[chore] add back exif-terminator and use only for jpeg,png,webp (#3161)

* add back exif-terminator and use only for jpeg,png,webp

* fix arguments passed to terminateExif()

* pull in latest exif-terminator

* fix test

* update processed img

---------

Co-authored-by: tobi <tobi.smethurst@protonmail.com>

1 files changed, 1816 insertions, 0 deletions

diff --git a/vendor/github.com/golang/geo/s2/loop.go b/vendor/github.com/golang/geo/s2/loop.go
new file mode 100644
index 000000000..882d8583c
--- /dev/null
+++ b/vendor/github.com/golang/geo/s2/loop.go
@@ -0,0 +1,1816 @@
+// Copyright 2015 Google Inc. All rights reserved.
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package s2
+
+import (
+	"fmt"
+	"io"
+	"math"
+
+	"github.com/golang/geo/r1"
+	"github.com/golang/geo/r3"
+	"github.com/golang/geo/s1"
+)
+
+// Loop represents a simple spherical polygon. It consists of a sequence
+// of vertices where the first vertex is implicitly connected to the
+// last. All loops are defined to have a CCW orientation, i.e. the interior of
+// the loop is on the left side of the edges. This implies that a clockwise
+// loop enclosing a small area is interpreted to be a CCW loop enclosing a
+// very large area.
+//
+// Loops are not allowed to have any duplicate vertices (whether adjacent or
+// not).  Non-adjacent edges are not allowed to intersect, and furthermore edges
+// of length 180 degrees are not allowed (i.e., adjacent vertices cannot be
+// antipodal). Loops must have at least 3 vertices (except for the "empty" and
+// "full" loops discussed below).
+//
+// There are two special loops: the "empty" loop contains no points and the
+// "full" loop contains all points. These loops do not have any edges, but to
+// preserve the invariant that every loop can be represented as a vertex
+// chain, they are defined as having exactly one vertex each (see EmptyLoop
+// and FullLoop).
+type Loop struct {
+	vertices []Point
+
+	// originInside keeps a precomputed value whether this loop contains the origin
+	// versus computing from the set of vertices every time.
+	originInside bool
+
+	// depth is the nesting depth of this Loop if it is contained by a Polygon
+	// or other shape and is used to determine if this loop represents a hole
+	// or a filled in portion.
+	depth int
+
+	// bound is a conservative bound on all points contained by this loop.
+	// If l.ContainsPoint(P), then l.bound.ContainsPoint(P).
+	bound Rect
+
+	// Since bound is not exact, it is possible that a loop A contains
+	// another loop B whose bounds are slightly larger. subregionBound
+	// has been expanded sufficiently to account for this error, i.e.
+	// if A.Contains(B), then A.subregionBound.Contains(B.bound).
+	subregionBound Rect
+
+	// index is the spatial index for this Loop.
+	index *ShapeIndex
+}
+
+// LoopFromPoints constructs a loop from the given points.
+func LoopFromPoints(pts []Point) *Loop {
+	l := &Loop{
+		vertices: pts,
+	}
+
+	l.initOriginAndBound()
+	return l
+}
+
+// LoopFromCell constructs a loop corresponding to the given cell.
+//
+// Note that the loop and cell *do not* contain exactly the same set of
+// points, because Loop and Cell have slightly different definitions of
+// point containment. For example, a Cell vertex is contained by all
+// four neighboring Cells, but it is contained by exactly one of four
+// Loops constructed from those cells. As another example, the cell
+// coverings of cell and LoopFromCell(cell) will be different, because the
+// loop contains points on its boundary that actually belong to other cells
+// (i.e., the covering will include a layer of neighboring cells).
+func LoopFromCell(c Cell) *Loop {
+	l := &Loop{
+		vertices: []Point{
+			c.Vertex(0),
+			c.Vertex(1),
+			c.Vertex(2),
+			c.Vertex(3),
+		},
+	}
+
+	l.initOriginAndBound()
+	return l
+}
+
+// These two points are used for the special Empty and Full loops.
+var (
+	emptyLoopPoint = Point{r3.Vector{X: 0, Y: 0, Z: 1}}
+	fullLoopPoint  = Point{r3.Vector{X: 0, Y: 0, Z: -1}}
+)
+
+// EmptyLoop returns a special "empty" loop.
+func EmptyLoop() *Loop {
+	return LoopFromPoints([]Point{emptyLoopPoint})
+}
+
+// FullLoop returns a special "full" loop.
+func FullLoop() *Loop {
+	return LoopFromPoints([]Point{fullLoopPoint})
+}
+
+// initOriginAndBound sets the origin containment for the given point and then calls
+// the initialization for the bounds objects and the internal index.
+func (l *Loop) initOriginAndBound() {
+	if len(l.vertices) < 3 {
+		// Check for the special "empty" and "full" loops (which have one vertex).
+		if !l.isEmptyOrFull() {
+			l.originInside = false
+			return
+		}
+
+		// This is the special empty or full loop, so the origin depends on if
+		// the vertex is in the southern hemisphere or not.
+		l.originInside = l.vertices[0].Z < 0
+	} else {
+		// Point containment testing is done by counting edge crossings starting
+		// at a fixed point on the sphere (OriginPoint). We need to know whether
+		// the reference point (OriginPoint) is inside or outside the loop before
+		// we can construct the ShapeIndex. We do this by first guessing that
+		// it is outside, and then seeing whether we get the correct containment
+		// result for vertex 1. If the result is incorrect, the origin must be
+		// inside the loop.
+		//
+		// A loop with consecutive vertices A,B,C contains vertex B if and only if
+		// the fixed vector R = B.Ortho is contained by the wedge ABC. The
+		// wedge is closed at A and open at C, i.e. the point B is inside the loop
+		// if A = R but not if C = R. This convention is required for compatibility
+		// with VertexCrossing. (Note that we can't use OriginPoint
+		// as the fixed vector because of the possibility that B == OriginPoint.)
+		l.originInside = false
+		v1Inside := OrderedCCW(Point{l.vertices[1].Ortho()}, l.vertices[0], l.vertices[2], l.vertices[1])
+		if v1Inside != l.ContainsPoint(l.vertices[1]) {
+			l.originInside = true
+		}
+	}
+
+	// We *must* call initBound before initializing the index, because
+	// initBound calls ContainsPoint which does a bounds check before using
+	// the index.
+	l.initBound()
+
+	// Create a new index and add us to it.
+	l.index = NewShapeIndex()
+	l.index.Add(l)
+}
+
+// initBound sets up the approximate bounding Rects for this loop.
+func (l *Loop) initBound() {
+	// Check for the special "empty" and "full" loops.
+	if l.isEmptyOrFull() {
+		if l.IsEmpty() {
+			l.bound = EmptyRect()
+		} else {
+			l.bound = FullRect()
+		}
+		l.subregionBound = l.bound
+		return
+	}
+
+	// The bounding rectangle of a loop is not necessarily the same as the
+	// bounding rectangle of its vertices. First, the maximal latitude may be
+	// attained along the interior of an edge. Second, the loop may wrap
+	// entirely around the sphere (e.g. a loop that defines two revolutions of a
+	// candy-cane stripe). Third, the loop may include one or both poles.
+	// Note that a small clockwise loop near the equator contains both poles.
+	bounder := NewRectBounder()
+	for i := 0; i <= len(l.vertices); i++ { // add vertex 0 twice
+		bounder.AddPoint(l.Vertex(i))
+	}
+	b := bounder.RectBound()
+
+	if l.ContainsPoint(Point{r3.Vector{0, 0, 1}}) {
+		b = Rect{r1.Interval{b.Lat.Lo, math.Pi / 2}, s1.FullInterval()}
+	}
+	// If a loop contains the south pole, then either it wraps entirely
+	// around the sphere (full longitude range), or it also contains the
+	// north pole in which case b.Lng.IsFull() due to the test above.
+	// Either way, we only need to do the south pole containment test if
+	// b.Lng.IsFull().
+	if b.Lng.IsFull() && l.ContainsPoint(Point{r3.Vector{0, 0, -1}}) {
+		b.Lat.Lo = -math.Pi / 2
+	}
+	l.bound = b
+	l.subregionBound = ExpandForSubregions(l.bound)
+}
+
+// Validate checks whether this is a valid loop.
+func (l *Loop) Validate() error {
+	if err := l.findValidationErrorNoIndex(); err != nil {
+		return err
+	}
+
+	// Check for intersections between non-adjacent edges (including at vertices)
+	// TODO(roberts): Once shapeutil gets findAnyCrossing uncomment this.
+	// return findAnyCrossing(l.index)
+
+	return nil
+}
+
+// findValidationErrorNoIndex reports whether this is not a valid loop, but
+// skips checks that would require a ShapeIndex to be built for the loop. This
+// is primarily used by Polygon to do validation so it doesn't trigger the
+// creation of unneeded ShapeIndices.
+func (l *Loop) findValidationErrorNoIndex() error {
+	// All vertices must be unit length.
+	for i, v := range l.vertices {
+		if !v.IsUnit() {
+			return fmt.Errorf("vertex %d is not unit length", i)
+		}
+	}
+
+	// Loops must have at least 3 vertices (except for empty and full).
+	if len(l.vertices) < 3 {
+		if l.isEmptyOrFull() {
+			return nil // Skip remaining tests.
+		}
+		return fmt.Errorf("non-empty, non-full loops must have at least 3 vertices")
+	}
+
+	// Loops are not allowed to have any duplicate vertices or edge crossings.
+	// We split this check into two parts. First we check that no edge is
+	// degenerate (identical endpoints). Then we check that there are no
+	// intersections between non-adjacent edges (including at vertices). The
+	// second check needs the ShapeIndex, so it does not fall within the scope
+	// of this method.
+	for i, v := range l.vertices {
+		if v == l.Vertex(i+1) {
+			return fmt.Errorf("edge %d is degenerate (duplicate vertex)", i)
+		}
+
+		// Antipodal vertices are not allowed.
+		if other := (Point{l.Vertex(i + 1).Mul(-1)}); v == other {
+			return fmt.Errorf("vertices %d and %d are antipodal", i,
+				(i+1)%len(l.vertices))
+		}
+	}
+
+	return nil
+}
+
+// Contains reports whether the region contained by this loop is a superset of the
+// region contained by the given other loop.
+func (l *Loop) Contains(o *Loop) bool {
+	// For a loop A to contain the loop B, all of the following must
+	// be true:
+	//
+	//  (1) There are no edge crossings between A and B except at vertices.
+	//
+	//  (2) At every vertex that is shared between A and B, the local edge
+	//      ordering implies that A contains B.
+	//
+	//  (3) If there are no shared vertices, then A must contain a vertex of B
+	//      and B must not contain a vertex of A. (An arbitrary vertex may be
+	//      chosen in each case.)
+	//
+	// The second part of (3) is necessary to detect the case of two loops whose
+	// union is the entire sphere, i.e. two loops that contains each other's
+	// boundaries but not each other's interiors.
+	if !l.subregionBound.Contains(o.bound) {
+		return false
+	}
+
+	// Special cases to handle either loop being empty or full.
+	if l.isEmptyOrFull() || o.isEmptyOrFull() {
+		return l.IsFull() || o.IsEmpty()
+	}
+
+	// Check whether there are any edge crossings, and also check the loop
+	// relationship at any shared vertices.
+	relation := &containsRelation{}
+	if hasCrossingRelation(l, o, relation) {
+		return false
+	}
+
+	// There are no crossings, and if there are any shared vertices then A
+	// contains B locally at each shared vertex.
+	if relation.foundSharedVertex {
+		return true
+	}
+
+	// Since there are no edge intersections or shared vertices, we just need to
+	// test condition (3) above. We can skip this test if we discovered that A
+	// contains at least one point of B while checking for edge crossings.
+	if !l.ContainsPoint(o.Vertex(0)) {
+		return false
+	}
+
+	// We still need to check whether (A union B) is the entire sphere.
+	// Normally this check is very cheap due to the bounding box precondition.
+	if (o.subregionBound.Contains(l.bound) || o.bound.Union(l.bound).IsFull()) &&
+		o.ContainsPoint(l.Vertex(0)) {
+		return false
+	}
+	return true
+}
+
+// Intersects reports whether the region contained by this loop intersects the region
+// contained by the other loop.
+func (l *Loop) Intersects(o *Loop) bool {
+	// Given two loops, A and B, A.Intersects(B) if and only if !A.Complement().Contains(B).
+	//
+	// This code is similar to Contains, but is optimized for the case
+	// where both loops enclose less than half of the sphere.
+	if !l.bound.Intersects(o.bound) {
+		return false
+	}
+
+	// Check whether there are any edge crossings, and also check the loop
+	// relationship at any shared vertices.
+	relation := &intersectsRelation{}
+	if hasCrossingRelation(l, o, relation) {
+		return true
+	}
+	if relation.foundSharedVertex {
+		return false
+	}
+
+	// Since there are no edge intersections or shared vertices, the loops
+	// intersect only if A contains B, B contains A, or the two loops contain
+	// each other's boundaries.  These checks are usually cheap because of the
+	// bounding box preconditions.  Note that neither loop is empty (because of
+	// the bounding box check above), so it is safe to access vertex(0).
+
+	// Check whether A contains B, or A and B contain each other's boundaries.
+	// (Note that A contains all the vertices of B in either case.)
+	if l.subregionBound.Contains(o.bound) || l.bound.Union(o.bound).IsFull() {
+		if l.ContainsPoint(o.Vertex(0)) {
+			return true
+		}
+	}
+	// Check whether B contains A.
+	if o.subregionBound.Contains(l.bound) {
+		if o.ContainsPoint(l.Vertex(0)) {
+			return true
+		}
+	}
+	return false
+}
+
+// Equal reports whether two loops have the same vertices in the same linear order
+// (i.e., cyclic rotations are not allowed).
+func (l *Loop) Equal(other *Loop) bool {
+	if len(l.vertices) != len(other.vertices) {
+		return false
+	}
+
+	for i, v := range l.vertices {
+		if v != other.Vertex(i) {
+			return false
+		}
+	}
+	return true
+}
+
+// BoundaryEqual reports whether the two loops have the same boundary. This is
+// true if and only if the loops have the same vertices in the same cyclic order
+// (i.e., the vertices may be cyclically rotated). The empty and full loops are
+// considered to have different boundaries.
+func (l *Loop) BoundaryEqual(o *Loop) bool {
+	if len(l.vertices) != len(o.vertices) {
+		return false
+	}
+
+	// Special case to handle empty or full loops.  Since they have the same
+	// number of vertices, if one loop is empty/full then so is the other.
+	if l.isEmptyOrFull() {
+		return l.IsEmpty() == o.IsEmpty()
+	}
+
+	// Loop through the vertices to find the first of ours that matches the
+	// starting vertex of the other loop. Use that offset to then 'align' the
+	// vertices for comparison.
+	for offset, vertex := range l.vertices {
+		if vertex == o.Vertex(0) {
+			// There is at most one starting offset since loop vertices are unique.
+			for i := 0; i < len(l.vertices); i++ {
+				if l.Vertex(i+offset) != o.Vertex(i) {
+					return false
+				}
+			}
+			return true
+		}
+	}
+	return false
+}
+
+// compareBoundary returns +1 if this loop contains the boundary of the other loop,
+// -1 if it excludes the boundary of the other, and 0 if the boundaries of the two
+// loops cross. Shared edges are handled as follows:
+//
+//   If XY is a shared edge, define Reversed(XY) to be true if XY
+//     appears in opposite directions in both loops.
+//   Then this loop contains XY if and only if Reversed(XY) == the other loop is a hole.
+//   (Intuitively, this checks whether this loop contains a vanishingly small region
+//   extending from the boundary of the other toward the interior of the polygon to
+//   which the other belongs.)
+//
+// This function is used for testing containment and intersection of
+// multi-loop polygons. Note that this method is not symmetric, since the
+// result depends on the direction of this loop but not on the direction of
+// the other loop (in the absence of shared edges).
+//
+// This requires that neither loop is empty, and if other loop IsFull, then it must not
+// be a hole.
+func (l *Loop) compareBoundary(o *Loop) int {
+	// The bounds must intersect for containment or crossing.
+	if !l.bound.Intersects(o.bound) {
+		return -1
+	}
+
+	// Full loops are handled as though the loop surrounded the entire sphere.
+	if l.IsFull() {
+		return 1
+	}
+	if o.IsFull() {
+		return -1
+	}
+
+	// Check whether there are any edge crossings, and also check the loop
+	// relationship at any shared vertices.
+	relation := newCompareBoundaryRelation(o.IsHole())
+	if hasCrossingRelation(l, o, relation) {
+		return 0
+	}
+	if relation.foundSharedVertex {
+		if relation.containsEdge {
+			return 1
+		}
+		return -1
+	}
+
+	// There are no edge intersections or shared vertices, so we can check
+	// whether A contains an arbitrary vertex of B.
+	if l.ContainsPoint(o.Vertex(0)) {
+		return 1
+	}
+	return -1
+}
+
+// ContainsOrigin reports true if this loop contains s2.OriginPoint().
+func (l *Loop) ContainsOrigin() bool {
+	return l.originInside
+}
+
+// ReferencePoint returns the reference point for this loop.
+func (l *Loop) ReferencePoint() ReferencePoint {
+	return OriginReferencePoint(l.originInside)
+}
+
+// NumEdges returns the number of edges in this shape.
+func (l *Loop) NumEdges() int {
+	if l.isEmptyOrFull() {
+		return 0
+	}
+	return len(l.vertices)
+}
+
+// Edge returns the endpoints for the given edge index.
+func (l *Loop) Edge(i int) Edge {
+	return Edge{l.Vertex(i), l.Vertex(i + 1)}
+}
+
+// NumChains reports the number of contiguous edge chains in the Loop.
+func (l *Loop) NumChains() int {
+	if l.IsEmpty() {
+		return 0
+	}
+	return 1
+}
+
+// Chain returns the i-th edge chain in the Shape.
+func (l *Loop) Chain(chainID int) Chain {
+	return Chain{0, l.NumEdges()}
+}
+
+// ChainEdge returns the j-th edge of the i-th edge chain.
+func (l *Loop) ChainEdge(chainID, offset int) Edge {
+	return Edge{l.Vertex(offset), l.Vertex(offset + 1)}
+}
+
+// ChainPosition returns a ChainPosition pair (i, j) such that edgeID is the
+// j-th edge of the Loop.
+func (l *Loop) ChainPosition(edgeID int) ChainPosition {
+	return ChainPosition{0, edgeID}
+}
+
+// Dimension returns the dimension of the geometry represented by this Loop.
+func (l *Loop) Dimension() int { return 2 }
+
+func (l *Loop) typeTag() typeTag { return typeTagNone }
+
+func (l *Loop) privateInterface() {}
+
+// IsEmpty reports true if this is the special empty loop that contains no points.
+func (l *Loop) IsEmpty() bool {
+	return l.isEmptyOrFull() && !l.ContainsOrigin()
+}
+
+// IsFull reports true if this is the special full loop that contains all points.
+func (l *Loop) IsFull() bool {
+	return l.isEmptyOrFull() && l.ContainsOrigin()
+}
+
+// isEmptyOrFull reports true if this loop is either the "empty" or "full" special loops.
+func (l *Loop) isEmptyOrFull() bool {
+	return len(l.vertices) == 1
+}
+
+// Vertices returns the vertices in the loop.
+func (l *Loop) Vertices() []Point {
+	return l.vertices
+}
+
+// RectBound returns a tight bounding rectangle. If the loop contains the point,
+// the bound also contains it.
+func (l *Loop) RectBound() Rect {
+	return l.bound
+}
+
+// CapBound returns a bounding cap that may have more padding than the corresponding
+// RectBound. The bound is conservative such that if the loop contains a point P,
+// the bound also contains it.
+func (l *Loop) CapBound() Cap {
+	return l.bound.CapBound()
+}
+
+// Vertex returns the vertex for the given index. For convenience, the vertex indices
+// wrap automatically for methods that do index math such as Edge.
+// i.e., Vertex(NumEdges() + n) is the same as Vertex(n).
+func (l *Loop) Vertex(i int) Point {
+	return l.vertices[i%len(l.vertices)]
+}
+
+// OrientedVertex returns the vertex in reverse order if the loop represents a polygon
+// hole. For example, arguments 0, 1, 2 are mapped to vertices n-1, n-2, n-3, where
+// n == len(vertices). This ensures that the interior of the polygon is always to
+// the left of the vertex chain.
+//
+// This requires: 0 <= i < 2 * len(vertices)
+func (l *Loop) OrientedVertex(i int) Point {
+	j := i - len(l.vertices)
+	if j < 0 {
+		j = i
+	}
+	if l.IsHole() {
+		j = len(l.vertices) - 1 - j
+	}
+	return l.Vertex(j)
+}
+
+// NumVertices returns the number of vertices in this loop.
+func (l *Loop) NumVertices() int {
+	return len(l.vertices)
+}
+
+// bruteForceContainsPoint reports if the given point is contained by this loop.
+// This method does not use the ShapeIndex, so it is only preferable below a certain
+// size of loop.
+func (l *Loop) bruteForceContainsPoint(p Point) bool {
+	origin := OriginPoint()
+	inside := l.originInside
+	crosser := NewChainEdgeCrosser(origin, p, l.Vertex(0))
+	for i := 1; i <= len(l.vertices); i++ { // add vertex 0 twice
+		inside = inside != crosser.EdgeOrVertexChainCrossing(l.Vertex(i))
+	}
+	return inside
+}
+
+// ContainsPoint returns true if the loop contains the point.
+func (l *Loop) ContainsPoint(p Point) bool {
+	// Empty and full loops don't need a special case, but invalid loops with
+	// zero vertices do, so we might as well handle them all at once.
+	if len(l.vertices) < 3 {
+		return l.originInside
+	}
+
+	// For small loops, and during initial construction, it is faster to just
+	// check all the crossing.
+	const maxBruteForceVertices = 32
+	if len(l.vertices) < maxBruteForceVertices || l.index == nil {
+		return l.bruteForceContainsPoint(p)
+	}
+
+	// Otherwise, look up the point in the index.
+	it := l.index.Iterator()
+	if !it.LocatePoint(p) {
+		return false
+	}
+	return l.iteratorContainsPoint(it, p)
+}
+
+// ContainsCell reports whether the given Cell is contained by this Loop.
+func (l *Loop) ContainsCell(target Cell) bool {
+	it := l.index.Iterator()
+	relation := it.LocateCellID(target.ID())
+
+	// If "target" is disjoint from all index cells, it is not contained.
+	// Similarly, if "target" is subdivided into one or more index cells then it
+	// is not contained, since index cells are subdivided only if they (nearly)
+	// intersect a sufficient number of edges.  (But note that if "target" itself
+	// is an index cell then it may be contained, since it could be a cell with
+	// no edges in the loop interior.)
+	if relation != Indexed {
+		return false
+	}
+
+	// Otherwise check if any edges intersect "target".
+	if l.boundaryApproxIntersects(it, target) {
+		return false
+	}
+
+	// Otherwise check if the loop contains the center of "target".
+	return l.iteratorContainsPoint(it, target.Center())
+}
+
+// IntersectsCell reports whether this Loop intersects the given cell.
+func (l *Loop) IntersectsCell(target Cell) bool {
+	it := l.index.Iterator()
+	relation := it.LocateCellID(target.ID())
+
+	// If target does not overlap any index cell, there is no intersection.
+	if relation == Disjoint {
+		return false
+	}
+	// If target is subdivided into one or more index cells, there is an
+	// intersection to within the ShapeIndex error bound (see Contains).
+	if relation == Subdivided {
+		return true
+	}
+	// If target is an index cell, there is an intersection because index cells
+	// are created only if they have at least one edge or they are entirely
+	// contained by the loop.
+	if it.CellID() == target.id {
+		return true
+	}
+	// Otherwise check if any edges intersect target.
+	if l.boundaryApproxIntersects(it, target) {
+		return true
+	}
+	// Otherwise check if the loop contains the center of target.
+	return l.iteratorContainsPoint(it, target.Center())
+}
+
+// CellUnionBound computes a covering of the Loop.
+func (l *Loop) CellUnionBound() []CellID {
+	return l.CapBound().CellUnionBound()
+}
+
+// boundaryApproxIntersects reports if the loop's boundary intersects target.
+// It may also return true when the loop boundary does not intersect target but
+// some edge comes within the worst-case error tolerance.
+//
+// This requires that it.Locate(target) returned Indexed.
+func (l *Loop) boundaryApproxIntersects(it *ShapeIndexIterator, target Cell) bool {
+	aClipped := it.IndexCell().findByShapeID(0)
+
+	// If there are no edges, there is no intersection.
+	if len(aClipped.edges) == 0 {
+		return false
+	}
+
+	// We can save some work if target is the index cell itself.
+	if it.CellID() == target.ID() {
+		return true
+	}
+
+	// Otherwise check whether any of the edges intersect target.
+	maxError := (faceClipErrorUVCoord + intersectsRectErrorUVDist)
+	bound := target.BoundUV().ExpandedByMargin(maxError)
+	for _, ai := range aClipped.edges {
+		v0, v1, ok := ClipToPaddedFace(l.Vertex(ai), l.Vertex(ai+1), target.Face(), maxError)
+		if ok && edgeIntersectsRect(v0, v1, bound) {
+			return true
+		}
+	}
+	return false
+}
+
+// iteratorContainsPoint reports if the iterator that is positioned at the ShapeIndexCell
+// that may contain p, contains the point p.
+func (l *Loop) iteratorContainsPoint(it *ShapeIndexIterator, p Point) bool {
+	// Test containment by drawing a line segment from the cell center to the
+	// given point and counting edge crossings.
+	aClipped := it.IndexCell().findByShapeID(0)
+	inside := aClipped.containsCenter
+	if len(aClipped.edges) > 0 {
+		center := it.Center()
+		crosser := NewEdgeCrosser(center, p)
+		aiPrev := -2
+		for _, ai := range aClipped.edges {
+			if ai != aiPrev+1 {
+				crosser.RestartAt(l.Vertex(ai))
+			}
+			aiPrev = ai
+			inside = inside != crosser.EdgeOrVertexChainCrossing(l.Vertex(ai+1))
+		}
+	}
+	return inside
+}
+
+// RegularLoop creates a loop with the given number of vertices, all
+// located on a circle of the specified radius around the given center.
+func RegularLoop(center Point, radius s1.Angle, numVertices int) *Loop {
+	return RegularLoopForFrame(getFrame(center), radius, numVertices)
+}
+
+// RegularLoopForFrame creates a loop centered around the z-axis of the given
+// coordinate frame, with the first vertex in the direction of the positive x-axis.
+func RegularLoopForFrame(frame matrix3x3, radius s1.Angle, numVertices int) *Loop {
+	return LoopFromPoints(regularPointsForFrame(frame, radius, numVertices))
+}
+
+// CanonicalFirstVertex returns a first index and a direction (either +1 or -1)
+// such that the vertex sequence (first, first+dir, ..., first+(n-1)*dir) does
+// not change when the loop vertex order is rotated or inverted. This allows the
+// loop vertices to be traversed in a canonical order. The return values are
+// chosen such that (first, ..., first+n*dir) are in the range [0, 2*n-1] as
+// expected by the Vertex method.
+func (l *Loop) CanonicalFirstVertex() (firstIdx, direction int) {
+	firstIdx = 0
+	n := len(l.vertices)
+	for i := 1; i < n; i++ {
+		if l.Vertex(i).Cmp(l.Vertex(firstIdx).Vector) == -1 {
+			firstIdx = i
+		}
+	}
+
+	// 0 <= firstIdx <= n-1, so (firstIdx+n*dir) <= 2*n-1.
+	if l.Vertex(firstIdx+1).Cmp(l.Vertex(firstIdx+n-1).Vector) == -1 {
+		return firstIdx, 1
+	}
+
+	// n <= firstIdx <= 2*n-1, so (firstIdx+n*dir) >= 0.
+	firstIdx += n
+	return firstIdx, -1
+}
+
+// TurningAngle returns the sum of the turning angles at each vertex. The return
+// value is positive if the loop is counter-clockwise, negative if the loop is
+// clockwise, and zero if the loop is a great circle. Degenerate and
+// nearly-degenerate loops are handled consistently with Sign. So for example,
+// if a loop has zero area (i.e., it is a very small CCW loop) then the turning
+// angle will always be negative.
+//
+// This quantity is also called the "geodesic curvature" of the loop.
+func (l *Loop) TurningAngle() float64 {
+	// For empty and full loops, we return the limit value as the loop area
+	// approaches 0 or 4*Pi respectively.
+	if l.isEmptyOrFull() {
+		if l.ContainsOrigin() {
+			return -2 * math.Pi
+		}
+		return 2 * math.Pi
+	}
+
+	// Don't crash even if the loop is not well-defined.
+	if len(l.vertices) < 3 {
+		return 0
+	}
+
+	// To ensure that we get the same result when the vertex order is rotated,
+	// and that the result is negated when the vertex order is reversed, we need
+	// to add up the individual turn angles in a consistent order. (In general,
+	// adding up a set of numbers in a different order can change the sum due to
+	// rounding errors.)
+	//
+	// Furthermore, if we just accumulate an ordinary sum then the worst-case
+	// error is quadratic in the number of vertices. (This can happen with
+	// spiral shapes, where the partial sum of the turning angles can be linear
+	// in the number of vertices.) To avoid this we use the Kahan summation
+	// algorithm (http://en.wikipedia.org/wiki/Kahan_summation_algorithm).
+	n := len(l.vertices)
+	i, dir := l.CanonicalFirstVertex()
+	sum := TurnAngle(l.Vertex((i+n-dir)%n), l.Vertex(i), l.Vertex((i+dir)%n))
+
+	compensation := s1.Angle(0)
+	for n-1 > 0 {
+		i += dir
+		angle := TurnAngle(l.Vertex(i-dir), l.Vertex(i), l.Vertex(i+dir))
+		oldSum := sum
+		angle += compensation
+		sum += angle
+		compensation = (oldSum - sum) + angle
+		n--
+	}
+	return float64(dir) * float64(sum+compensation)
+}
+
+// turningAngleMaxError return the maximum error in TurningAngle. The value is not
+// constant; it depends on the loop.
+func (l *Loop) turningAngleMaxError() float64 {
+	// The maximum error can be bounded as follows:
+	//   2.24 * dblEpsilon    for RobustCrossProd(b, a)
+	//   2.24 * dblEpsilon    for RobustCrossProd(c, b)
+	//   3.25 * dblEpsilon    for Angle()
+	//   2.00 * dblEpsilon    for each addition in the Kahan summation
+	//   ------------------
+	//   9.73 * dblEpsilon
+	maxErrorPerVertex := 9.73 * dblEpsilon
+	return maxErrorPerVertex * float64(len(l.vertices))
+}
+
+// IsHole reports whether this loop represents a hole in its containing polygon.
+func (l *Loop) IsHole() bool { return l.depth&1 != 0 }
+
+// Sign returns -1 if this Loop represents a hole in its containing polygon, and +1 otherwise.
+func (l *Loop) Sign() int {
+	if l.IsHole() {
+		return -1
+	}
+	return 1
+}
+
+// IsNormalized reports whether the loop area is at most 2*pi. Degenerate loops are
+// handled consistently with Sign, i.e., if a loop can be
+// expressed as the union of degenerate or nearly-degenerate CCW triangles,
+// then it will always be considered normalized.
+func (l *Loop) IsNormalized() bool {
+	// Optimization: if the longitude span is less than 180 degrees, then the
+	// loop covers less than half the sphere and is therefore normalized.
+	if l.bound.Lng.Length() < math.Pi {
+		return true
+	}
+
+	// We allow some error so that hemispheres are always considered normalized.
+	// TODO(roberts): This is no longer required by the Polygon implementation,
+	// so alternatively we could create the invariant that a loop is normalized
+	// if and only if its complement is not normalized.
+	return l.TurningAngle() >= -l.turningAngleMaxError()
+}
+
+// Normalize inverts the loop if necessary so that the area enclosed by the loop
+// is at most 2*pi.
+func (l *Loop) Normalize() {
+	if !l.IsNormalized() {
+		l.Invert()
+	}
+}
+
+// Invert reverses the order of the loop vertices, effectively complementing the
+// region represented by the loop. For example, the loop ABCD (with edges
+// AB, BC, CD, DA) becomes the loop DCBA (with edges DC, CB, BA, AD).
+// Notice that the last edge is the same in both cases except that its
+// direction has been reversed.
+func (l *Loop) Invert() {
+	l.index.Reset()
+	if l.isEmptyOrFull() {
+		if l.IsFull() {
+			l.vertices[0] = emptyLoopPoint
+		} else {
+			l.vertices[0] = fullLoopPoint
+		}
+	} else {
+		// For non-special loops, reverse the slice of vertices.
+		for i := len(l.vertices)/2 - 1; i >= 0; i-- {
+			opp := len(l.vertices) - 1 - i
+			l.vertices[i], l.vertices[opp] = l.vertices[opp], l.vertices[i]
+		}
+	}
+
+	// originInside must be set correctly before building the ShapeIndex.
+	l.originInside = !l.originInside
+	if l.bound.Lat.Lo > -math.Pi/2 && l.bound.Lat.Hi < math.Pi/2 {
+		// The complement of this loop contains both poles.
+		l.bound = FullRect()
+		l.subregionBound = l.bound
+	} else {
+		l.initBound()
+	}
+	l.index.Add(l)
+}
+
+// findVertex returns the index of the vertex at the given Point in the range
+// 1..numVertices, and a boolean indicating if a vertex was found.
+func (l *Loop) findVertex(p Point) (index int, ok bool) {
+	const notFound = 0
+	if len(l.vertices) < 10 {
+		// Exhaustive search for loops below a small threshold.
+		for i := 1; i <= len(l.vertices); i++ {
+			if l.Vertex(i) == p {
+				return i, true
+			}
+		}
+		return notFound, false
+	}
+
+	it := l.index.Iterator()
+	if !it.LocatePoint(p) {
+		return notFound, false
+	}
+
+	aClipped := it.IndexCell().findByShapeID(0)
+	for i := aClipped.numEdges() - 1; i >= 0; i-- {
+		ai := aClipped.edges[i]
+		if l.Vertex(ai) == p {
+			if ai == 0 {
+				return len(l.vertices), true
+			}
+			return ai, true
+		}
+
+		if l.Vertex(ai+1) == p {
+			return ai + 1, true
+		}
+	}
+	return notFound, false
+}
+
+// ContainsNested reports whether the given loops is contained within this loop.
+// This function does not test for edge intersections. The two loops must meet
+// all of the Polygon requirements; for example this implies that their
+// boundaries may not cross or have any shared edges (although they may have
+// shared vertices).
+func (l *Loop) ContainsNested(other *Loop) bool {
+	if !l.subregionBound.Contains(other.bound) {
+		return false
+	}
+
+	// Special cases to handle either loop being empty or full.  Also bail out
+	// when B has no vertices to avoid heap overflow on the vertex(1) call
+	// below.  (This method is called during polygon initialization before the
+	// client has an opportunity to call IsValid().)
+	if l.isEmptyOrFull() || other.NumVertices() < 2 {
+		return l.IsFull() || other.IsEmpty()
+	}
+
+	// We are given that A and B do not share any edges, and that either one
+	// loop contains the other or they do not intersect.
+	m, ok := l.findVertex(other.Vertex(1))
+	if !ok {
+		// Since other.vertex(1) is not shared, we can check whether A contains it.
+		return l.ContainsPoint(other.Vertex(1))
+	}
+
+	// Check whether the edge order around other.Vertex(1) is compatible with
+	// A containing B.
+	return WedgeContains(l.Vertex(m-1), l.Vertex(m), l.Vertex(m+1), other.Vertex(0), other.Vertex(2))
+}
+
+// surfaceIntegralFloat64 computes the oriented surface integral of some quantity f(x)
+// over the loop interior, given a function f(A,B,C) that returns the
+// corresponding integral over the spherical triangle ABC. Here "oriented
+// surface integral" means:
+//
+// (1) f(A,B,C) must be the integral of f if ABC is counterclockwise,
+//     and the integral of -f if ABC is clockwise.
+//
+// (2) The result of this function is *either* the integral of f over the
+//     loop interior, or the integral of (-f) over the loop exterior.
+//
+// Note that there are at least two common situations where it easy to work
+// around property (2) above:
+//
+//  - If the integral of f over the entire sphere is zero, then it doesn't
+//    matter which case is returned because they are always equal.
+//
+//  - If f is non-negative, then it is easy to detect when the integral over
+//    the loop exterior has been returned, and the integral over the loop
+//    interior can be obtained by adding the integral of f over the entire
+//    unit sphere (a constant) to the result.
+//
+// Any changes to this method may need corresponding changes to surfaceIntegralPoint as well.
+func (l *Loop) surfaceIntegralFloat64(f func(a, b, c Point) float64) float64 {
+	// We sum f over a collection T of oriented triangles, possibly
+	// overlapping. Let the sign of a triangle be +1 if it is CCW and -1
+	// otherwise, and let the sign of a point x be the sum of the signs of the
+	// triangles containing x. Then the collection of triangles T is chosen
+	// such that either:
+	//
+	//  (1) Each point in the loop interior has sign +1, and sign 0 otherwise; or
+	//  (2) Each point in the loop exterior has sign -1, and sign 0 otherwise.
+	//
+	// The triangles basically consist of a fan from vertex 0 to every loop
+	// edge that does not include vertex 0. These triangles will always satisfy
+	// either (1) or (2). However, what makes this a bit tricky is that
+	// spherical edges become numerically unstable as their length approaches
+	// 180 degrees. Of course there is not much we can do if the loop itself
+	// contains such edges, but we would like to make sure that all the triangle
+	// edges under our control (i.e., the non-loop edges) are stable. For
+	// example, consider a loop around the equator consisting of four equally
+	// spaced points. This is a well-defined loop, but we cannot just split it
+	// into two triangles by connecting vertex 0 to vertex 2.
+	//
+	// We handle this type of situation by moving the origin of the triangle fan
+	// whenever we are about to create an unstable edge. We choose a new
+	// location for the origin such that all relevant edges are stable. We also
+	// create extra triangles with the appropriate orientation so that the sum
+	// of the triangle signs is still correct at every point.
+
+	// The maximum length of an edge for it to be considered numerically stable.
+	// The exact value is fairly arbitrary since it depends on the stability of
+	// the function f. The value below is quite conservative but could be
+	// reduced further if desired.
+	const maxLength = math.Pi - 1e-5
+
+	var sum float64
+	origin := l.Vertex(0)
+	for i := 1; i+1 < len(l.vertices); i++ {
+		// Let V_i be vertex(i), let O be the current origin, and let length(A,B)
+		// be the length of edge (A,B). At the start of each loop iteration, the
+		// "leading edge" of the triangle fan is (O,V_i), and we want to extend
+		// the triangle fan so that the leading edge is (O,V_i+1).
+		//
+		// Invariants:
+		//  1. length(O,V_i) < maxLength for all (i > 1).
+		//  2. Either O == V_0, or O is approximately perpendicular to V_0.
+		//  3. "sum" is the oriented integral of f over the area defined by
+		//     (O, V_0, V_1, ..., V_i).
+		if l.Vertex(i+1).Angle(origin.Vector) > maxLength {
+			// We are about to create an unstable edge, so choose a new origin O'
+			// for the triangle fan.
+			oldOrigin := origin
+			if origin == l.Vertex(0) {
+				// The following point is well-separated from V_i and V_0 (and
+				// therefore V_i+1 as well).
+				origin = Point{l.Vertex(0).PointCross(l.Vertex(i)).Normalize()}
+			} else if l.Vertex(i).Angle(l.Vertex(0).Vector) < maxLength {
+				// All edges of the triangle (O, V_0, V_i) are stable, so we can
+				// revert to using V_0 as the origin.
+				origin = l.Vertex(0)
+			} else {
+				// (O, V_i+1) and (V_0, V_i) are antipodal pairs, and O and V_0 are
+				// perpendicular. Therefore V_0.CrossProd(O) is approximately
+				// perpendicular to all of {O, V_0, V_i, V_i+1}, and we can choose
+				// this point O' as the new origin.
+				origin = Point{l.Vertex(0).Cross(oldOrigin.Vector)}
+
+				// Advance the edge (V_0,O) to (V_0,O').
+				sum += f(l.Vertex(0), oldOrigin, origin)
+			}
+			// Advance the edge (O,V_i) to (O',V_i).
+			sum += f(oldOrigin, l.Vertex(i), origin)
+		}
+		// Advance the edge (O,V_i) to (O,V_i+1).
+		sum += f(origin, l.Vertex(i), l.Vertex(i+1))
+	}
+	// If the origin is not V_0, we need to sum one more triangle.
+	if origin != l.Vertex(0) {
+		// Advance the edge (O,V_n-1) to (O,V_0).
+		sum += f(origin, l.Vertex(len(l.vertices)-1), l.Vertex(0))
+	}
+	return sum
+}
+
+// surfaceIntegralPoint mirrors the surfaceIntegralFloat64 method but over Points;
+// see that method for commentary. The C++ version uses a templated method.
+// Any changes to this method may need corresponding changes to surfaceIntegralFloat64 as well.
+func (l *Loop) surfaceIntegralPoint(f func(a, b, c Point) Point) Point {
+	const maxLength = math.Pi - 1e-5
+	var sum r3.Vector
+
+	origin := l.Vertex(0)
+	for i := 1; i+1 < len(l.vertices); i++ {
+		if l.Vertex(i+1).Angle(origin.Vector) > maxLength {
+			oldOrigin := origin
+			if origin == l.Vertex(0) {
+				origin = Point{l.Vertex(0).PointCross(l.Vertex(i)).Normalize()}
+			} else if l.Vertex(i).Angle(l.Vertex(0).Vector) < maxLength {
+				origin = l.Vertex(0)
+			} else {
+				origin = Point{l.Vertex(0).Cross(oldOrigin.Vector)}
+				sum = sum.Add(f(l.Vertex(0), oldOrigin, origin).Vector)
+			}
+			sum = sum.Add(f(oldOrigin, l.Vertex(i), origin).Vector)
+		}
+		sum = sum.Add(f(origin, l.Vertex(i), l.Vertex(i+1)).Vector)
+	}
+	if origin != l.Vertex(0) {
+		sum = sum.Add(f(origin, l.Vertex(len(l.vertices)-1), l.Vertex(0)).Vector)
+	}
+	return Point{sum}
+}
+
+// Area returns the area of the loop interior, i.e. the region on the left side of
+// the loop. The return value is between 0 and 4*pi. (Note that the return
+// value is not affected by whether this loop is a "hole" or a "shell".)
+func (l *Loop) Area() float64 {
+	// It is surprisingly difficult to compute the area of a loop robustly. The
+	// main issues are (1) whether degenerate loops are considered to be CCW or
+	// not (i.e., whether their area is close to 0 or 4*pi), and (2) computing
+	// the areas of small loops with good relative accuracy.
+	//
+	// With respect to degeneracies, we would like Area to be consistent
+	// with ContainsPoint in that loops that contain many points
+	// should have large areas, and loops that contain few points should have
+	// small areas. For example, if a degenerate triangle is considered CCW
+	// according to s2predicates Sign, then it will contain very few points and
+	// its area should be approximately zero. On the other hand if it is
+	// considered clockwise, then it will contain virtually all points and so
+	// its area should be approximately 4*pi.
+	//
+	// More precisely, let U be the set of Points for which IsUnitLength
+	// is true, let P(U) be the projection of those points onto the mathematical
+	// unit sphere, and let V(P(U)) be the Voronoi diagram of the projected
+	// points. Then for every loop x, we would like Area to approximately
+	// equal the sum of the areas of the Voronoi regions of the points p for
+	// which x.ContainsPoint(p) is true.
+	//
+	// The second issue is that we want to compute the area of small loops
+	// accurately. This requires having good relative precision rather than
+	// good absolute precision. For example, if the area of a loop is 1e-12 and
+	// the error is 1e-15, then the area only has 3 digits of accuracy. (For
+	// reference, 1e-12 is about 40 square meters on the surface of the earth.)
+	// We would like to have good relative accuracy even for small loops.
+	//
+	// To achieve these goals, we combine two different methods of computing the
+	// area. This first method is based on the Gauss-Bonnet theorem, which says
+	// that the area enclosed by the loop equals 2*pi minus the total geodesic
+	// curvature of the loop (i.e., the sum of the "turning angles" at all the
+	// loop vertices). The big advantage of this method is that as long as we
+	// use Sign to compute the turning angle at each vertex, then
+	// degeneracies are always handled correctly. In other words, if a
+	// degenerate loop is CCW according to the symbolic perturbations used by
+	// Sign, then its turning angle will be approximately 2*pi.
+	//
+	// The disadvantage of the Gauss-Bonnet method is that its absolute error is
+	// about 2e-15 times the number of vertices (see turningAngleMaxError).
+	// So, it cannot compute the area of small loops accurately.
+	//
+	// The second method is based on splitting the loop into triangles and
+	// summing the area of each triangle. To avoid the difficulty and expense
+	// of decomposing the loop into a union of non-overlapping triangles,
+	// instead we compute a signed sum over triangles that may overlap (see the
+	// comments for surfaceIntegral). The advantage of this method
+	// is that the area of each triangle can be computed with much better
+	// relative accuracy (using l'Huilier's theorem). The disadvantage is that
+	// the result is a signed area: CCW loops may yield a small positive value,
+	// while CW loops may yield a small negative value (which is converted to a
+	// positive area by adding 4*pi). This means that small errors in computing
+	// the signed area may translate into a very large error in the result (if
+	// the sign of the sum is incorrect).
+	//
+	// So, our strategy is to combine these two methods as follows. First we
+	// compute the area using the "signed sum over triangles" approach (since it
+	// is generally more accurate). We also estimate the maximum error in this
+	// result. If the signed area is too close to zero (i.e., zero is within
+	// the error bounds), then we double-check the sign of the result using the
+	// Gauss-Bonnet method. (In fact we just call IsNormalized, which is
+	// based on this method.) If the two methods disagree, we return either 0
+	// or 4*pi based on the result of IsNormalized. Otherwise we return the
+	// area that we computed originally.
+	if l.isEmptyOrFull() {
+		if l.ContainsOrigin() {
+			return 4 * math.Pi
+		}
+		return 0
+	}
+	area := l.surfaceIntegralFloat64(SignedArea)
+
+	// TODO(roberts): This error estimate is very approximate. There are two
+	// issues: (1) SignedArea needs some improvements to ensure that its error
+	// is actually never higher than GirardArea, and (2) although the number of
+	// triangles in the sum is typically N-2, in theory it could be as high as
+	// 2*N for pathological inputs. But in other respects this error bound is
+	// very conservative since it assumes that the maximum error is achieved on
+	// every triangle.
+	maxError := l.turningAngleMaxError()
+
+	// The signed area should be between approximately -4*pi and 4*pi.
+	if area < 0 {
+		// We have computed the negative of the area of the loop exterior.
+		area += 4 * math.Pi
+	}
+
+	if area > 4*math.Pi {
+		area = 4 * math.Pi
+	}
+	if area < 0 {
+		area = 0
+	}
+
+	// If the area is close enough to zero or 4*pi so that the loop orientation
+	// is ambiguous, then we compute the loop orientation explicitly.
+	if area < maxError && !l.IsNormalized() {
+		return 4 * math.Pi
+	} else if area > (4*math.Pi-maxError) && l.IsNormalized() {
+		return 0
+	}
+
+	return area
+}
+
+// Centroid returns the true centroid of the loop multiplied by the area of the
+// loop. The result is not unit length, so you may want to normalize it. Also
+// note that in general, the centroid may not be contained by the loop.
+//
+// We prescale by the loop area for two reasons: (1) it is cheaper to
+// compute this way, and (2) it makes it easier to compute the centroid of
+// more complicated shapes (by splitting them into disjoint regions and
+// adding their centroids).
+//
+// Note that the return value is not affected by whether this loop is a
+// "hole" or a "shell".
+func (l *Loop) Centroid() Point {
+	// surfaceIntegralPoint() returns either the integral of position over loop
+	// interior, or the negative of the integral of position over the loop
+	// exterior. But these two values are the same (!), because the integral of
+	// position over the entire sphere is (0, 0, 0).
+	return l.surfaceIntegralPoint(TrueCentroid)
+}
+
+// Encode encodes the Loop.
+func (l Loop) Encode(w io.Writer) error {
+	e := &encoder{w: w}
+	l.encode(e)
+	return e.err
+}
+
+func (l Loop) encode(e *encoder) {
+	e.writeInt8(encodingVersion)
+	e.writeUint32(uint32(len(l.vertices)))
+	for _, v := range l.vertices {
+		e.writeFloat64(v.X)
+		e.writeFloat64(v.Y)
+		e.writeFloat64(v.Z)
+	}
+
+	e.writeBool(l.originInside)
+	e.writeInt32(int32(l.depth))
+
+	// Encode the bound.
+	l.bound.encode(e)
+}
+
+// Decode decodes a loop.
+func (l *Loop) Decode(r io.Reader) error {
+	*l = Loop{}
+	d := &decoder{r: asByteReader(r)}
+	l.decode(d)
+	return d.err
+}
+
+func (l *Loop) decode(d *decoder) {
+	version := int8(d.readUint8())
+	if d.err != nil {
+		return
+	}
+	if version != encodingVersion {
+		d.err = fmt.Errorf("cannot decode version %d", version)
+		return
+	}
+
+	// Empty loops are explicitly allowed here: a newly created loop has zero vertices
+	// and such loops encode and decode properly.
+	nvertices := d.readUint32()
+	if nvertices > maxEncodedVertices {
+		if d.err == nil {
+			d.err = fmt.Errorf("too many vertices (%d; max is %d)", nvertices, maxEncodedVertices)
+
+		}
+		return
+	}
+	l.vertices = make([]Point, nvertices)
+	for i := range l.vertices {
+		l.vertices[i].X = d.readFloat64()
+		l.vertices[i].Y = d.readFloat64()
+		l.vertices[i].Z = d.readFloat64()
+	}
+	l.originInside = d.readBool()
+	l.depth = int(d.readUint32())
+	l.bound.decode(d)
+	l.subregionBound = ExpandForSubregions(l.bound)
+
+	l.index = NewShapeIndex()
+	l.index.Add(l)
+}
+
+// Bitmasks to read from properties.
+const (
+	originInside = 1 << iota
+	boundEncoded
+)
+
+func (l *Loop) xyzFaceSiTiVertices() []xyzFaceSiTi {
+	ret := make([]xyzFaceSiTi, len(l.vertices))
+	for i, v := range l.vertices {
+		ret[i].xyz = v
+		ret[i].face, ret[i].si, ret[i].ti, ret[i].level = xyzToFaceSiTi(v)
+	}
+	return ret
+}
+
+func (l *Loop) encodeCompressed(e *encoder, snapLevel int, vertices []xyzFaceSiTi) {
+	if len(l.vertices) != len(vertices) {
+		panic("encodeCompressed: vertices must be the same length as l.vertices")
+	}
+	if len(vertices) > maxEncodedVertices {
+		if e.err == nil {
+			e.err = fmt.Errorf("too many vertices (%d; max is %d)", len(vertices), maxEncodedVertices)
+		}
+		return
+	}
+	e.writeUvarint(uint64(len(vertices)))
+	encodePointsCompressed(e, vertices, snapLevel)
+
+	props := l.compressedEncodingProperties()
+	e.writeUvarint(props)
+	e.writeUvarint(uint64(l.depth))
+	if props&boundEncoded != 0 {
+		l.bound.encode(e)
+	}
+}
+
+func (l *Loop) compressedEncodingProperties() uint64 {
+	var properties uint64
+	if l.originInside {
+		properties |= originInside
+	}
+
+	// Write whether there is a bound so we can change the threshold later.
+	// Recomputing the bound multiplies the decode time taken per vertex
+	// by a factor of about 3.5.  Without recomputing the bound, decode
+	// takes approximately 125 ns / vertex.  A loop with 63 vertices
+	// encoded without the bound will take ~30us to decode, which is
+	// acceptable.  At ~3.5 bytes / vertex without the bound, adding
+	// the bound will increase the size by <15%, which is also acceptable.
+	const minVerticesForBound = 64
+	if len(l.vertices) >= minVerticesForBound {
+		properties |= boundEncoded
+	}
+
+	return properties
+}
+
+func (l *Loop) decodeCompressed(d *decoder, snapLevel int) {
+	nvertices := d.readUvarint()
+	if d.err != nil {
+		return
+	}
+	if nvertices > maxEncodedVertices {
+		d.err = fmt.Errorf("too many vertices (%d; max is %d)", nvertices, maxEncodedVertices)
+		return
+	}
+	l.vertices = make([]Point, nvertices)
+	decodePointsCompressed(d, snapLevel, l.vertices)
+	properties := d.readUvarint()
+
+	// Make sure values are valid before using.
+	if d.err != nil {
+		return
+	}
+
+	l.originInside = (properties & originInside) != 0
+
+	l.depth = int(d.readUvarint())
+
+	if (properties & boundEncoded) != 0 {
+		l.bound.decode(d)
+		if d.err != nil {
+			return
+		}
+		l.subregionBound = ExpandForSubregions(l.bound)
+	} else {
+		l.initBound()
+	}
+
+	l.index = NewShapeIndex()
+	l.index.Add(l)
+}
+
+// crossingTarget is an enum representing the possible crossing target cases for relations.
+type crossingTarget int
+
+const (
+	crossingTargetDontCare crossingTarget = iota
+	crossingTargetDontCross
+	crossingTargetCross
+)
+
+// loopRelation defines the interface for checking a type of relationship between two loops.
+// Some examples of relations are Contains, Intersects, or CompareBoundary.
+type loopRelation interface {
+	// Optionally, aCrossingTarget and bCrossingTarget can specify an early-exit
+	// condition for the loop relation. If any point P is found such that
+	//
+	//   A.ContainsPoint(P) == aCrossingTarget() &&
+	//   B.ContainsPoint(P) == bCrossingTarget()
+	//
+	// then the loop relation is assumed to be the same as if a pair of crossing
+	// edges were found. For example, the ContainsPoint relation has
+	//
+	//   aCrossingTarget() == crossingTargetDontCross
+	//   bCrossingTarget() == crossingTargetCross
+	//
+	// because if A.ContainsPoint(P) == false and B.ContainsPoint(P) == true
+	// for any point P, then it is equivalent to finding an edge crossing (i.e.,
+	// since Contains returns false in both cases).
+	//
+	// Loop relations that do not have an early-exit condition of this form
+	// should return crossingTargetDontCare for both crossing targets.
+
+	// aCrossingTarget reports whether loop A crosses the target point with
+	// the given relation type.
+	aCrossingTarget() crossingTarget
+	// bCrossingTarget reports whether loop B crosses the target point with
+	// the given relation type.
+	bCrossingTarget() crossingTarget
+
+	// wedgesCross reports if a shared vertex ab1 and the two associated wedges
+	// (a0, ab1, b2) and (b0, ab1, b2) are equivalent to an edge crossing.
+	// The loop relation is also allowed to maintain its own internal state, and
+	// can return true if it observes any sequence of wedges that are equivalent
+	// to an edge crossing.
+	wedgesCross(a0, ab1, a2, b0, b2 Point) bool
+}
+
+// loopCrosser is a helper type for determining whether two loops cross.
+// It is instantiated twice for each pair of loops to be tested, once for the
+// pair (A,B) and once for the pair (B,A), in order to be able to process
+// edges in either loop nesting order.
+type loopCrosser struct {
+	a, b            *Loop
+	relation        loopRelation
+	swapped         bool
+	aCrossingTarget crossingTarget
+	bCrossingTarget crossingTarget
+
+	// state maintained by startEdge and edgeCrossesCell.
+	crosser    *EdgeCrosser
+	aj, bjPrev int
+
+	// temporary data declared here to avoid repeated memory allocations.
+	bQuery *CrossingEdgeQuery
+	bCells []*ShapeIndexCell
+}
+
+// newLoopCrosser creates a loopCrosser from the given values. If swapped is true,
+// the loops A and B have been swapped. This affects how arguments are passed to
+// the given loop relation, since for example A.Contains(B) is not the same as
+// B.Contains(A).
+func newLoopCrosser(a, b *Loop, relation loopRelation, swapped bool) *loopCrosser {
+	l := &loopCrosser{
+		a:               a,
+		b:               b,
+		relation:        relation,
+		swapped:         swapped,
+		aCrossingTarget: relation.aCrossingTarget(),
+		bCrossingTarget: relation.bCrossingTarget(),
+		bQuery:          NewCrossingEdgeQuery(b.index),
+	}
+	if swapped {
+		l.aCrossingTarget, l.bCrossingTarget = l.bCrossingTarget, l.aCrossingTarget
+	}
+
+	return l
+}
+
+// startEdge sets the crossers state for checking the given edge of loop A.
+func (l *loopCrosser) startEdge(aj int) {
+	l.crosser = NewEdgeCrosser(l.a.Vertex(aj), l.a.Vertex(aj+1))
+	l.aj = aj
+	l.bjPrev = -2
+}
+
+// edgeCrossesCell reports whether the current edge of loop A has any crossings with
+// edges of the index cell of loop B.
+func (l *loopCrosser) edgeCrossesCell(bClipped *clippedShape) bool {
+	// Test the current edge of A against all edges of bClipped
+	bNumEdges := bClipped.numEdges()
+	for j := 0; j < bNumEdges; j++ {
+		bj := bClipped.edges[j]
+		if bj != l.bjPrev+1 {
+			l.crosser.RestartAt(l.b.Vertex(bj))
+		}
+		l.bjPrev = bj
+		if crossing := l.crosser.ChainCrossingSign(l.b.Vertex(bj + 1)); crossing == DoNotCross {
+			continue
+		} else if crossing == Cross {
+			return true
+		}
+
+		// We only need to check each shared vertex once, so we only
+		// consider the case where l.aVertex(l.aj+1) == l.b.Vertex(bj+1).
+		if l.a.Vertex(l.aj+1) == l.b.Vertex(bj+1) {
+			if l.swapped {
+				if l.relation.wedgesCross(l.b.Vertex(bj), l.b.Vertex(bj+1), l.b.Vertex(bj+2), l.a.Vertex(l.aj), l.a.Vertex(l.aj+2)) {
+					return true
+				}
+			} else {
+				if l.relation.wedgesCross(l.a.Vertex(l.aj), l.a.Vertex(l.aj+1), l.a.Vertex(l.aj+2), l.b.Vertex(bj), l.b.Vertex(bj+2)) {
+					return true
+				}
+			}
+		}
+	}
+
+	return false
+}
+
+// cellCrossesCell reports whether there are any edge crossings or wedge crossings
+// within the two given cells.
+func (l *loopCrosser) cellCrossesCell(aClipped, bClipped *clippedShape) bool {
+	// Test all edges of aClipped against all edges of bClipped.
+	for _, edge := range aClipped.edges {
+		l.startEdge(edge)
+		if l.edgeCrossesCell(bClipped) {
+			return true
+		}
+	}
+
+	return false
+}
+
+// cellCrossesAnySubcell reports whether given an index cell of A, if there are any
+// edge or wedge crossings with any index cell of B contained within bID.
+func (l *loopCrosser) cellCrossesAnySubcell(aClipped *clippedShape, bID CellID) bool {
+	// Test all edges of aClipped against all edges of B. The relevant B
+	// edges are guaranteed to be children of bID, which lets us find the
+	// correct index cells more efficiently.
+	bRoot := PaddedCellFromCellID(bID, 0)
+	for _, aj := range aClipped.edges {
+		// Use an CrossingEdgeQuery starting at bRoot to find the index cells
+		// of B that might contain crossing edges.
+		l.bCells = l.bQuery.getCells(l.a.Vertex(aj), l.a.Vertex(aj+1), bRoot)
+		if len(l.bCells) == 0 {
+			continue
+		}
+		l.startEdge(aj)
+		for c := 0; c < len(l.bCells); c++ {
+			if l.edgeCrossesCell(l.bCells[c].shapes[0]) {
+				return true
+			}
+		}
+	}
+
+	return false
+}
+
+// hasCrossing reports whether given two iterators positioned such that
+// ai.cellID().ContainsCellID(bi.cellID()), there is an edge or wedge crossing
+// anywhere within ai.cellID(). This function advances bi only past ai.cellID().
+func (l *loopCrosser) hasCrossing(ai, bi *rangeIterator) bool {
+	// If ai.CellID() intersects many edges of B, then it is faster to use
+	// CrossingEdgeQuery to narrow down the candidates. But if it intersects
+	// only a few edges, it is faster to check all the crossings directly.
+	// We handle this by advancing bi and keeping track of how many edges we
+	// would need to test.
+	const edgeQueryMinEdges = 20 // Tuned from benchmarks.
+	var totalEdges int
+	l.bCells = nil
+
+	for {
+		if n := bi.it.IndexCell().shapes[0].numEdges(); n > 0 {
+			totalEdges += n
+			if totalEdges >= edgeQueryMinEdges {
+				// There are too many edges to test them directly, so use CrossingEdgeQuery.
+				if l.cellCrossesAnySubcell(ai.it.IndexCell().shapes[0], ai.cellID()) {
+					return true
+				}
+				bi.seekBeyond(ai)
+				return false
+			}
+			l.bCells = append(l.bCells, bi.indexCell())
+		}
+		bi.next()
+		if bi.cellID() > ai.rangeMax {
+			break
+		}
+	}
+
+	// Test all the edge crossings directly.
+	for _, c := range l.bCells {
+		if l.cellCrossesCell(ai.it.IndexCell().shapes[0], c.shapes[0]) {
+			return true
+		}
+	}
+
+	return false
+}
+
+// containsCenterMatches reports if the clippedShapes containsCenter boolean corresponds
+// to the crossing target type given. (This is to work around C++ allowing false == 0,
+// true == 1 type implicit conversions and comparisons)
+func containsCenterMatches(a *clippedShape, target crossingTarget) bool {
+	return (!a.containsCenter && target == crossingTargetDontCross) ||
+		(a.containsCenter && target == crossingTargetCross)
+}
+
+// hasCrossingRelation reports whether given two iterators positioned such that
+// ai.cellID().ContainsCellID(bi.cellID()), there is a crossing relationship
+// anywhere within ai.cellID(). Specifically, this method returns true if there
+// is an edge crossing, a wedge crossing, or a point P that matches both relations
+// crossing targets. This function advances both iterators past ai.cellID.
+func (l *loopCrosser) hasCrossingRelation(ai, bi *rangeIterator) bool {
+	aClipped := ai.it.IndexCell().shapes[0]
+	if aClipped.numEdges() != 0 {
+		// The current cell of A has at least one edge, so check for crossings.
+		if l.hasCrossing(ai, bi) {
+			return true
+		}
+		ai.next()
+		return false
+	}
+
+	if containsCenterMatches(aClipped, l.aCrossingTarget) {
+		// The crossing target for A is not satisfied, so we skip over these cells of B.
+		bi.seekBeyond(ai)
+		ai.next()
+		return false
+	}
+
+	// All points within ai.cellID() satisfy the crossing target for A, so it's
+	// worth iterating through the cells of B to see whether any cell
+	// centers also satisfy the crossing target for B.
+	for bi.cellID() <= ai.rangeMax {
+		bClipped := bi.it.IndexCell().shapes[0]
+		if containsCenterMatches(bClipped, l.bCrossingTarget) {
+			return true
+		}
+		bi.next()
+	}
+	ai.next()
+	return false
+}
+
+// hasCrossingRelation checks all edges of loop A for intersection against all edges
+// of loop B and reports if there are any that satisfy the given relation. If there
+// is any shared vertex, the wedges centered at this vertex are sent to the given
+// relation to be tested.
+//
+// If the two loop boundaries cross, this method is guaranteed to return
+// true. It also returns true in certain cases if the loop relationship is
+// equivalent to crossing. For example, if the relation is Contains and a
+// point P is found such that B contains P but A does not contain P, this
+// method will return true to indicate that the result is the same as though
+// a pair of crossing edges were found (since Contains returns false in
+// both cases).
+//
+// See Contains, Intersects and CompareBoundary for the three uses of this function.
+func hasCrossingRelation(a, b *Loop, relation loopRelation) bool {
+	// We look for CellID ranges where the indexes of A and B overlap, and
+	// then test those edges for crossings.
+	ai := newRangeIterator(a.index)
+	bi := newRangeIterator(b.index)
+
+	ab := newLoopCrosser(a, b, relation, false) // Tests edges of A against B
+	ba := newLoopCrosser(b, a, relation, true)  // Tests edges of B against A
+
+	for !ai.done() || !bi.done() {
+		if ai.rangeMax < bi.rangeMin {
+			// The A and B cells don't overlap, and A precedes B.
+			ai.seekTo(bi)
+		} else if bi.rangeMax < ai.rangeMin {
+			// The A and B cells don't overlap, and B precedes A.
+			bi.seekTo(ai)
+		} else {
+			// One cell contains the other. Determine which cell is larger.
+			abRelation := int64(ai.it.CellID().lsb() - bi.it.CellID().lsb())
+			if abRelation > 0 {
+				// A's index cell is larger.
+				if ab.hasCrossingRelation(ai, bi) {
+					return true
+				}
+			} else if abRelation < 0 {
+				// B's index cell is larger.
+				if ba.hasCrossingRelation(bi, ai) {
+					return true
+				}
+			} else {
+				// The A and B cells are the same. Since the two cells
+				// have the same center point P, check whether P satisfies
+				// the crossing targets.
+				aClipped := ai.it.IndexCell().shapes[0]
+				bClipped := bi.it.IndexCell().shapes[0]
+				if containsCenterMatches(aClipped, ab.aCrossingTarget) &&
+					containsCenterMatches(bClipped, ab.bCrossingTarget) {
+					return true
+				}
+				// Otherwise test all the edge crossings directly.
+				if aClipped.numEdges() > 0 && bClipped.numEdges() > 0 && ab.cellCrossesCell(aClipped, bClipped) {
+					return true
+				}
+				ai.next()
+				bi.next()
+			}
+		}
+	}
+	return false
+}
+
+// containsRelation implements loopRelation for a contains operation. If
+// A.ContainsPoint(P) == false && B.ContainsPoint(P) == true, it is equivalent
+// to having an edge crossing (i.e., Contains returns false).
+type containsRelation struct {
+	foundSharedVertex bool
+}
+
+func (c *containsRelation) aCrossingTarget() crossingTarget { return crossingTargetDontCross }
+func (c *containsRelation) bCrossingTarget() crossingTarget { return crossingTargetCross }
+func (c *containsRelation) wedgesCross(a0, ab1, a2, b0, b2 Point) bool {
+	c.foundSharedVertex = true
+	return !WedgeContains(a0, ab1, a2, b0, b2)
+}
+
+// intersectsRelation implements loopRelation for an intersects operation. Given
+// two loops, A and B, if A.ContainsPoint(P) == true && B.ContainsPoint(P) == true,
+// it is equivalent to having an edge crossing (i.e., Intersects returns true).
+type intersectsRelation struct {
+	foundSharedVertex bool
+}
+
+func (i *intersectsRelation) aCrossingTarget() crossingTarget { return crossingTargetCross }
+func (i *intersectsRelation) bCrossingTarget() crossingTarget { return crossingTargetCross }
+func (i *intersectsRelation) wedgesCross(a0, ab1, a2, b0, b2 Point) bool {
+	i.foundSharedVertex = true
+	return WedgeIntersects(a0, ab1, a2, b0, b2)
+}
+
+// compareBoundaryRelation implements loopRelation for comparing boundaries.
+//
+// The compare boundary relation does not have a useful early-exit condition,
+// so we return crossingTargetDontCare for both crossing targets.
+//
+// Aside: A possible early exit condition could be based on the following.
+//   If A contains a point of both B and ~B, then A intersects Boundary(B).
+//   If ~A contains a point of both B and ~B, then ~A intersects Boundary(B).
+//   So if the intersections of {A, ~A} with {B, ~B} are all non-empty,
+//   the return value is 0, i.e., Boundary(A) intersects Boundary(B).
+// Unfortunately it isn't worth detecting this situation because by the
+// time we have seen a point in all four intersection regions, we are also
+// guaranteed to have seen at least one pair of crossing edges.
+type compareBoundaryRelation struct {
+	reverse           bool // True if the other loop should be reversed.
+	foundSharedVertex bool // True if any wedge was processed.
+	containsEdge      bool // True if any edge of the other loop is contained by this loop.
+	excludesEdge      bool // True if any edge of the other loop is excluded by this loop.
+}
+
+func newCompareBoundaryRelation(reverse bool) *compareBoundaryRelation {
+	return &compareBoundaryRelation{reverse: reverse}
+}
+
+func (c *compareBoundaryRelation) aCrossingTarget() crossingTarget { return crossingTargetDontCare }
+func (c *compareBoundaryRelation) bCrossingTarget() crossingTarget { return crossingTargetDontCare }
+func (c *compareBoundaryRelation) wedgesCross(a0, ab1, a2, b0, b2 Point) bool {
+	// Because we don't care about the interior of the other, only its boundary,
+	// it is sufficient to check whether this one contains the semiwedge (ab1, b2).
+	c.foundSharedVertex = true
+	if wedgeContainsSemiwedge(a0, ab1, a2, b2, c.reverse) {
+		c.containsEdge = true
+	} else {
+		c.excludesEdge = true
+	}
+	return c.containsEdge && c.excludesEdge
+}
+
+// wedgeContainsSemiwedge reports whether the wedge (a0, ab1, a2) contains the
+// "semiwedge" defined as any non-empty open set of rays immediately CCW from
+// the edge (ab1, b2). If reverse is true, then substitute clockwise for CCW;
+// this simulates what would happen if the direction of the other loop was reversed.
+func wedgeContainsSemiwedge(a0, ab1, a2, b2 Point, reverse bool) bool {
+	if b2 == a0 || b2 == a2 {
+		// We have a shared or reversed edge.
+		return (b2 == a0) == reverse
+	}
+	return OrderedCCW(a0, a2, b2, ab1)
+}
+
+// containsNonCrossingBoundary reports whether given two loops whose boundaries
+// do not cross (see compareBoundary), if this loop contains the boundary of the
+// other loop. If reverse is true, the boundary of the other loop is reversed
+// first (which only affects the result when there are shared edges). This method
+// is cheaper than compareBoundary because it does not test for edge intersections.
+//
+// This function requires that neither loop is empty, and that if the other is full,
+// then reverse == false.
+func (l *Loop) containsNonCrossingBoundary(other *Loop, reverseOther bool) bool {
+	// The bounds must intersect for containment.
+	if !l.bound.Intersects(other.bound) {
+		return false
+	}
+
+	// Full loops are handled as though the loop surrounded the entire sphere.
+	if l.IsFull() {
+		return true
+	}
+	if other.IsFull() {
+		return false
+	}
+
+	m, ok := l.findVertex(other.Vertex(0))
+	if !ok {
+		// Since the other loops vertex 0 is not shared, we can check if this contains it.
+		return l.ContainsPoint(other.Vertex(0))
+	}
+	// Otherwise check whether the edge (b0, b1) is contained by this loop.
+	return wedgeContainsSemiwedge(l.Vertex(m-1), l.Vertex(m), l.Vertex(m+1),
+		other.Vertex(1), reverseOther)
+}
+
+// TODO(roberts): Differences from the C++ version:
+// DistanceToPoint
+// DistanceToBoundary
+// Project
+// ProjectToBoundary
+// BoundaryApproxEqual
+// BoundaryNear