Implement shapeutil_visit_crossing_edge_pairs

s2/shapeutil_visit_crossing_edge_pairs.go

@@ -0,0 +1,176 @@
+package s2
+
+import "fmt"
+
+type ShapeEdgeVector []ShapeEdge
+
+type EdgePairVisitor func(a, b ShapeEdge, isInterior bool) bool
+
+// getShapeEdges returns all edges in the given S2ShapeIndexCell.
+func getShapeEdges(index *ShapeIndex, cell *ShapeIndexCell) ShapeEdgeVector {
+	var shapeEdges ShapeEdgeVector
+	for _, clipped := range cell.shapes {
+		shape := index.Shape(clipped.shapeID)
+		for _, edgeID := range clipped.edges {
+			shapeEdges = append(shapeEdges, ShapeEdge{
+				ID:   ShapeEdgeID{
+					ShapeID: clipped.shapeID,
+					EdgeID: int32(edgeID),
+				},
+				Edge: shape.Edge(edgeID),
+			})
+		}
+	}
+	return shapeEdges
+}
+
+// VisitCrossings finds and processes all crossing edge pairs.
+func visitCrossings(shapeEdges ShapeEdgeVector, crossingType CrossingType, needAdjacent bool, visitor EdgePairVisitor) bool {
+	minCrossingSign := MaybeCross
+	if crossingType == CrossingTypeInterior {
+		minCrossingSign = Cross
+	}
+	for i := 0; i < len(shapeEdges) - 1; i++ {
+		a := shapeEdges[i]
+		j := i + 1
+		// A common situation is that an edge AB is followed by an edge BC.  We
+		// only need to visit such crossings if "needAdjacent" is true (even if
+		// AB and BC belong to different edge chains).
+		if !needAdjacent && a.Edge.V1 == shapeEdges[j].Edge.V0 {
+			j++
+			if j >= len(shapeEdges) {
+				break
+			}
+		}
+		crosser := NewEdgeCrosser(a.Edge.V0, a.Edge.V1)
+		for ; j < len(shapeEdges); j++ {
+			b := shapeEdges[j]
+			if crosser.c != b.Edge.V0 {
+				crosser.RestartAt(b.Edge.V0)
+			}
+			sign := crosser.ChainCrossingSign(b.Edge.V1)
+			// missinglink: enum ordering is reversed compared to C++
+			if sign <= minCrossingSign {
+				if !visitor(a, b, sign == Cross) {
+					return false
+				}
+			}
+		}
+	}
+	return true
+}
+
+// Visits all pairs of crossing edges in the given S2ShapeIndex, terminating
+// early if the given EdgePairVisitor function returns false (in which case
+// VisitCrossings returns false as well).  "type" indicates whether all
+// crossings should be visited, or only interior crossings.
+//
+// If "needAdjacent" is false, then edge pairs of the form (AB, BC) may
+// optionally be ignored (even if the two edges belong to different edge
+// chains).  This option exists for the benefit of FindSelfIntersection(),
+// which does not need such edge pairs (see below).
+func VisitCrossings(index *ShapeIndex, crossingType CrossingType, needAdjacent bool, visitor EdgePairVisitor) bool {
+	// TODO(b/262264880): Use brute force if the total number of edges is small
+	// enough (using a larger threshold if the S2ShapeIndex is not constructed
+	// yet).
+	for it := index.Iterator(); !it.Done(); it.Next() {
+		shapeEdges := getShapeEdges(index, it.cell)
+		if !visitCrossings(shapeEdges, crossingType, needAdjacent, visitor) {
+			return false
+		}
+	}
+	return true
+}
+
+// VisitCrossingEdgePairs finds all crossing edge pairs in an index.
+func VisitCrossingEdgePairs(index *ShapeIndex, crossingType CrossingType, visitor EdgePairVisitor) bool {
+	needAdjacent := crossingType == CrossingTypeAll
+	for it := index.Iterator(); !it.Done(); it.Next() {
+		shapeEdges := getShapeEdges(index, it.cell)
+		if !visitCrossings(shapeEdges, crossingType, needAdjacent, visitor) {
+			return false
+		}
+	}
+	return true
+}
+
+func FindCrossingError(shape Shape, a, b ShapeEdge, isInterior bool) error {
+	ap := shape.ChainPosition(int(a.ID.EdgeID))
+	bp := shape.ChainPosition(int(b.ID.EdgeID))
+
+	if isInterior {
+		if ap.ChainID != bp.ChainID {
+			return fmt.Errorf(
+				"Loop %d edge %d crosses loop %d edge %d",
+				ap.ChainID, ap.Offset, bp.ChainID, bp.Offset)
+		}
+		return fmt.Errorf("Edge %d crosses edge %d", ap, bp)
+	}
+
+	// Loops are not allowed to have duplicate vertices, and separate loops
+  // are not allowed to share edges or cross at vertices.  We only need to
+  // check a given vertex once, so we also require that the two edges have
+  // the same end vertex
+	if a.Edge.V1 != b.Edge.V1 {
+		return nil
+	}
+
+	if ap.ChainID == bp.ChainID {
+		return fmt.Errorf("Edge %d has duplicate vertex with edge %d", ap, bp)
+	}
+
+	aLen := shape.Chain(ap.ChainID).Length
+	bLen := shape.Chain(bp.ChainID).Length
+	aNext := ap.Offset + 1
+	if aNext == aLen {
+		aNext = 0
+	}
+
+	bNext := bp.Offset + 1
+	if bNext == bLen {
+		bNext = 0
+	}
+
+	a2 := shape.ChainEdge(ap.ChainID, aNext).V1
+	b2 := shape.ChainEdge(bp.ChainID, bNext).V1
+
+	if a.Edge.V0 == b.Edge.V0 || a.Edge.V0 == b2 {
+		// The second edge index is sometimes off by one, hence "near".
+		return fmt.Errorf(
+			"Loop %d edge %d has duplicate near loop %d edge %d",
+			ap.ChainID, ap.Offset, bp.ChainID, bp.Offset)
+	}
+
+	// Since S2ShapeIndex loops are oriented such that the polygon interior is
+  // always on the left, we need to handle the case where one wedge contains
+  // the complement of the other wedge.  This is not specifically detected by
+  // GetWedgeRelation, so there are two cases to check for.
+  //
+  // Note that we don't need to maintain any state regarding loop crossings
+  // because duplicate edges are detected and rejected above.
+	if WedgeRelation(a.Edge.V0, a.Edge.V1, a2, b.Edge.V0, b2) == WedgeProperlyOverlaps &&
+		WedgeRelation(a.Edge.V0, a.Edge.V1, a2, b2, b.Edge.V0) == WedgeProperlyOverlaps {
+		return fmt.Errorf(
+			"Loop %d edge %d crosses loop %d edge %d",
+			ap.ChainID, ap.Offset, bp.ChainID, bp.Offset)
+	}
+
+	return nil
+}
+
+func FindSelfIntersection(index *ShapeIndex) bool {
+	if len(index.shapes) == 0 {
+		return false
+	}
+	shape := index.Shape(0)
+
+	// Visit all crossing pairs except possibly for ones of the form (AB, BC),
+	// since such pairs are very common and FindCrossingError() only needs pairs
+	// of the form (AB, AC).
+	return !VisitCrossings(
+		index, CrossingTypeAll, false,
+		func(a, b ShapeEdge, isInterior bool) bool {
+			return FindCrossingError(shape, a, b, isInterior) == nil
+		},
+	)
+}

s2/shapeutil_visit_crossing_edge_pairs_test.go

@@ -0,0 +1,150 @@
+package s2
+
+import (
+	"slices"
+	"sort"
+	"testing"
+)
+
+type EdgePair struct {
+	A, B ShapeEdgeID
+}
+
+// A set of edge pairs within an S2ShapeIndex.
+type EdgePairVector []EdgePair
+
+// Get crossings in one index.
+func getCrossings(index *ShapeIndex, crossingType CrossingType) EdgePairVector {
+	edgePairs := EdgePairVector{}
+	VisitCrossingEdgePairs(index, crossingType, func(a, b ShapeEdge, _ bool) bool {
+		edgePairs = append(edgePairs, EdgePair{a.ID, b.ID})
+		return true // Continue visiting.
+	})
+	if len(edgePairs) > 1 {
+		sort.Slice(edgePairs, func(i, j int) bool {
+			return edgePairs[i].A.Cmp(edgePairs[j].A) == -1 || edgePairs[i].B.Cmp(edgePairs[j].B) == -1
+		})
+		slices.Compact(edgePairs)
+	}
+	return edgePairs
+}
+
+// Brute force crossings in one index.
+func getCrossingEdgePairsBruteForce(index *ShapeIndex, crossingType CrossingType) EdgePairVector {
+	var result EdgePairVector
+	minSign := Cross
+	if crossingType == CrossingTypeAll {
+		minSign = MaybeCross
+	}
+
+	for aIter := NewEdgeIterator(index); !aIter.Done(); aIter.Next() {
+		a := aIter.Edge()
+		bIter := EdgeIterator{
+			index:    aIter.index,
+			shapeID:  aIter.shapeID,
+			numEdges: aIter.numEdges,
+			edgeID:   aIter.edgeID,
+		}
+		for bIter.Next(); !bIter.Done(); bIter.Next() {
+			b := bIter.Edge()
+			// missinglink: enum ordering is reversed compared to C++
+			if CrossingSign(a.V0, a.V1, b.V0, b.V1) <= minSign {
+				result = append(result, EdgePair{
+					aIter.ShapeEdgeID(),
+					bIter.ShapeEdgeID(),
+				})
+			}
+		}
+	}
+	return result
+}
+
+func TestGetCrossingEdgePairs(t *testing.T) {
+	var index ShapeIndex
+	if len(getCrossings(&index, CrossingTypeAll)) != 0 {
+		t.Error("Expected 0 crossings in empty index")
+	}
+	if len(getCrossings(&index, CrossingTypeInterior)) != 0 {
+		t.Error("Expected 0 interior crossings in empty index")
+	}
+}
+
+func TestGetCrossingEdgePairsGrid(t *testing.T) {
+	kGridSize := 10.0
+  epsilon := 1e-10
+
+	// There are 11 horizontal and 11 vertical lines. The expected number of
+  // interior crossings is 9x9, plus 9 "touching" intersections along each of
+  // the left, right, and bottom edges. "epsilon" is used to make the interior
+  // lines slightly longer so the "touches" actually cross, otherwise 3 of the
+  // 27 touches are not considered intersecting.
+  // However, the vertical lines do not reach the top line as it curves on the
+  // surface of the sphere: despite "epsilon" those 9 are not even very close
+  // to intersecting. Thus 9 * 12 = 108 interior and four more at the corners
+  // when CrossingType::ALL is used.
+
+	index :=  NewShapeIndex()
+	shape := edgeVectorShape{}
+
+  for i := 0.0; i <= kGridSize; i++ {
+    var e = epsilon
+		if i == 0 || i == kGridSize {
+			e = 0
+		}
+
+    shape.Add(PointFromLatLng(LatLngFromDegrees(-e, i)), PointFromLatLng(LatLngFromDegrees(kGridSize + e, i)));
+    shape.Add(PointFromLatLng(LatLngFromDegrees(i, -e)), PointFromLatLng(LatLngFromDegrees(i, kGridSize + e)));
+  }
+
+	index.Add(&shape)
+	if len(getCrossingEdgePairsBruteForce(index, CrossingTypeAll)) != 112 {
+		t.Errorf("Fail")
+	}
+	if len(getCrossingEdgePairsBruteForce(index, CrossingTypeInterior)) != 108 {
+		t.Errorf("Fail")
+	}
+}
+
+func testHasCrossingPermutations(t *testing.T, loops []*Loop, i int, hasCrossing bool) {
+	if i == len(loops) {
+			index := NewShapeIndex()
+			polygon := PolygonFromLoops(loops)
+			index.Add(polygon)
+
+			if hasCrossing != FindSelfIntersection(index) {
+					t.Error("Test failed: expected and actual crossing results do not match")
+			}
+			return
+	}
+
+	origLoop := loops[i]
+	for j := 0; j < origLoop.NumVertices(); j++ {
+			vertices := make([]Point, origLoop.NumVertices())
+			for k := 0; k < origLoop.NumVertices(); k++ {
+					vertices[k] = origLoop.Vertex((j + k) % origLoop.NumVertices())
+			}
+
+			loops[i] = LoopFromPoints(vertices)
+			testHasCrossingPermutations(t, loops, i+1, hasCrossing)
+	}
+	loops[i] = origLoop
+}
+
+func TestHasCrossing(t *testing.T) {
+	// Coordinates are (lat,lng), which can be visualized as (y,x).
+	cases := []struct {
+		polygonStr   string
+		hasCrossing  bool
+	}{
+		{"0:0, 0:1, 0:2, 1:2, 1:1, 1:0", false},
+		{"0:0, 0:1, 0:2, 1:2, 0:1, 1:0", true}, // duplicate vertex
+		{"0:0, 0:1, 1:0, 1:1", true}, // edge crossing
+		{"0:0, 1:1, 0:1; 0:0, 1:1, 1:0", true}, // duplicate edge
+		{"0:0, 1:1, 0:1; 1:1, 0:0, 1:0", true}, // reversed edge
+		{"0:0, 0:2, 2:2, 2:0; 1:1, 0:2, 3:1, 2:0", true}, // vertex crossing
+	}
+	for _, tc := range cases {
+		polygon := makePolygon(tc.polygonStr, true)
+		testHasCrossingPermutations(t, polygon.loops, 0, tc.hasCrossing)
+	}
+}