25,21], [6,27,47,17], [7,30,46,14], [8,33,45,11]]
- r: [[27,29,35,33], [28,32,34,30], [8,36,53,26], [5,39,50,23], [2,42,47,20]]
- b: [[36,38,44,42], [37,41,43,39], [2,9,51,35], [1,12,52,32], [0,15,53,29]]
- d: [[45,47,53,51], [46,50,52,51], [24,33,42,15], [25,34,43,16], [26,35,44,17]]
The Cube.js prototype class is used to define a cube as an object. This class handle basic cube manipulations including:
- perm() - this method accepts an input permutation sequence from the user and performs the permutations on the cube in order
- checkState() - this method tests to see if the cube is in a solved state
- show() - displays cube in 2d format on canvas
- scramble() - scrambles cube with randomly generated sequence