diff --git a/src/main/java/com/mapconductor/core/polygon/PolygonHoleUnion.kt b/src/main/java/com/mapconductor/core/polygon/PolygonHoleUnion.kt index 35d6245..aa0ad07 100644 --- a/src/main/java/com/mapconductor/core/polygon/PolygonHoleUnion.kt +++ b/src/main/java/com/mapconductor/core/polygon/PolygonHoleUnion.kt @@ -5,9 +5,12 @@ import com.mapconductor.core.features.GeoPointInterface import kotlin.math.PI import kotlin.math.abs import kotlin.math.atan2 +import kotlin.math.ceil +import kotlin.math.floor import kotlin.math.hypot import kotlin.math.min import kotlin.math.roundToLong +import kotlin.math.sqrt /** * 重なり合う穴リング同士を平面（経度緯度）座標系で結合する。外部ジオメトリライブラリ非依存。 @@ -71,6 +74,9 @@ private const val Q = 1e-9 // フィーチャースケール座標での平行・共線・線分上判定の許容誤差。 private const val EPS = 1e-12 +// 中点からこれより近い部分辺はその中点を通っている（度。Q よりはるかに小さい）。 +private const val ON_EDGE = 1e-12 + private fun unionRings(rings: List>): List> { // 全リングの有向辺（閉じたものとして扱う）。 val edges = mutableListOf() @@ -87,9 +93,127 @@ private fun unionRings(rings: List>): List> { return traceRings(boundary) } +// intersectionPoints が線分の外接矩形の外まで拾う距離（度）。共線判定は直線から EPS / |seg| までの +// 辺を受け入れ、sqrt(EPS) = 1e-6 より短い線分はそこで除かれるので、高々 2e-6。 +private const val MEET_PAD = 4e-6 + +// 部分辺の中点から左右の標本点までの距離の上限の 2 倍（度）。 +private const val CLEARANCE_CAP = 2e-5 + +/** + * 辺を外接矩形で一様格子に登録し、探索をすべての辺ではなく矩形の近くの辺だけに絞る。 + * 辺の矩形が触れるすべてのセルに登録するので、矩形が触れるセルを全部見れば、 + * その矩形と出会い得る辺はすべて見つかる。 + */ +private class EdgeGrid( + edges: List, + pad: Double, +) { + private val side: Int + private val minX: Double + private val minY: Double + private val cellW: Double + private val cellH: Double + private val cells = HashMap() + private val seen = IntArray(edges.size) + private var stamp = 0 + + init { + var x0 = Double.POSITIVE_INFINITY + var y0 = Double.POSITIVE_INFINITY + var x1 = Double.NEGATIVE_INFINITY + var y1 = Double.NEGATIVE_INFINITY + for (e in edges) { + x0 = minOf(x0, e.a.x, e.b.x) + x1 = maxOf(x1, e.a.x, e.b.x) + y0 = minOf(y0, e.a.y, e.b.y) + y1 = maxOf(y1, e.a.y, e.b.y) + } + side = ceil(sqrt(edges.size.toDouble())).toInt().coerceIn(1, 1024) + minX = x0 + minY = y0 + cellW = ((x1 - x0) / side).let { if (it > 0.0) it else 1.0 } + cellH = ((y1 - y0) / side).let { if (it > 0.0) it else 1.0 } + for (i in edges.indices) { + val e = edges[i] + forCells( + minOf(e.a.x, e.b.x) - pad, + minOf(e.a.y, e.b.y) - pad, + maxOf(e.a.x, e.b.x) + pad, + maxOf(e.a.y, e.b.y) + pad, + ) { key -> cells.getOrPut(key) { IntArrayList() }.add(i) } + } + } + + /** 矩形が触れるセルに登録された辺の番号。各辺 1 回、順序は不定。 */ + fun near( + minX: Double, + minY: Double, + maxX: Double, + maxY: Double, + out: IntArrayList, + ): IntArrayList { + out.clear() + val current = ++stamp + forCells(minX, minY, maxX, maxY) { key -> + val bucket = cells[key] ?: return@forCells + for (k in 0 until bucket.size) { + val i = bucket[k] + if (seen[i] == current) continue + seen[i] = current + out.add(i) + } + } + return out + } + + private inline fun forCells( + minX: Double, + minY: Double, + maxX: Double, + maxY: Double, + visit: (Int) -> Unit, + ) { + val cx0 = cell(minX, this.minX, cellW) + val cx1 = cell(maxX, this.minX, cellW) + val cy0 = cell(minY, this.minY, cellH) + val cy1 = cell(maxY, this.minY, cellH) + for (cx in cx0..cx1) { + for (cy in cy0..cy1) visit(cx * side + cy) + } + } + + private fun cell( + v: Double, + min: Double, + size: Double, + ): Int = floor((v - min) / size).coerceIn(0.0, (side - 1).toDouble()).toInt() +} + +/** 箱詰めしない Int の可変長配列。 */ +private class IntArrayList { + private var items = IntArray(4) + var size = 0 + private set + + operator fun get(index: Int): Int = items[index] + + fun add(value: Int) { + if (size == items.size) items = items.copyOf(size * 2) + items[size++] = value + } + + fun clear() { + size = 0 + } +} + /** 各辺を、他の辺が交差・接触する全ての点で分割する。 */ private fun splitEdges(edges: List): List { val result = mutableListOf() + // この辺の矩形から MEET_PAD 以内に矩形が来る辺だけが、この辺と出会い得る。 + val grid = EdgeGrid(edges, MEET_PAD) + val near = IntArrayList() for (i in edges.indices) { val seg = edges[i] val dir = sub(seg.b, seg.a) @@ -105,7 +229,15 @@ private fun splitEdges(edges: List): List { } add(seg.a) add(seg.b) - for (j in edges.indices) { + grid.near( + minOf(seg.a.x, seg.b.x) - MEET_PAD, + minOf(seg.a.y, seg.b.y) - MEET_PAD, + maxOf(seg.a.x, seg.b.x) + MEET_PAD, + maxOf(seg.a.y, seg.b.y) + MEET_PAD, + near, + ) + for (k in 0 until near.size) { + val j = near[k] if (i == j) continue for (p in intersectionPoints(seg, edges[j])) add(p) } @@ -133,6 +265,9 @@ private fun classifyBoundary( ): List { val out = mutableListOf() val seen = HashSet>() + val grid = EdgeGrid(subEdges, 0.0) + val near = IntArrayList() + val ringsBounds = rings.map(::ringBounds) for (seg in subEdges) { val dir = sub(seg.b, seg.a) val len = hypot(dir.x, dir.y) @@ -140,12 +275,15 @@ private fun classifyBoundary( val mid = add2(seg.a, scale(dir, 0.5)) // 単位左法線。中点の左右すぐ横でカバレッジを標本化する。分割後は他の辺が - // この部分辺の内部を横切らないため、微小オフセットはこの辺が隔てる 2 セル内に収まる。 + // この部分辺の内部を横切らないため、最寄りの他の辺までの距離より短いオフセットなら + // この辺が隔てる 2 セル内に収まる。固定オフセットでは収まらない: 別の穴がそれより + // 近くを通る（1e-5 度離れた 2 つの穴）と標本点がその穴に入り、辺が両側とも内部に + // 見えて落とされ、繋ぎ直したリングが穴を横切る。 val nx = -dir.y / len val ny = dir.x / len - val off = min(len * 0.25, 1e-5) - val leftInside = coverage(Vec(mid.x + nx * off, mid.y + ny * off), rings) > 0 - val rightInside = coverage(Vec(mid.x - nx * off, mid.y - ny * off), rings) > 0 + val off = min(len * 0.25, 0.5 * clearance(mid, CLEARANCE_CAP, subEdges, grid, near)) + val leftInside = coverage(Vec(mid.x + nx * off, mid.y + ny * off), rings, ringsBounds) > 0 + val rightInside = coverage(Vec(mid.x - nx * off, mid.y - ny * off), rings, ringsBounds) > 0 if (leftInside == rightInside) continue // 両側とも内部、または両側とも外部 // 内部が左側に来る向きへ揃える。 @@ -158,6 +296,46 @@ private fun classifyBoundary( return out } +/** + * `point`（部分辺の中点）から、それを通らない最寄りの部分辺までの距離。`cap` より近いものが + * 無ければ `cap`。その部分辺自身と、他のリングから来た同じ部分辺は中点を通るので除く。 + * 点のまわり `cap` の矩形の近くに登録された部分辺だけを調べる。`cap` より近いものはその中にある。 + */ +private fun clearance( + point: Vec, + cap: Double, + subEdges: List, + grid: EdgeGrid, + near: IntArrayList, +): Double { + var best = cap + grid.near(point.x - cap, point.y - cap, point.x + cap, point.y + cap, near) + for (k in 0 until near.size) { + val e = subEdges[near[k]] + if (minOf(e.a.x, e.b.x) > point.x + best || + maxOf(e.a.x, e.b.x) < point.x - best || + minOf(e.a.y, e.b.y) > point.y + best || + maxOf(e.a.y, e.b.y) < point.y - best + ) { + continue + } + val d = distanceToSegment(point, e) + if (d > ON_EDGE && d < best) best = d + } + return best +} + +private fun distanceToSegment( + p: Vec, + e: Edge, +): Double { + val d = sub(e.b, e.a) + val lenSq = dot(d, d) + val t = if (lenSq > 0.0) clamp01(dot(sub(p, e.a), d) / lenSq) else 0.0 + val q = add2(e.a, scale(d, t)) + return hypot(p.x - q.x, p.y - q.y) +} + /** 有向境界辺を連結して閉リングにする。 */ private fun traceRings(edges: List): List> { val byStart = HashMap>() @@ -250,11 +428,23 @@ private fun intersectionPoints( return listOf(add2(seg.a, scale(r, clamp01(t)))) } -/** 点を内部に含むリングの数。 */ +/** + * 点を内部に含むリングの数。緯度の範囲が点の緯度をまたがないリングには pointInRing が数える辺が + * 無いので飛ばす。 + */ private fun coverage( point: Vec, rings: List>, -): Int = rings.count { pointInRing(point, it) } + bounds: List, +): Int { + var count = 0 + for (i in rings.indices) { + val b = bounds[i] + if (point.y < b[1] || point.y >= b[3]) continue + if (pointInRing(point, rings[i])) count++ + } + return count +} /** 偶奇規則のレイキャスティングによる点包含判定（巻き方向に依存しない）。 */ private fun pointInRing( @@ -307,6 +497,21 @@ private fun toRing( return if (points.size >= 3) points else null } +/** リングの外接矩形 [minX, minY, maxX, maxY]。 */ +private fun ringBounds(ring: List): DoubleArray { + var minX = Double.POSITIVE_INFINITY + var minY = Double.POSITIVE_INFINITY + var maxX = Double.NEGATIVE_INFINITY + var maxY = Double.NEGATIVE_INFINITY + for (p in ring) { + if (p.x < minX) minX = p.x + if (p.x > maxX) maxX = p.x + if (p.y < minY) minY = p.y + if (p.y > maxY) maxY = p.y + } + return doubleArrayOf(minX, minY, maxX, maxY) +} + private fun signedArea(ring: List): Double { var area = 0.0 for (i in ring.indices) { diff --git a/src/test/java/com/mapconductor/core/polygon/PolygonHoleUnionFixtureTest.kt b/src/test/java/com/mapconductor/core/polygon/PolygonHoleUnionFixtureTest.kt new file mode 100644 index 0000000..79055bd --- /dev/null +++ b/src/test/java/com/mapconductor/core/polygon/PolygonHoleUnionFixtureTest.kt @@ -0,0 +1,101 @@ +package com.mapconductor.core.polygon + +import com.mapconductor.core.features.GeoPoint +import com.mapconductor.core.features.GeoPointInterface +import org.junit.Assert.assertSame +import org.junit.Assert.assertTrue +import org.junit.Test +import kotlin.math.abs + +/** + * unionHoleRings keeps the area of the union of the holes: holes that touch at a + * point or share (part of) an edge add up, overlaps count once. + * + * js-sdk-core (`PolygonHoleUnion.test.mjs`) and ios-sdk-core + * (`PolygonHoleUnionFixtureTests`) read the same `polygon-hole-union-fixture.txt`; + * the expected areas are shapely's unary_union. + */ +class PolygonHoleUnionFixtureTest { + private class Case( + val name: String, + val unit: Double, + val originLon: Double, + val originLat: Double, + val unionArea: Double, + ) { + var outer: List? = null + val holes = mutableListOf>() + + fun toGeo(flat: List): List = + flat.chunked(2).map { (x, y) -> + GeoPoint.fromLatLong(latitude = originLat + y * unit, longitude = originLon + x * unit) + } + + /** Planar area in grid units². */ + fun areaInUnits(ring: List): Double { + var a = 0.0 + for (i in ring.indices) { + val p = ring[i] + val q = ring[(i + 1) % ring.size] + val px = (p.longitude - originLon) / unit + val py = (p.latitude - originLat) / unit + val qx = (q.longitude - originLon) / unit + val qy = (q.latitude - originLat) / unit + a += px * qy - qx * py + } + return a / 2.0 + } + } + + private fun readCases(): List { + val stream = + requireNotNull(javaClass.classLoader?.getResourceAsStream("polygon-hole-union-fixture.txt")) { + "polygon-hole-union-fixture.txt not on the test classpath" + } + val cases = mutableListOf() + stream.bufferedReader().forEachLine { line -> + if (line.isBlank() || line.startsWith("#")) return@forEachLine + val parts = line.split("|") + when (parts[0]) { + "case" -> + cases.add( + Case( + name = parts[1], + unit = parts[2].toDouble(), + originLon = parts[3].toDouble(), + originLat = parts[4].toDouble(), + unionArea = parts[5].toDouble(), + ), + ) + "outer" -> cases.last().outer = parts[1].split(",").map { it.toDouble() } + "hole" -> cases.last().holes.add(parts[1].split(",").map { it.toDouble() }) + } + } + return cases + } + + @Test + fun unionKeepsTheAreaOfTheUnion() { + val cases = readCases() + assertTrue("fixture has cases", cases.size >= 20) + val failures = mutableListOf() + for (c in cases) { + val holes = c.holes.map { c.toGeo(it) } + val result = + c.outer?.let { outer -> + val state = PolygonState(points = c.toGeo(outer), holes = holes) + val unioned = state.unionHoles() + assertSame("${c.name}: the outline is left alone", state.points, unioned.points) + unioned.holes + } ?: unionHoleRings(holes) + val area = result.sumOf { abs(c.areaInUnits(it)) } + if (abs(area - c.unionArea) > 1e-6 * c.unionArea) { + failures.add("${c.name}: area $area != union ${c.unionArea} (${result.size} rings from ${holes.size})") + } + if (result.any { c.areaInUnits(it) >= 0.0 }) { + failures.add("${c.name}: a hole came back counter-clockwise") + } + } + assertTrue(failures.joinToString("\n"), failures.isEmpty()) + } +} diff --git a/src/test/resources/polygon-hole-union-fixture.txt b/src/test/resources/polygon-hole-union-fixture.txt new file mode 100644 index 0000000..1156d86 --- /dev/null +++ b/src/test/resources/polygon-hole-union-fixture.txt @@ -0,0 +1,231 @@ +# Hole-union fixture. The same file in js-sdk-core, android-sdk-core and ios-sdk-core. +# +# unionHoleRings must keep the area of the union of the holes: holes that touch +# at a point or share an edge (or part of one) add up, an overlap counts once. +# unionArea is shapely's unary_union of the holes. +# +# case|name|unit|originLongitude|originLatitude|unionArea +# outer|x,y,x,y,... (optional: the polygon's outline) +# hole|x,y,x,y,... (one line per hole, not closed) +# +# A vertex is (originLongitude + x * unit, originLatitude + y * unit) degrees, +# and areas are in unit². The Boston street parcels are Analyze Boston's +# Parcels 2025 (ODC PDDL) rounded to 1e-5 degree, before their holes were +# moved apart (examples/basic/tools/boston/pack.py in react-sdk). + +case|corner touch (1e-05 degree grid)|1e-05|-71.06|42.36|200.0 +hole|0,0,10,0,10,10,0,10 +hole|10,10,20,10,20,20,10,20 + +case|shared edge (1e-05 degree grid)|1e-05|-71.06|42.36|200.0 +hole|0,0,10,0,10,10,0,10 +hole|10,0,20,0,20,10,10,10 + +case|part of an edge shared (1e-05 degree grid)|1e-05|-71.06|42.36|200.0 +hole|0,0,10,0,10,10,0,10 +hole|10,5,20,5,20,15,10,15 + +case|chain of four: edge, corner, part of an edge (1e-05 degree grid)|1e-05|-71.06|42.36|400.0 +hole|0,0,10,0,10,10,0,10 +hole|10,0,20,0,20,10,10,10 +hole|20,10,30,10,30,20,20,20 +hole|25,20,35,20,35,30,25,30 + +case|three around one vertex (1e-05 degree grid)|1e-05|-71.06|42.36|300.0 +hole|0,0,10,0,10,10,0,10 +hole|10,10,20,10,20,20,10,20 +hole|0,10,10,10,10,20,0,20 + +case|overlap (1e-05 degree grid)|1e-05|-71.06|42.36|175.0 +hole|0,0,10,0,10,10,0,10 +hole|5,5,15,5,15,15,5,15 + +case|three overlapping (1e-05 degree grid)|1e-05|-71.06|42.36|221.0 +hole|0,0,10,0,10,10,0,10 +hole|5,5,15,5,15,15,5,15 +hole|8,0,18,0,18,7,8,7 + +case|touching pair beside a hole one unit away (1e-05 degree grid)|1e-05|-71.06|42.36|700.0 +hole|0,0,30,0,30,10,0,10 +hole|30,0,40,0,40,10,30,10 +hole|0,11,30,11,30,21,0,21 + +case|slanted holes one unit apart, one touching a third (1e-05 degree grid)|1e-05|-71.06|42.36|274.0 +hole|0,0,29,-10,32,-7,3,3 +hole|3,4,32,-6,35,-3,6,7 +hole|32,-12,40,-12,40,-7,32,-7 + +case|two holes one unit apart, none touching (1e-05 degree grid)|1e-05|-71.06|42.36|600.0 +hole|0,0,30,0,30,10,0,10 +hole|0,11,30,11,30,21,0,21 + +case|one-unit edges: a diamond across a square, and a square at their corner (1e-05 degree grid)|1e-05|-71.06|42.36|3.5 +hole|1,0,2,1,1,2,0,1 +hole|0,0,1,0,1,1,0,1 +hole|1,-1,2,-1,2,0,1,0 + +case|hole touching the outline, sharing an edge with another hole (1e-05 degree grid)|1e-05|-71.06|42.36|200.0 +outer|-10,-10,50,-10,50,50,-10,50 +hole|-10,0,0,0,0,10,-10,10 +hole|0,0,10,0,10,10,0,10 + +case|corner touch (1e-06 degree grid)|1e-06|-71.06|42.36|200.0 +hole|0,0,10,0,10,10,0,10 +hole|10,10,20,10,20,20,10,20 + +case|shared edge (1e-06 degree grid)|1e-06|-71.06|42.36|200.0 +hole|0,0,10,0,10,10,0,10 +hole|10,0,20,0,20,10,10,10 + +case|part of an edge shared (1e-06 degree grid)|1e-06|-71.06|42.36|200.0 +hole|0,0,10,0,10,10,0,10 +hole|10,5,20,5,20,15,10,15 + +case|chain of four: edge, corner, part of an edge (1e-06 degree grid)|1e-06|-71.06|42.36|400.0 +hole|0,0,10,0,10,10,0,10 +hole|10,0,20,0,20,10,10,10 +hole|20,10,30,10,30,20,20,20 +hole|25,20,35,20,35,30,25,30 + +case|three around one vertex (1e-06 degree grid)|1e-06|-71.06|42.36|300.0 +hole|0,0,10,0,10,10,0,10 +hole|10,10,20,10,20,20,10,20 +hole|0,10,10,10,10,20,0,20 + +case|overlap (1e-06 degree grid)|1e-06|-71.06|42.36|175.0 +hole|0,0,10,0,10,10,0,10 +hole|5,5,15,5,15,15,5,15 + +case|three overlapping (1e-06 degree grid)|1e-06|-71.06|42.36|221.0 +hole|0,0,10,0,10,10,0,10 +hole|5,5,15,5,15,15,5,15 +hole|8,0,18,0,18,7,8,7 + +case|touching pair beside a hole one unit away (1e-06 degree grid)|1e-06|-71.06|42.36|700.0 +hole|0,0,30,0,30,10,0,10 +hole|30,0,40,0,40,10,30,10 +hole|0,11,30,11,30,21,0,21 + +case|slanted holes one unit apart, one touching a third (1e-06 degree grid)|1e-06|-71.06|42.36|274.0 +hole|0,0,29,-10,32,-7,3,3 +hole|3,4,32,-6,35,-3,6,7 +hole|32,-12,40,-12,40,-7,32,-7 + +case|two holes one unit apart, none touching (1e-06 degree grid)|1e-06|-71.06|42.36|600.0 +hole|0,0,30,0,30,10,0,10 +hole|0,11,30,11,30,21,0,21 + +case|one-unit edges: a diamond across a square, and a square at their corner (1e-06 degree grid)|1e-06|-71.06|42.36|3.5 +hole|1,0,2,1,1,2,0,1 +hole|0,0,1,0,1,1,0,1 +hole|1,-1,2,-1,2,0,1,0 + +case|hole touching the outline, sharing an edge with another hole (1e-06 degree grid)|1e-06|-71.06|42.36|200.0 +outer|-10,-10,50,-10,50,50,-10,50 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