public void GetQueryBlocks_SingleCell()
{
var q1 = ZCurve.Encode(6, 4); // 52
var blocks1 = ZCurve.GetQueryBlocks(q1, q1); // single cell, all levels
var expected1 = Blocks(52, 0);
Assert.Equal(expected1, blocks1);
var q2 = ZCurve.Encode(11, 11); // 207
var blocks2 = ZCurve.GetQueryBlocks(q2, q2); // single cell, all levels
var expected2 = Blocks(207, 0);
Assert.Equal(expected2, blocks2);
var q3 = ZCurve.Encode(5, 1); // 19
var blocks3 = ZCurve.GetQueryBlocks(q3, q3, new[] { 2 }); // single cell, specific levels
var expected3 = Blocks(16, 2);
Assert.Equal(expected3, blocks3);
var q4 = ZCurve.Encode(uint.MaxValue, uint.MaxValue); // ulong.MaxValue
var blocks4 = ZCurve.GetQueryBlocks(q4, q4, new[] { 3 });
var expected4 = Blocks(ulong.MaxValue - 63, 3);
Assert.Equal(expected4, blocks4);
}
public void NextInsideBoxTest()
{
Assert.Equal(27UL, ZCurve.NextInsideBox(0, 27, 102));
Assert.Equal(74UL, ZCurve.NextInsideBox(58, 27, 102));
Assert.Equal(74UL, ZCurve.NextInsideBox(67, 27, 102));
Assert.Equal(96UL, ZCurve.NextInsideBox(79, 27, 102));
Assert.Equal(74UL, ZCurve.NextInsideBox(61, 27, 102));
// What if z is within box(qlo,qhi)? Drill down, cutting
// off parts of the box, until a single cell remains.
Assert.Equal(6UL, ZCurve.NextInsideBox(3, 3, 49));
Assert.Equal(11UL, ZCurve.NextInsideBox(9, 3, 49));
Assert.Equal(14UL, ZCurve.NextInsideBox(13, 3, 49));
Assert.Equal(19UL, ZCurve.NextInsideBox(18, 3, 49));
Assert.Equal(49UL, ZCurve.NextInsideBox(48, 3, 49));
Assert.Equal(0UL, ZCurve.NextInsideBox(49, 3, 49));
Assert.Equal(0UL, ZCurve.NextInsideBox(54, 54, 54));
// What if z > qhi? Only keys 000 or 100 or 101 can occur,
// drilling down (possibly cutting off lower parts of the
// query box) until the box is below and z is above the
// dividing line (key 100) and we return the result so far,
// which is zero (result's initial value).
Assert.Equal(0UL, ZCurve.NextInsideBox(50, 3, 49, 5)); // x within, y beyond
Assert.Equal(0UL, ZCurve.NextInsideBox(51, 3, 49, 5)); // x within, y beyond
Assert.Equal(0UL, ZCurve.NextInsideBox(52, 3, 49, 5)); // x beyond, y within
Assert.Equal(0UL, ZCurve.NextInsideBox(53, 3, 49, 5)); // x beyond, y within
Assert.Equal(0UL, ZCurve.NextInsideBox(54, 3, 49, 5)); // both x and y beyond
// Enumerate cells within query box qlo..qhi:
var result = new List <ulong>();
var expected = new ulong[] { 3, 6, 7, 9, 11, 12, 13, 14, 15, 18, 19, 24, 25, 26, 27, 33, 36, 37, 48, 49 };
ulong qlo = ZCurve.Encode(1U, 1U); // 3
ulong qhi = ZCurve.Encode(5U, 4U); // 49
ulong cur = qlo;
while (true)
{
result.Add(cur);
cur += 1;
if (cur > qhi)
{
break;
}
const int starti = 5;
if (!ZCurve.IsInsideBox(cur, qlo, qhi))
{
cur = ZCurve.NextInsideBox(cur, qlo, qhi, starti);
}
}
Assert.Equal(expected, result);
}
public void EncodeDecodeTest()
{
const uint ux = 0xFFFFFFFF;
const uint uy = 0x5555AAAA;
ulong uz = ZCurve.Encode(ux, uy);
Assert.Equal(0x77777777DDDDDDDDUL, uz);
Assert.Equal(ux, ZCurve.DecodeX(uz));
Assert.Equal(uy, ZCurve.DecodeY(uz));
Assert.Equal(0U, ZCurve.DecodeX(ZCurve.Encode(0, 0)));
Assert.Equal(0U, ZCurve.DecodeY(ZCurve.Encode(0, 0)));
Assert.Equal(123456789U, ZCurve.DecodeX(ZCurve.Encode(123456789, 999999)));
Assert.Equal(999999U, ZCurve.DecodeY(ZCurve.Encode(12345689, 999999)));
Assert.Equal(ulong.MaxValue, ZCurve.Encode(uint.MaxValue, uint.MaxValue));
}
public void GetQueryBlocks_AcrossBlock()
{
var qlo = ZCurve.Encode(7, 7); // 63
var qhi = ZCurve.Encode(8, 8); // 192
var blocks1 = ZCurve.GetQueryBlocks(qlo, qhi); // all levels
var expected1 = Blocks(63, 0, 106, 0, 149, 0, 192, 0);
Assert.Equal(expected1, blocks1);
var blocks2 = ZCurve.GetQueryBlocks(qlo, qhi, new[] { 1, 2 });
var expected2 = Blocks(60, 1, 104, 1, 148, 1, 192, 1);
Assert.Equal(expected2, blocks2);
var blocks3 = ZCurve.GetQueryBlocks(qlo, qhi, new[] { 2 });
var expected3 = Blocks(48, 2, 96, 2, 144, 2, 192, 2);
Assert.Equal(expected3, blocks3);
}
public void GetQueryBlocks_WithinBlock()
{
var q = ZCurve.Encode(7, 10); // 157
var blocks1 = ZCurve.GetQueryBlocks(q, q, new[] { 0, 1, 2, 3 });
Assert.Equal(Blocks(157, 0), blocks1);
var blocks2 = ZCurve.GetQueryBlocks(q, q, new[] { 1, 2, 3 });
Assert.Equal(Blocks(156, 1), blocks2);
var blocks3 = ZCurve.GetQueryBlocks(q, q, new[] { 2, 3 });
Assert.Equal(Blocks(144, 2), blocks3);
var blocks4 = ZCurve.GetQueryBlocks(q, q, new[] { 3 });
Assert.Equal(Blocks(128, 3), blocks4);
}
public void IsInsideBoxTest()
{
ulong min = ZCurve.Encode(1U, 1U); // 3
ulong max = ZCurve.Encode(5U, 4U); // 49
Assert.False(ZCurve.IsInsideBox(0, min, max));
Assert.True(ZCurve.IsInsideBox(3, min, max));
Assert.True(ZCurve.IsInsideBox(19, min, max));
Assert.False(ZCurve.IsInsideBox(20, min, max));
Assert.False(ZCurve.IsInsideBox(8, min, max));
Assert.True(ZCurve.IsInsideBox(15, min, max));
Assert.True(ZCurve.IsInsideBox(49, min, max));
Assert.False(ZCurve.IsInsideBox(50, min, max));
min = ZCurve.Encode(int.MaxValue - 1, int.MaxValue - 1);
max = ZCurve.Encode(int.MaxValue, int.MaxValue);
Assert.False(ZCurve.IsInsideBox(ZCurve.Encode(int.MaxValue - 2, int.MaxValue - 2), min, max));
Assert.True(ZCurve.IsInsideBox(ZCurve.Encode(int.MaxValue - 1, int.MaxValue - 1), min, max));
Assert.True(ZCurve.IsInsideBox(ZCurve.Encode(int.MaxValue, int.MaxValue), min, max));
Assert.False(ZCurve.IsInsideBox(ZCurve.Encode(1U + int.MaxValue, 1U + int.MaxValue), min, max));
}
public void QueryBlocksTrial()
{
// Expect shortest ordered sequence of blocks covering query box
// Query box:
ulong qlo = ZCurve.Encode(1U, 1U); // 3
ulong qhi = ZCurve.Encode(5U, 4U); // 49
// Expected result: 3 6 7 9 11 (12..15) 18 19 (24..27) 33 36 37 48 49
var starts = new ulong[] { 3, 6, 7, 9, 11, 12, 18, 19, 24, 33, 36, 37, 48, 49 };
var levels = new[] { 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0 };
var expected = starts.Zip(levels, (s, l) => new ZCurve.Block(s, l)).ToList();
var actual = new List <ZCurve.Block>();
ulong first = ZCurve.FirstInBlock(qlo, 0);
ulong last = ZCurve.FirstInBlock(qhi, 0);
for (ulong cursor = first; ;)
{
int level = ZCurve.LargestLevel(cursor, last);
ulong increment = ZCurve.CellsPerBlock(level);
actual.Add(new ZCurve.Block(cursor, level));
cursor += increment;
if (cursor > last)
{
break;
}
if (!ZCurve.IsInsideBox(cursor, first, last))
{
cursor = ZCurve.NextInsideBox(cursor, first, last);
}
}
Assert.Equal(expected, actual);
}
public void NearestBelowTest()
{
Assert.Equal(0UL, ZCurve.NearestBelow(0, 0));
Assert.Equal(0UL, ZCurve.NearestBelow(0, 1));
Assert.Equal(1UL, ZCurve.NearestBelow(0, 2));
Assert.Equal(2UL, ZCurve.NearestBelow(0, 3));
Assert.Equal(0x2AAAAAAAUL, ZCurve.NearestBelow(0, 31));
Assert.Equal(0x2AAAAAAAAAAAAAAAUL, ZCurve.NearestBelow(0, 63));
// 55 = Z(7,5) // 0111b 0101b => 0011 0111b
Assert.Equal(54UL, ZCurve.NearestBelow(55, 0));
Assert.Equal(53UL, ZCurve.NearestBelow(55, 1));
Assert.Equal(51UL, ZCurve.NearestBelow(55, 2));
Assert.Equal(55UL, ZCurve.NearestBelow(55, 3));
Assert.Equal(39UL, ZCurve.NearestBelow(55, 4));
Assert.Equal(31UL, ZCurve.NearestBelow(55, 5));
Assert.Equal(55UL, ZCurve.NearestBelow(55, 6));
Assert.Equal(63UL, ZCurve.NearestBelow(55, 7));
Assert.Equal(ZCurve.Encode(7, 0x7FFF), ZCurve.NearestBelow(55, 31));
Assert.Equal(ZCurve.Encode(7, int.MaxValue), ZCurve.NearestBelow(55, 63));
// TODO More
}