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Hilbert and quadkey 128-bit encodings are reversible

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This commit is contained in:
Erica Fischer
2024-04-05 14:02:58 -07:00
parent 77f5e9677f
commit 3556142d80
2 changed files with 30 additions and 21 deletions
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projection.cpp
+15 -15
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@@ -107,22 +107,22 @@ void tiletoepsg3857(long long ix, long long iy, int zoom, double *ox, double *oy
// https://en.wikipedia.org/wiki/Hilbert_curve // https://en.wikipedia.org/wiki/Hilbert_curve
void hilbert_rot(unsigned long long n, unsigned long long *x, unsigned long long *y, unsigned long long rx, unsigned long long ry) { static void hilbert_rot(index_t n, unsigned long long *x, unsigned long long *y, index_t rx, index_t ry) {
if (ry == 0) { if (ry == 0) {
if (rx == 1) { if (rx == 1) {
*x = n - 1 - *x; *x = n - 1 - *x;
*y = n - 1 - *y; *y = n - 1 - *y;
} }
unsigned t = *x; unsigned long long t = *x;
*x = *y; *x = *y;
*y = t; *y = t;
} }
} }
index_t hilbert_xy2d(unsigned long long n, unsigned long long x, unsigned long long y) { static index_t hilbert_xy2d(index_t n, unsigned long long x, unsigned long long y) {
index_t d = 0; index_t d = 0;
unsigned long long rx, ry; index_t rx, ry;
for (index_t s = n / 2; s > 0; s /= 2) { for (index_t s = n / 2; s > 0; s /= 2) {
rx = (x & s) != 0; rx = (x & s) != 0;
@@ -135,8 +135,8 @@ index_t hilbert_xy2d(unsigned long long n, unsigned long long x, unsigned long l
return d; return d;
} }
void hilbert_d2xy(index_t n, index_t d, unsigned long long *x, unsigned long long *y) { static void hilbert_d2xy(index_t n, index_t d, unsigned long long *x, unsigned long long *y) {
unsigned long long rx, ry; index_t rx, ry;
index_t t = d; index_t t = d;
*x = *y = 0; *x = *y = 0;
@@ -151,21 +151,21 @@ void hilbert_d2xy(index_t n, index_t d, unsigned long long *x, unsigned long lon
} }
index_t encode_hilbert(unsigned long long wx, unsigned long long wy) { index_t encode_hilbert(unsigned long long wx, unsigned long long wy) {
return hilbert_xy2d(1LL << UINT_BITS, wx, wy); return hilbert_xy2d((index_t) 1 << 64, wx, wy);
} }
void decode_hilbert(index_t index, unsigned long long *wx, unsigned long long *wy) { void decode_hilbert(index_t index, unsigned long long *wx, unsigned long long *wy) {
hilbert_d2xy(1LL << UINT_BITS, index, wx, wy); hilbert_d2xy((index_t) 1 << 64, index, wx, wy);
} }
index_t encode_quadkey(unsigned long long wx, unsigned long long wy) { index_t encode_quadkey(unsigned long long wx, unsigned long long wy) {
index_t out = 0; index_t out = 0;
int i; int i;
for (i = 0; i < UINT_BITS; i++) { for (i = 0; i < 64; i++) {
index_t v = ((wx >> (UINT_BITS - (i + 1))) & 1) << 1; index_t v = ((wx >> (64 - (i + 1))) & 1) << 1;
v |= (wy >> (UINT_BITS - (i + 1))) & 1; v |= (wy >> (64 - (i + 1))) & 1;
v = v << (64 - 2 * (i + 1)); v = v << (128 - 2 * (i + 1));
out |= v; out |= v;
} }
@@ -196,9 +196,9 @@ void decode_quadkey(index_t index, unsigned long long *wx, unsigned long long *w
*wx = *wy = 0; *wx = *wy = 0;
for (size_t i = 0; i < 8; i++) { for (size_t i = 0; i < 16; i++) {
*wx |= ((unsigned long long) decodex[(index >> (8 * i)) & 0xFF]) << (4 * i); *wx |= ((index_t) decodex[(index >> (8 * i)) & 0xFF]) << (4 * i);
*wy |= ((unsigned long long) decodey[(index >> (8 * i)) & 0xFF]) << (4 * i); *wy |= ((index_t) decodey[(index >> (8 * i)) & 0xFF]) << (4 * i);
} }
} }
unit.cpp
+15 -6
View File
@@ -124,20 +124,29 @@ TEST_CASE("Projection", "projection") {
} }
TEST_CASE("Quadkey index", "quadkey index") { TEST_CASE("Quadkey index", "quadkey index") {
unsigned x = (unsigned) 1234567890; unsigned long long a = (unsigned) 1234567890;
unsigned y = (unsigned) 3210987654; unsigned long long b = (unsigned) 3210987654;
unsigned long long x = (b << 32) | a;
unsigned long long y = (a << 32) | b;
index_t encoded; index_t encoded;
unsigned long long nx, ny; unsigned long long nx, ny;
encoded = encode_quadkey(x, y); encoded = encode_quadkey(x, y);
REQUIRE((unsigned long long) encoded == 7338499239188161052); // the *bottom* 64 bits of the 128-bit encoding
// are the same as the 64-bit encoding of a, b
REQUIRE((unsigned long long) encoded == 7338499239188161052ULL);
REQUIRE((unsigned long long) (encoded >> 64) == 11163131681630900524ULL);
decode_quadkey(encoded, &nx, &ny); decode_quadkey(encoded, &nx, &ny);
REQUIRE(nx == x); REQUIRE(nx == x);
REQUIRE(ny == y); REQUIRE(ny == y);
encoded = encode_hilbert(x, y); encoded = encode_hilbert(y, x);
REQUIRE((unsigned long long) encoded == 8447864191955811122); // the *top* 64 bits of the 128-bit encoding
decode_hilbert(encoded, &nx, &ny); // of the 64-bit encoding of a, b
REQUIRE((unsigned long long) (encoded >> 64) == 8447864191955811122ULL);
REQUIRE((unsigned long long) encoded == 16122461378071376152ULL);
decode_hilbert(encoded, &ny, &nx);
REQUIRE(nx == x); REQUIRE(nx == x);
REQUIRE(ny == y); REQUIRE(ny == y);
} }