From 9658133fd02fe90ccd3b07b8a6c0d5c1c18de9eb Mon Sep 17 00:00:00 2001
From: Adam Spragg <adam@spra.gg>
Date: Thu, 12 Jan 2023 17:49:57 +0000
Subject: Puzzle 22: Add functions for orienting a cube

To figure out where you're going on a net (as far as I can figure) you
need to be able to tell which faces of a cube are connected to each
other, and which direction they are in relative to each other.
---
 22.c | 108 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 108 insertions(+)

diff --git a/22.c b/22.c
index 180969f..e877c5a 100644
--- a/22.c
+++ b/22.c
@@ -39,6 +39,114 @@ direction_name(enum direction dir)
 }
 
 
+// For each face of a cuboid, list adjoining faces in anti-clockwise order
+//
+// The faces are numbered as a right-handed six-sided die labelled 0 to 5.
+// Opposite pairs add up to 5 (0/5, 1/4 and 2/3), and if you imagine curling the
+// fingers of your right hand from the 0 to the 1, the 2 is on the face that
+// your thumb is pointing to. e.g. if the 0 is on the front, and the 1 is on
+// top, the 2 is on the left side.
+//
+// When a face is "oriented" a certain way, then if that face is on top, the
+// first adjoining face listed in table below is in that direction.
+//
+// e.g. If the 3 face is on the top of the cuboid and "oriented" west, then the
+// 4 face is to its west, the 5 is to its south, the 1 is to its east, and the 0
+// is to its north.
+static int const faceids[6][4] = {
+	{ 1, 2, 4, 3 },		// 0 sees 1, 2, 4, 3
+	{ 0, 3, 5, 2 },		// 1 sees 0, 3, 5, 2
+	{ 5, 4, 0, 1 },		// 2 sees 5, 4, 0, 1
+	{ 4, 5, 1, 0 },		// 3 sees 4, 5, 1, 0
+	{ 3, 0, 2, 5 },		// 4 sees 3, 0, 2, 5
+	{ 2, 1, 3, 4 },		// 5 sees 2, 1, 3, 4
+};
+
+
+// Given an oriented top face, which face do we see in a given direction?
+int
+faceid_look(int topid, enum direction orient, enum direction look)
+{
+	static enum direction const dirs[] = { D_NORTH, D_WEST, D_SOUTH, D_EAST };
+	int topdir, destdir;
+
+	if (topid < 0 || topid >= 6)
+		return -1;
+
+	// Go through `dirs` until we find the one that topid is pointing to
+	for (topdir = 0; topdir < 4; ++topdir)
+		if (dirs[topdir % 4] == orient)
+			break;
+	if (topdir >= 4)
+		return -1;
+
+	// Keep going through `dirs` until we find the one that the caller wants
+	for (destdir = topdir; destdir < topdir + 4; ++destdir)
+		if (dirs[destdir % 4] == look)
+			break;
+	if (destdir >= topdir + 4)
+		return -1;
+
+	// Look up the destination face id.
+	return faceids[topid][destdir - topdir];
+}
+
+
+// Given an oriented top face, which direction do we look to see another face?
+enum direction
+faceid_find(int topid, enum direction orient, int destid)
+{
+	static enum direction const dirs[] = { D_NORTH, D_WEST, D_SOUTH, D_EAST };
+	int topdir, destix;
+
+	// Go through the directions until we find the one that fsrc is pointing
+	for (topdir = 0; topdir < 4; ++topdir)
+		if (dirs[topdir % 4] == orient)
+			break;
+	if (topdir >= 4)
+		return -1;
+
+	// Go through topid's faces until we find destid
+	for (destix = 0; destix < 4; ++destix)
+		if (faceids[topid][destix] == destid)
+			break;
+	if (destix >= 4)
+		return -1;
+
+	// Return the direction that dest should be in
+	return dirs[(topdir + destix) % 4];
+}
+
+
+// Given a top face, if we see another face in one direction, what is the
+// orientation of the top face?
+enum direction
+faceid_orientation(int topid, int destid, enum direction destdir)
+{
+	static enum direction const dirs[] = { D_NORTH, D_WEST, D_SOUTH, D_EAST };
+	int topdir, destix;
+
+	// Go through topid's faces until we find destid
+	for (destix = 0; destix < 4; ++destix)
+		if (faceids[topid][destix] == destid)
+			break;
+	if (destix >= 4)
+		return -1;
+
+	// From faceid_find(), if dirs[topdir + destix] points to destdir,
+	// then we just go through possible topdirs until we find the one
+	// that makes this true
+	for (topdir = 0; topdir < 4; ++topdir)
+		if (dirs[(topdir + destix) % 4] == destdir)
+			break;
+	if (topdir >= 4)
+		return -1;
+
+	// Return the direction that dest should be in
+	return dirs[topdir];
+}
+
+
 struct map {
 	char * _buf;
 	int cols;
-- 
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