From 0c49ed5afc2ae9e4bc4aa1af9c655bbe1f3d14b8 Mon Sep 17 00:00:00 2001
From: Sebastiano Tronto <sebastiano@tronto.net>
Date: Sun, 22 Oct 2023 14:48:42 +0200
Subject: Small change of plans, moved stuff around

---
 doc/CUBE_INTERNAL.md   | 24 ++++++++++++++++++++++++
 doc/CUBE_TEXT.md       | 37 +++++++++++++++++++++++++++++++++++++
 doc/TRANSFORMATIONS.md | 23 +++++++++++++++++++++++
 3 files changed, 84 insertions(+)
 create mode 100644 doc/CUBE_INTERNAL.md
 create mode 100644 doc/CUBE_TEXT.md
 create mode 100644 doc/TRANSFORMATIONS.md

(limited to 'doc')

diff --git a/doc/CUBE_INTERNAL.md b/doc/CUBE_INTERNAL.md
new file mode 100644
index 0000000..fd3148a
--- /dev/null
+++ b/doc/CUBE_INTERNAL.md
@@ -0,0 +1,24 @@
+# Internal representation of the cube
+
+The plan (TODO) is to have multiple implementations: some that
+take advantage of advanced CPU instructions (SIMD) and a fallback
+"array" representation that works on any architecture.
+
+# Array representation (fallback)
+
+In this implementation of the cube.h interface, the cube is represented
+by two arrays of 8-bit unsigned integers, one for centers and one for
+corners.  The 4 leas-significant digits of each bit determine the piece,
+the other 4 are used for orientation or kept to 0.
+
+Edges:
+        xxxopppp (x = unused, o = orientation, p = piece)
+
+Corners:
+        xooxpppp (x = unused, o = orientation, p = piece)
+
+The two bits for CO are shifted to make it possible to perform mod 3
+operations (sum, inverse) using only addition and bitwise operators.
+See below for details.
+
+The third bit is needed because x+y+1 can exceed 4.
diff --git a/doc/CUBE_TEXT.md b/doc/CUBE_TEXT.md
new file mode 100644
index 0000000..b9234fc
--- /dev/null
+++ b/doc/CUBE_TEXT.md
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+# Textual representation of the cube
+
+The functions readcube() and writecube() use different formats to read
+and write a cube to text. Not all formats are supported for both input
+and output.
+
+## H48 - standard format for h48 (read, write)
+
+Each edge is represented by two letters denoting the sides it belongs to
+and one number denoting its orientation (0 oriented, 1 mis-oriented).
+Similarly, each corner is represented by three letters and a number
+(0 oriented, 1 twisted clockwise, 2 twisted counter-clockwise).
+Edge orientation is relative to the F / B axis, corner orientation is
+relative to the U / D axis.
+
+The pieces are ordered such that the solved cube looks like this:
+
+UF0 UB0 DB0 DF0 UR0 UL0 DL0 DR0 FR0 FL0 BL0 BR0
+UFR0 UBL0 DFL0 DBR0 UFL0 UBR0 DFR0 DBL0
+
+Whitespace (including newlines) between pieces is ignored when reading
+the cube, and a single whitespace character is added between pieces
+when writing.
+
+The cube after the moves R'U'F looks like this:
+
+FL1 BR0 DB0 UR1 UF0 UB0 DL0 FR0 UL1 DF1 BL0 DR0
+UBL1 DBR1 UFR2 DFR2 DFL2 UBL2 UFL2 DBL0
+
+## SRC - representation of the object in C code for cube_array (write)
+
+The exact format depends on the internal cube representation. It is
+guaranteed that, if OUT is the output in this format, the line
+
+cube_t cube = OUT;
+
+is interpreted correctly by h48.
diff --git a/doc/TRANSFORMATIONS.md b/doc/TRANSFORMATIONS.md
new file mode 100644
index 0000000..58446e8
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+++ b/doc/TRANSFORMATIONS.md
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+Transformations can be either simple rotations or a rotation composed
+with a mirroring.
+
+Simple rotations are denoted by two letters corresponding to the faces
+to be moved to the U and F positions, respectively. For example FD is
+the rotation that brings the F face on top and the D face on front.
+
+A composed rotation + mirror is obtained by applying the corresponding
+rotation to the solved cube mirrored along the M plane.
+
+For example, to apply the transformation RBm (mirrored RB) to a cube C:
+	1a. Apply a mirror along the M plane to the solved cube
+	1b. Rotate the mirrored cube with z' y2
+	3.  Apply the cube C to the transformed solved cube
+	4.  Apply the transformations of step 1a and 1b in reverse
+
+The orientation of pieces after a rotation ignores the new position
+of centers.  A rotated cube can technically be inconsistent, because
+the parity of the edge permutation has to be adjusted considering the
+parity of the centers, which we ignore.
+
+The utility script mirror.sh transforms a solved, rotated cube to its
+mirrored and rotated version.
-- 
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