276 lines
6.9 KiB
Plaintext
276 lines
6.9 KiB
Plaintext
// echo ALGORITHM.adoc | entr sh -c "podman run --rm -it --network none -v "${PWD}:/documents/" asciidoctor/docker-asciidoctor asciidoctor -r asciidoctor-mathematical -a mathematical-format=svg ALGORITHM.adoc; printf 'Done ($(date -Isecond))\n'"
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:toc:
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:nofooter:
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:!webfonts:
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:source-highlighter: rouge
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:rouge-style: molokai
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// :stem:
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:sectlinks:
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= Algorithm
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== Data format
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[source]
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----
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Example: Face 2, level 23
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# Most significant 3 bits are for the face
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face_number = 0b010
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# This algorithm is always level 23
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data_bits = level * 2 = 23 * 2 = 46
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# The bit after the data bits is always 1
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# All subsequent bits are always 0
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Bit : 64 48 32 16 1
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: | | | | |
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: 01001011101010001011100010010011 1001001100100l001100000000000000
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Face number : ^^^
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Data bits : ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^
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Bit after data bits (1) : ^
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All remaining bits (0) : ^^^^^^^^^^^^^^
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----
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[source]
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----
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All remaining bits (0) : vvvvvvvvvvvvvv
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Bit after data bits (1) : v
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Data bits : vvvvvvvvvvvvvvvvvvvvvvvvvvvvv vvvvvvvvvvvvvvvvv
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Face number : vvv
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Bit : 64 48 32 16 1
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: | | | | |
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: 01001011101010001011100010010011 1001001100100l001100000000000000
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Not represented : ^^^^^^^^^^^^^^^
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0000 (10 bits) : ^^^^^^^^^^
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WORD1 (13 bits) : ^^^^^^ ^^^^^^^
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WORD2 (13 bits) : ^^^^^^^^^^^^^
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WORD3 (13 bits) : ^^^^^^^^^^^^^
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----
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Alternative format (generated using link:https://github.com/luismartingarcia/protocol[protocol^])
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[source]
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----
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./protocol 'Face:3,Data:46,1:1,0:14?bits=32'
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0 1 2 3
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0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
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+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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| Face| Data |
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+-+-+-+ +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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| |1| 0 |
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+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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----
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[source]
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----
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./protocol 'WORD3:13,WORD2:13,WORD1:13,Number:10?bits=32'
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0 1 2 3
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0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
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+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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| WORD3 | WORD2 | |
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+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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| WORD1 | Number |
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+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
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----
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== Encoding
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[%header,cols="2m,5a"]
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|===
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|Step |Code
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|(lat, lon)
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|Given
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|(x, y, z)/Point
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| [source,rust]
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----
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fn lat_lon_to_xyz(lat: f64, lon: f64) -> (f64, f64, f64) {
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let x = cos(lon) * cos(lat);
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let y = sin(lon) * cos(lat);
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let z = sin(lat);
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(x, y, z)
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}
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----
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|(face, u, v)
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| [source,rust]
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----
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fn face(x: f64, y: f64, z: f64) -> u8 {
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let (x_abs, y_abs, z_abs) = (x.abs(), y.abs(), z.abs());
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let mut id = 0;
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let mut value = x;
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if y_abs > x_abs {
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id = 1;
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value = y;
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}
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if z_abs > value.abs() {
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id = 2;
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value = z;
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}
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if value < 0. {
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id += 3;
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}
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id
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}
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fn xyz_to_fuv(x: f64, y: f64, z: f64) -> (u8, f64, f64) {
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let f: u8 = face(x, y, z);
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let (u, v) = match face {
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0 => (y / x, z / x),
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1 => (-x / y, z / y),
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2 => (-x / z, -y / z),
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3 => (z / x, y / x),
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4 => (z / y, -x / y),
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5 => (-y / z, -x / z),
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_ => panic!("Face {f} out of bounds"),
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};
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(f, u, v)
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}
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----
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|(face, s, t)
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| [source,rust]
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----
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pub fn u_or_v_to_s_or_t(u_or_v: f64) -> f64 {
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if u_or_v >= 0.0 {
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0.5 * (1.0 + 3.0 * u_or_v).sqrt()
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} else {
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1.0 - 0.5 * (1.0 - 3.0 * u_or_v).sqrt()
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}
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}
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fn fuv_to_fst(f: u8, u: u64, v: u64) -> (u8, f64, f64) {
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let s = u_or_v_to_s_or_t(u);
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let t = u_or_v_to_s_or_t(v);
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(f, s, t)
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}
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----
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|(face, i, j)
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| [source,rust]
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----
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fn st_to_ij(s: f64) -> u32 {
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clamp((MAX_SIZE as f64 * s).floor() as u32, 0, MAX_SIZE_I32 - 1)
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}
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fn fst_to_fij(f: u8, s: u64, t: u64) -> (u8, u32, u32) {
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let i = st_to_ij(s);
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let j = st_to_ij(t);
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(f, i, j)
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}
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----
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|(cellid)
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| [source,go]
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----
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func cellIDFromFaceIJ(f, i, j int) CellID {
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// Note that this value gets shifted one bit to the left at the end
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// of the function.
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n := uint64(f) << (posBits - 1)
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// Alternating faces have opposite Hilbert curve orientations; this
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// is necessary in order for all faces to have a right-handed
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// coordinate system.
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bits := f & swapMask
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// Each iteration maps 4 bits of "i" and "j" into 8 bits of the Hilbert
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// curve position. The lookup table transforms a 10-bit key of the form
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// "iiiijjjjoo" to a 10-bit value of the form "ppppppppoo", where the
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// letters [ijpo] denote bits of "i", "j", Hilbert curve position, and
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// Hilbert curve orientation respectively.
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for k := 7; k >= 0; k-- {
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mask := (1 << lookupBits) - 1
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bits += ((i >> uint(k*lookupBits)) & mask) << (lookupBits + 2)
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bits += ((j >> uint(k*lookupBits)) & mask) << 2
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bits = lookupPos[bits]
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n \|= uint64(bits>>2) << (uint(k) * 2 * lookupBits)
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bits &= (swapMask \| invertMask)
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}
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return CellID(n*2 + 1)
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}
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----
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[source,rust]
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----
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fn fij_to_cellid(f: u8, s: u32, t: u32) -> u64 {
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let mut n = u64::from(f) << (POS_BITS - 1);
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let mut bits = u32::from(f & SWAP_MASK);
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let mut k = 7;
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let mask = (1 << LOOKUP_BITS) - 1;
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loop {
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bits += ((i >> (k * LOOKUP_BITS)) & mask) << (LOOKUP_BITS + 2);
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bits += ((j >> (k * LOOKUP_BITS)) & mask) << 2;
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bits = LOOKUP_POS[bits as usize] as u32;
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n \|= ((bits >> 2) as u64) << ((k * 2 * LOOKUP_BITS) as u64);
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bits &= u32::from(SWAP_MASK \| INVERT_MASK);
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if k == 0 {
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break;
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}
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k -= 1;
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}
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n * 2 + 1
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}
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----
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|(number, word1, word2, word3)
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|===
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== Decoding
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[%header,cols="m,a,"]
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|===
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|Step |Formula |Description
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|(number, word1, word2, word3)
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|Given
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|(cellid)
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|(face, i, j)
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|(face, s, t)
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|(face, u, v)
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|(x, y, z)/Point
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|(lat, lon)
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|===
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== Wordlist
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++++
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<style>
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#header, #content, #footnotes, #footer {
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max-width: unset !important;
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}
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.hll {
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background-color: #ff0;
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}
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</style>
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++++
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