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I'm working on an augmented reality rubik's cube solving project. We want the user to be able to use an smartphone application for collecting hints on to solving a rubiks cube.

For this we need to rebuild the cube in the smartphone memory. We were unable to find scanning algorithms which can rebuild a rubik's cube with only scanning ONE side of the cube.

Does somebody know a rubik's cube scanning algorithm which can do this, or could at least mention if this algorithm could be mathematically possible?

Wouter
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    You're asking if you can conclude the full state of the cube just from the state of one face? No, you can't. – avishayp Nov 13 '12 at 09:11
  • Avip's definition is correct. What number of faces would be necessary for defining the full state? – Wouter Nov 13 '12 at 09:14

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there's no way you can deduce the cubic's position after scanning only one side. most solvers scan all 6 sides, though, you might get away with scanning only 5 of them, but i really doubt it.

in other words, you need only 5 scans to prove the cube is completely solved. not sure if 5 scans give you enough information to recreate the full state for any random cube position.

lenik
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    The "no way" is easily provable. Scan a single cube side. Now turn the side opposite 90 degrees. Scan the same cube side again, it is identical. As for "is five side enough", the only cubelet you don't know the exact state of is the center cubelet, but as its orientation is moot, you can recreate the state of the corner and probably side cubelets (you have full info for the corners, since you know 4 fully and have all-but-one side for the remaining 4; you could have a situation where you have a choice of side cubelets, but you would know if you have full info or not). – Vatine Nov 13 '12 at 10:24
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    @Vatine You need to scan all 6 sides. With only 5 sides scanned, there are 4 edge cubelets which are half hidden on the side you cannot see; if the half you can see have all white sides (for example) then you have no knowledge of which permutation of colours are on the hidden side so you cannot determine where all the edges are. – MT0 Jun 15 '22 at 20:59
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You might wanna check this for grabing all edges within a scaned pic.

http://www.codeproject.com/Articles/93642/Canny-Edge-Detection-in-C

This is a problem being solved with Hough transformation using matrix.

On the other side, you have to compare those 2 images to detect color of each field.

Gustav Klimt
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I don't know what is cube scanning algorithm. But you are talking about algorithm which finds, is cube solved or not?

To check this you need to scan four sides of the cube out of 6( Only for 3 by 3 cube) Even, you have to select 4 side like in manner that remaining 2 side must be beside of each other.( Remaining sides shouldn't be opposite to each other)

As I'm also cuber. And doing cubing since 5 years. I can guarantee you the above scanning is optimal.

AAYUSH CUBING
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  • No, this does not work. You always have to scan 5 sides. For example if you do not scan the F and the R face (which are not opposite to each other), you can exchange the UF and UR edge and exchange the DF and DR edge and the other 4 faces still are solved. Generator for this position is R2 U' F2 R2 F2 U2 R2 F2 R2 U' R. If the two faces you do not scan are opposite like the F and B face, an exchange of the UF and UB edge and the exchange of the DF and DB edge shows that this does not work either. Generator here: L2 R2 D2 L2 R2 U2 – Herbert Kociemba May 27 '22 at 07:46
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    @HerbertKociemba Why only 5 sides? If you do not scan the U face and the UF, UL, UR and UB faces are all in place (in some order) but flipped so that you can only see the U facelet on the five scanned sides then you cannot determine what the permutation of edge cubelet positions is. Generator: `M U M U M U2 M' U M' U M' U2 S U S U S U2 S' U S' U S' U2` – MT0 Jun 15 '22 at 21:15
  • @MT0 Yes you are right. B2 F' D L' D' B2 F R' F' U F R is I suppose the shortest generator for a position of this kind. – Herbert Kociemba Jun 17 '22 at 07:21