Polar ZBLL Recognition

This recognition method is based around finding the L/R (or F/B) stickers, the stickers of the opposite sides (and so the name Polar). The idea for this recognition method came soon after the development of NMLL. It is part of the natural lineage of the opposite stickers concept seen in ATCRM, NMCLL, NMLL, MI2, and Polar Last Slot. Originally the idea was to use NMCLL recognition, but with the development of ATCRM this recognition method has been improved. This can be said to be related to Tv2 recognition since both have a step that involves looking for opposite edges.

Advantages

Works well for prediction.
Makes fast pseudo ZBLL recognition possible. The last layer can be easily recognized when non-matching blocks were used in the F2L (NMZBLL), when a U layer pair was placed in a slot (CZBLL), or even a combination of the two (NMCZBLL). An interesting property is that the edge from the F2L on the U layer in these pseudo situations has a different color on top and makes finding the two edges even easier.
No need for a specific AUF position, reference corner, or reference sticker for recognition.

Disadvantages

Requires learning two patterns per CLL case.

Step 1: ATCRM

The first step is to recognize the ATCRM case. ATCRM consists of two steps. The first is to find the orientation of the L/R (or F/B) stickers of the corners. The second step is to check two predetermined sticker locations. After that you know the full CLL case.

ATCRM Step 1

Find the orientation of the L/R stickers on the corners. In the example image the orientation of the red and orange stickers is shown.

You can also check the F/B stickers instead.

ATCRM Step 2

Check two predetermined sticker locations. In the example image the UBL and FUL stickers are checked. After this the full CLL case is known.

Step 2: Opposite Edges

Find the location of the L/R edges. If the F/B orientation was found for the corners during the first step, then find the F/B edges. The corner L/R orientation already contains built in corner permutation information, so the location of the edges is all that is needed to finish determination of the last layer case.

NMZBLL, CZBLL, and NMCZBLL Visualized

Pair can be built into EOXCross or starting steps of other methods.

NMZBLL

Setup: R

CZBLL

Setup: U' R

NMCZBLL Example 1

Setup: R U' R'

NMCZBLL Example 2

Setup: R U2 R'

Techniques

Using the ZZ method as an example, the edge placed at DR can be any edge from the right side layer. The same applies to other edges on the bottom layer. From here, there are several options.

Complete Block - ZBLL and NMZBLL

Solve two pairs around the edge to from a complete block, matching or non-matching.

Normal Block

1. Any edge

2. Pair 1

3. Pair 2

4. Align

Non-Matching Block

1. Any edge

2. Pair 1

3. Pair 2

U Layer Pair - CZBLL

Solve a pair that belongs with the edge, add a U layer pair above the 1x2x2, then move to the bottom two layers.

1. Any edge

2. Pair 1

3. U layer pair

4. Align

U Layer Pair + Non-Matching Block

A U layer pair can be added such that, after ZBLL and moving the U layer pair back to the U layer, the right side block is non-matching.

Example 1 - Setup = U' R' U2 R

1. Any edge

2. Adjacent pair

3. Adjacent pair from U layer

4. Align

Example 2 - Setup = R U' R'

1. Any edge

2. Pair 1

3. U layer pair

Offset Pair

A more advanced technique is to add a pair above the edge then perform a turn of the layer. This creates an offset pair slot. This pair can be solved using algorithms from LXS.

Normal Block

1. Any edge

2. Pair opposite to edge

3. Align

4. Offset pair

CZBLL

1. Any edge

2. U layer pair

3. Align

4. Offset pair

Front and Back Layer Use

With CZBLL, a U layer pair doesn't always have to be placed into the L or R layer. It can also be moved to the front or back then a turn of that layer is performed. This is useful when the U layer pair is facing a different direction from desired when attempting to use a turn of L or R to place the pair. Although there is now a misoriented edge on the U layer, relative to the starting orientation, it doesn't affect the ZBLL algorithm. This technique is easiest when implemented into the final slot, but can also be used earlier in the solve depending on the locations of other edges. It is also possible to combine the use of the front and back layer with the pair techniques above.

1. Counter-clockwise pair, move above R layer

2. Align

1. Clockwise pair, move above F layer

2. Align

Other Considerations

ATCRM could also be used with the techniques of some other recognition methods. Such as BH and recognizing the two edges around a corner. This recognition method and Tv2 are already related, but the edges of Tran V1 style could also be used. This may also have some value for 1LLL recognition, where the steps would be ATCRM then finding the two edges and the overall edge orientation. But that hasn't yet been looked into or compared against other recognition methods since 1LLL isn't commonly used.