From 3180087ca6a0cf30f3f75bb8907e03fcaa7e54bf Mon Sep 17 00:00:00 2001
From: Brandon Liu <bdon@bdon.org>
Date: Mon, 9 Jan 2023 16:07:46 +0800
Subject: [PATCH] add fast parent tile ID calculation [#31]

---
 pmtiles/bitmap.go       | 10 +++-------
 pmtiles/tile_id.go      | 20 +++++++++++++++++++-
 pmtiles/tile_id_test.go | 24 ++++++++++++++++++++++++
 3 files changed, 46 insertions(+), 8 deletions(-)

diff --git a/pmtiles/bitmap.go b/pmtiles/bitmap.go
index 1d0a839..e88bc85 100644
--- a/pmtiles/bitmap.go
+++ b/pmtiles/bitmap.go
@@ -59,11 +59,8 @@ func generalizeOr(r *roaring64.Bitmap) {
 	for current_z := int(max_z); current_z > 0; current_z-- {
 		iter := to_iterate.Iterator()
 		for iter.HasNext() {
-			z, x, y := IdToZxy(iter.Next())
-			parent_z := z - 1
-			parent_x := x >> 1
-			parent_y := y >> 1
-			temp.Add(ZxyToId(parent_z, parent_x, parent_y))
+			parent_id := ParentId(iter.Next())
+			temp.Add(parent_id)
 		}
 		to_iterate = temp
 		r.Or(temp)
@@ -89,8 +86,7 @@ func generalizeAnd(r *roaring64.Bitmap) {
 		current := uint64(0) // check me...
 		for iter.HasNext() {
 			id := iter.Next()
-			z, x, y := IdToZxy(id)
-			parent_id := ZxyToId(z-1, x>>1, y>>1)
+			parent_id := ParentId(id)
 			if parent_id == current {
 				filled += 1
 				if filled == 4 {
diff --git a/pmtiles/tile_id.go b/pmtiles/tile_id.go
index 741265d..c818ccc 100644
--- a/pmtiles/tile_id.go
+++ b/pmtiles/tile_id.go
@@ -57,10 +57,10 @@ func ZxyToId(z uint8, x uint32, y uint32) uint64 {
 }
 
 func IdToZxy(i uint64) (uint8, uint32, uint32) {
-	var num_tiles uint64
 	var acc uint64
 	var z uint8
 	for {
+		var num_tiles uint64
 		num_tiles = (1 << z) * (1 << z)
 		if acc+num_tiles > i {
 			return t_on_level(z, i-acc)
@@ -69,3 +69,21 @@ func IdToZxy(i uint64) (uint8, uint32, uint32) {
 		z++
 	}
 }
+
+// fast parent ID calculation without converting to ZXY.
+func ParentId(i uint64) uint64 {
+	var acc uint64
+	var last_acc uint64
+	var z uint8
+	for {
+		var num_tiles uint64
+		num_tiles = (1 << z) * (1 << z)
+		if acc+num_tiles > i {
+			return last_acc + (i-acc)/4
+		}
+		last_acc = acc
+		acc += num_tiles
+		z++
+	}
+
+}
diff --git a/pmtiles/tile_id_test.go b/pmtiles/tile_id_test.go
index 7b4ea01..41a5c52 100644
--- a/pmtiles/tile_id_test.go
+++ b/pmtiles/tile_id_test.go
@@ -69,3 +69,27 @@ func TestExtremes(t *testing.T) {
 		assert.Equal(t, dim, y)
 	}
 }
+
+func TestParent(t *testing.T) {
+	assert.Equal(t, ZxyToId(0,0,0), ParentId(ZxyToId(1,0,0)))
+
+	assert.Equal(t, ZxyToId(1,0,0), ParentId(ZxyToId(2,0,0)))
+	assert.Equal(t, ZxyToId(1,0,0), ParentId(ZxyToId(2,0,1)))
+	assert.Equal(t, ZxyToId(1,0,0), ParentId(ZxyToId(2,1,0)))
+	assert.Equal(t, ZxyToId(1,0,0), ParentId(ZxyToId(2,1,1)))
+
+	assert.Equal(t, ZxyToId(1,0,1), ParentId(ZxyToId(2,0,2)))
+	assert.Equal(t, ZxyToId(1,0,1), ParentId(ZxyToId(2,0,3)))
+	assert.Equal(t, ZxyToId(1,0,1), ParentId(ZxyToId(2,1,2)))
+	assert.Equal(t, ZxyToId(1,0,1), ParentId(ZxyToId(2,1,3)))
+
+	assert.Equal(t, ZxyToId(1,1,0), ParentId(ZxyToId(2,2,0)))
+	assert.Equal(t, ZxyToId(1,1,0), ParentId(ZxyToId(2,2,1)))
+	assert.Equal(t, ZxyToId(1,1,0), ParentId(ZxyToId(2,3,0)))
+	assert.Equal(t, ZxyToId(1,1,0), ParentId(ZxyToId(2,3,1)))
+
+	assert.Equal(t, ZxyToId(1,1,1), ParentId(ZxyToId(2,2,2)))
+	assert.Equal(t, ZxyToId(1,1,1), ParentId(ZxyToId(2,2,3)))
+	assert.Equal(t, ZxyToId(1,1,1), ParentId(ZxyToId(2,3,2)))
+	assert.Equal(t, ZxyToId(1,1,1), ParentId(ZxyToId(2,3,3)))
+}