polygon_test.go

// 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 (
	"math"
	"math/rand"
	"testing"

	"github.com/golang/geo/s1"
)

const (
	// A set of nested loops around the LatLng point 0:0.
	// Every vertex of nearLoop0 is also a vertex of nearLoop1.
	nearPoint    = "0:0"
	nearLoop0    = "-1:0, 0:1, 1:0, 0:-1;"
	nearLoop1    = "-1:-1, -1:0, -1:1, 0:1, 1:1, 1:0, 1:-1, 0:-1;"
	nearLoop2    = "-1:-2, -2:5, 5:-2;"
	nearLoop3    = "-2:-2, -3:6, 6:-3;"
	nearLoopHemi = "0:-90, -90:0, 0:90, 90:0;"

	// A set of nested loops around the LatLng point 0:180. Every vertex of
	// farLoop0 and farLoop2 belongs to farLoop1, and all the loops except
	// farLoop2 are non-convex.
	farPoint    = "0:180"
	farLoop0    = "0:179, 1:180, 0:-179, 2:-180;"
	farLoop1    = "0:179, -1:179, 1:180, -1:-179, 0:-179, 3:-178, 2:-180, 3:178;"
	farLoop2    = "3:-178, 3:178, -1:179, -1:-179;"
	farLoop3    = "-3:-178, 4:-177, 4:177, -3:178, -2:179;"
	farLoopHemi = "0:-90, 60:90, -60:90;"

	// A set of nested loops around the LatLng point -90:0.
	southLoopPoint = "-89.9999:0.001"
	southLoop0a    = "-90:0, -89.99:0.01, -89.99:0;"
	southLoop0b    = "-90:0, -89.99:0.03, -89.99:0.02;"
	southLoop0c    = "-90:0, -89.99:0.05, -89.99:0.04;"
	southLoop1     = "-90:0, -89.9:0.1, -89.9:-0.1;"
	southLoop2     = "-90:0, -89.8:0.2, -89.8:-0.2;"
	southLoopHemi  = "0:-180, 0:60, 0:-60;"

	// Two different loops that surround all the near and far loops except
	// for the hemispheres.
	nearFarLoop1 = "-1:-9, -9:-9, -9:9, 9:9, 9:-9, 1:-9, " +
		"1:-175, 9:-175, 9:175, -9:175, -9:-175, -1:-175;"
	nearFarLoop2 = "-2:15, -2:170, -8:-175, 8:-175, " +
		"2:170, 2:15, 8:-4, -8:-4;"

	// Loop that results from intersection of other loops.
	farHemiSouthHemiLoop = "0:-180, 0:90, -60:90, 0:-90;"

	// Rectangles that form a cross, with only shared vertices, no crossing
	// edges. Optional holes outside the intersecting region.
	loopCross1          = "-2:1, -1:1, 1:1, 2:1, 2:-1, 1:-1, -1:-1, -2:-1;"
	loopCross1SideHole  = "-1.5:0.5, -1.2:0.5, -1.2:-0.5, -1.5:-0.5;"
	loopCrossCenterHole = "-0.5:0.5, 0.5:0.5, 0.5:-0.5, -0.5:-0.5;"
	loopCross2SideHole  = "0.5:-1.5, 0.5:-1.2, -0.5:-1.2, -0.5:-1.5;"
	loopCross2          = "1:-2, 1:-1, 1:1, 1:2, -1:2, -1:1, -1:-1, -1:-2;"

	// Two rectangles that intersect, but no edges cross and there's always
	// local containment (rather than crossing) at each shared vertex.
	// In this ugly ASCII art, 1 is A+B, 2 is B+C:
	//   +---+---+---+
	//   | A | B | C |
	//   +---+---+---+
	loopOverlap1          = "0:1, 1:1, 2:1, 2:0, 1:0, 0:0;"
	loopOverlap1SideHole  = "0.2:0.8, 0.8:0.8, 0.8:0.2, 0.2:0.2;"
	loopOverlapCenterHole = "1.2:0.8, 1.8:0.8, 1.8:0.2, 1.2:0.2;"
	loopOverlap2SideHole  = "2.2:0.8, 2.8:0.8, 2.8:0.2, 2.2:0.2;"
	loopOverlap2          = "1:1, 2:1, 3:1, 3:0, 2:0, 1:0;"

	// By symmetry, the intersection of the two polygons has almost half the area
	// of either polygon.
	//   +---+
	//   | 3 |
	//   +---+---+
	//   |3+4| 4 |
	//   +---+---+
	loopOverlap3 = "-10:10, 0:10, 0:-10, -10:-10, -10:0"
	loopOverlap4 = "-10:0, 10:0, 10:-10, -10:-10"
)

var (
	// Some standard polygons to use in the tests.
	emptyPolygon = &Polygon{}
	fullPolygon  = FullPolygon()

	near0Polygon     = makePolygon(nearLoop0, true)
	near01Polygon    = makePolygon(nearLoop0+nearLoop1, true)
	near30Polygon    = makePolygon(nearLoop3+nearLoop0, true)
	near23Polygon    = makePolygon(nearLoop2+nearLoop3, true)
	near0231Polygon  = makePolygon(nearLoop0+nearLoop2+nearLoop3+nearLoop1, true)
	near023H1Polygon = makePolygon(nearLoop0+nearLoop2+nearLoop3+nearLoopHemi+nearLoop1, true)

	far01Polygon    = makePolygon(farLoop0+farLoop1, true)
	far21Polygon    = makePolygon(farLoop2+farLoop1, true)
	far231Polygon   = makePolygon(farLoop2+farLoop3+farLoop1, true)
	far2H0Polygon   = makePolygon(farLoop2+farLoopHemi+farLoop0, true)
	far2H013Polygon = makePolygon(farLoop2+farLoopHemi+farLoop0+farLoop1+farLoop3, true)

	south0abPolygon     = makePolygon(southLoop0a+southLoop0b, true)
	south2Polygon       = makePolygon(southLoop2, true)
	south20b1Polygon    = makePolygon(southLoop2+southLoop0b+southLoop1, true)
	south2H1Polygon     = makePolygon(southLoop2+southLoopHemi+southLoop1, true)
	south20bH0acPolygon = makePolygon(southLoop2+southLoop0b+southLoopHemi+
		southLoop0a+southLoop0c, true)

	nf1N10F2S10abcPolygon = makePolygon(southLoop0c+farLoop2+nearLoop1+
		nearFarLoop1+nearLoop0+southLoop1+southLoop0b+southLoop0a, true)

	nf2N2F210S210abPolygon = makePolygon(farLoop2+southLoop0a+farLoop1+
		southLoop1+farLoop0+southLoop0b+nearFarLoop2+southLoop2+nearLoop2, true)

	f32n0Polygon  = makePolygon(farLoop2+nearLoop0+farLoop3, true)
	n32s0bPolygon = makePolygon(nearLoop3+southLoop0b+nearLoop2, true)

	cross1Polygon           = makePolygon(loopCross1, true)
	cross1SideHolePolygon   = makePolygon(loopCross1+loopCross1SideHole, true)
	cross1CenterHolePolygon = makePolygon(loopCross1+loopCrossCenterHole, true)
	cross2Polygon           = makePolygon(loopCross2, true)
	cross2SideHolePolygon   = makePolygon(loopCross2+loopCross2SideHole, true)
	cross2CenterHolePolygon = makePolygon(loopCross2+loopCrossCenterHole, true)

	overlap1Polygon           = makePolygon(loopOverlap1, true)
	overlap1SideHolePolygon   = makePolygon(loopOverlap1+loopOverlap1SideHole, true)
	overlap1CenterHolePolygon = makePolygon(loopOverlap1+loopOverlapCenterHole, true)
	overlap2Polygon           = makePolygon(loopOverlap2, true)
	overlap2SideHolePolygon   = makePolygon(loopOverlap2+loopOverlap2SideHole, true)
	overlap2CenterHolePolygon = makePolygon(loopOverlap2+loopOverlapCenterHole, true)

	overlap3Polygon = makePolygon(loopOverlap3, true)
	overlap4Polygon = makePolygon(loopOverlap4, true)

	farHemiPolygon      = makePolygon(farLoopHemi, true)
	southHemiPolygon    = makePolygon(southLoopHemi, true)
	farSouthHemiPolygon = makePolygon(farHemiSouthHemiLoop, true)
)

func TestPolygonInitSingleLoop(t *testing.T) {
	if !PolygonFromLoops([]*Loop{EmptyLoop()}).IsEmpty() {
		t.Errorf("polygon from Empty Loop should make an EmptyPolygon")
	}
	if !PolygonFromLoops([]*Loop{FullLoop()}).IsFull() {
		t.Errorf("polygon from Full Loop should make a FullPolygon")
	}
	p := PolygonFromLoops([]*Loop{makeLoop("0:0, 0:10, 10:0")})
	if got, want := p.numVertices, 3; got != want {
		t.Errorf("%v.numVertices = %v, want %v", p, got, want)
	}
}

func TestPolygonEmpty(t *testing.T) {
	shape := emptyPolygon

	if got, want := shape.NumEdges(), 0; got != want {
		t.Errorf("shape.NumEdges() = %v, want %v", got, want)
	}
	if got, want := shape.NumChains(), 0; got != want {
		t.Errorf("shape.NumChains() = %v, want %v", got, want)
	}
	if got, want := shape.Dimension(), 2; got != want {
		t.Errorf("shape.Dimension() = %v, want %v", got, want)
	}
	if !shape.IsEmpty() {
		t.Errorf("shape.IsEmpty() = false, want true")
	}
	if shape.IsFull() {
		t.Errorf("shape.IsFull() = true, want false")
	}
	if shape.ReferencePoint().Contained {
		t.Errorf("shape.ReferencePoint().Contained = true, want false")
	}
}

func TestPolygonFull(t *testing.T) {
	shape := fullPolygon

	if got, want := shape.NumEdges(), 0; got != want {
		t.Errorf("shape.NumEdges() = %v, want %v", got, want)
	}
	if got, want := shape.NumChains(), 1; got != want {
		t.Errorf("shape.NumChains() = %v, want %v", got, want)
	}
	if got, want := shape.Chain(0).Start, 0; got != want {
		t.Errorf("fullPolygon.Chain(0).Start = %d, want %d", got, want)
	}
	if got, want := shape.Chain(0).Length, 0; got != want {
		t.Errorf("fullPolygon.Chain(0).Length = %d, want %d", got, want)
	}
	if got, want := shape.Dimension(), 2; got != want {
		t.Errorf("shape.Dimension() = %v, want %v", got, want)
	}
	if shape.IsEmpty() {
		t.Errorf("shape.IsEmpty() = true, want false")
	}
	if !shape.IsFull() {
		t.Errorf("shape.IsFull() = false, want true")
	}
	if !shape.ReferencePoint().Contained {
		t.Errorf("shape.ReferencePoint().Contained = false, want true")
	}
}

func TestPolygonInitLoopPropertiesGetsRightBounds(t *testing.T) {
	// Before the change to initLoopProperties to start the bounds as an
	// EmptyRect instead of it default to the zero rect, the bounds
	// computations failed. Lo was set to min (0, 12.55) and Hi was set to
	// max (0, -70.02).  So this poly would have a bounds of
	//   Lo: [0, -70.05],     Hi: [12.58, 0]]      instead of:
	//   Lo: [12.55, -70.05], Hi: [12.58, -70.02]]

	p := PolygonFromLoops([]*Loop{
		makeLoop("12.55:-70.05, 12.55:-70.02, 12.58:-70.02, 12.58:-70.05"),
		makeLoop("12.56:-70.04, 12.56:-70.03, 12.58:-70.03, 12.58:-70.04"),
	})
	want := rectFromDegrees(12.55, -70.05, 12.58, -70.02)
	if got := p.RectBound(); !rectsApproxEqual(got, want, 1e-6, 1e-6) {
		t.Errorf("%v.RectBound() = %v, want %v", p, got, want)
	}
}

func TestPolygonShape(t *testing.T) {
	const numLoops = 100
	const numVerticesPerLoop = 6
	concentric := concentricLoopsPolygon(PointFromCoords(1, 0, 0), numLoops, numVerticesPerLoop)

	tests := []struct {
		p *Polygon
	}{
		{near0Polygon},    // one loop polygon
		{near0231Polygon}, // several loops polygon
		{concentric},      // many loops polygon
	}

	for _, test := range tests {
		shape := Shape(test.p)

		if got, want := shape.NumEdges(), test.p.numVertices; got != want {
			t.Errorf("the number of vertices in a polygon should equal the number of edges. got %v, want %v", got, want)
		}
		if got, want := shape.NumChains(), test.p.NumLoops(); got != want {
			t.Errorf("the number of loops in a polygon should equal the number of chains. got %v, want %v", got, want)
		}

		edgeID := 0
		for i, l := range test.p.loops {
			if edgeID != shape.Chain(i).Start {
				t.Errorf("the edge id of the start of loop(%d) should equal the sum of vertices so far in the polygon. got %d, want %d", i, shape.Chain(i).Start, edgeID)
			}
			if len(l.vertices) != shape.Chain(i).Length {
				t.Errorf("the length of Chain(%d) should equal the length of loop(%d), got %v, want %v", i, i, shape.Chain(i).Length, len(l.vertices))
			}
			for j := 0; j < len(l.Vertices()); j++ {
				edge := shape.Edge(edgeID)
				if l.OrientedVertex(j) != edge.V0 {
					t.Errorf("l.Vertex(%d) = %v, want %v", j, l.Vertex(j), edge.V0)
				}
				if l.OrientedVertex(j+1) != edge.V1 {
					t.Errorf("l.Vertex(%d) = %v, want %v", j+1, l.Vertex(j+1), edge.V1)
				}
				edgeID++
			}
		}
		if got, want := shape.Dimension(), 2; got != want {
			t.Errorf("shape.Dimension() = %v, want %v", got, want)
		}
		if shape.IsEmpty() {
			t.Errorf("shape.IsEmpty() = true, want false")
		}
		if shape.IsFull() {
			t.Errorf("shape.IsFull() = true, want false")
		}

		if got, want := test.p.ContainsPoint(OriginPoint()), shape.ReferencePoint().Contained; got != want {
			t.Errorf("p.ContainsPoint(OriginPoint()) != shape.ReferencePoint().Contained")
		}
	}
}

// reverseLoopVertices reverses the order of all vertices in the given loop.
func reverseLoopVertices(l *Loop) {
	for i := 0; i < len(l.vertices)/2; i++ {
		l.vertices[i], l.vertices[len(l.vertices)-i-1] = l.vertices[len(l.vertices)-i-1], l.vertices[i]
	}
}

// shuffleLoops randomizes the slice of loops using Fisher-Yates shuffling.
func shuffleLoops(loops []*Loop) {
	n := len(loops)
	for i := 0; i < n; i++ {
		// choose index uniformly in [i, n-1]
		r := i + rand.Intn(n-i)
		loops[r], loops[i] = loops[i], loops[r]
	}
}

// modifyPolygonFunc declares a function that can tweak a Polygon for testing.
type modifyPolygonFunc func(p *Polygon)

// polygonSetInvalidLoopNesting flips a random loops orientation within the polygon.
func polygonSetInvalidLoopNesting(p *Polygon) {
	if len(p.loops) > 0 {
		i := randomUniformInt(len(p.loops))
		p.loops[i].Invert()
	}
}

// polygonSetInvalidLoopDepth randomly changes a loops depth value in the given polygon
func polygonSetInvalidLoopDepth(p *Polygon) {
	i := randomUniformInt(len(p.loops))
	if i == 0 || oneIn(3) {
		p.loops[i].depth = -1
	} else {
		p.loops[i].depth = p.loops[i-1].depth + 2
	}
}

// generatePolygonConcentricTestLoops creates the given number of nested regular
// loops around a common center point. All loops will have the same number of
// vertices (at least minVertices). Furthermore, the vertices at the same index
// position are collinear with the common center point of all the loops. The
// loop radii decrease exponentially in order to prevent accidental loop crossings
// when one of the loops is modified.
func generatePolygonConcentricTestLoops(numLoops, minVertices int) []*Loop {
	var loops []*Loop
	center := randomPoint()
	numVertices := minVertices + randomUniformInt(10)
	for i := 0; i < numLoops; i++ {
		radius := s1.Angle(80*math.Pow(0.1, float64(i))) * s1.Degree
		loops = append(loops, RegularLoop(center, radius, numVertices))
	}
	return loops
}

func checkPolygonInvalid(t *testing.T, label string, loops []*Loop, initOriented bool, f modifyPolygonFunc) {
	shuffleLoops(loops)
	var polygon *Polygon
	if initOriented {
		polygon = PolygonFromOrientedLoops(loops)
	} else {
		polygon = PolygonFromLoops(loops)
	}

	if f != nil {
		f(polygon)
	}

	if err := polygon.Validate(); err == nil {
		t.Errorf("%s: %v.Validate() = %v, want non-nil", label, polygon, err)
	}
}

func TestPolygonUninitializedIsValid(t *testing.T) {
	p := &Polygon{}
	if err := p.Validate(); err != nil {
		t.Errorf("an uninitialized polygon failed validation: %v", err)
	}
}

func TestPolygonIsValidLoopNestingInvalid(t *testing.T) {
	const iters = 1000

	for iter := 0; iter < iters; iter++ {
		loops := generatePolygonConcentricTestLoops(2+randomUniformInt(4), 3)
		// Randomly invert all the loops in order to generate cases where the
		// outer loop encompasses almost the entire sphere. This tests different
		// code paths because bounding box checks are not as useful.
		if oneIn(2) {
			for _, loop := range loops {
				reverseLoopVertices(loop)
			}
		}
		checkPolygonInvalid(t, "invalid nesting", loops, false, polygonSetInvalidLoopNesting)
	}
}

// TODO(roberts): Implement remaining validity tests.
// IsValidTests
//   TestUnitLength
//   TestVertexCount
//   TestDuplicateVertex
//   TestSelfIntersection
//   TestEmptyLoop
//   TestFullLoop
//   TestLoopsCrossing
//   TestDuplicateEdge
//   TestInconsistentOrientations
//   TestLoopDepthNegative
//   TestLoopNestingInvalid
//   TestFuzzTest

func TestPolygonParent(t *testing.T) {
	p1 := PolygonFromLoops([]*Loop{{}})
	tests := []struct {
		p    *Polygon
		have int
		want int
		ok   bool
	}{
		{fullPolygon, 0, -1, false},
		{p1, 0, -1, false},

		// TODO: When multiple loops are supported, add more test cases to
		// more fully show the parent levels.
	}

	for _, test := range tests {
		if got, ok := test.p.Parent(test.have); ok != test.ok || got != test.want {
			t.Errorf("%v.Parent(%d) = %d,%v, want %d,%v", test.p, test.have, got, ok, test.want, test.ok)
		}
	}
}

func TestPolygonLastDescendant(t *testing.T) {
	p1 := PolygonFromLoops([]*Loop{{}})

	tests := []struct {
		p    *Polygon
		have int
		want int
	}{
		{fullPolygon, 0, 0},
		{fullPolygon, -1, 0},

		{p1, 0, 0},
		{p1, -1, 0},

		// TODO: When multiple loops are supported, add more test cases.
	}

	for _, test := range tests {
		if got := test.p.LastDescendant(test.have); got != test.want {
			t.Errorf("%v.LastDescendant(%d) = %d, want %d", test.p, test.have, got, test.want)
		}
	}
}

func TestPolygonContainsPoint(t *testing.T) {
	tests := []struct {
		polygon string
		point   string
	}{
		{nearLoop0, nearPoint},
		{nearLoop1, nearPoint},
		{nearLoop2, nearPoint},
		{nearLoop3, nearPoint},
		{nearLoopHemi, nearPoint},
		{southLoop0a, southLoopPoint},
		{southLoop1, southLoopPoint},
		{southLoop2, southLoopPoint},
		{southLoopHemi, southLoopPoint},
	}

	for _, test := range tests {
		poly := makePolygon(test.polygon, true)
		pt := parsePoint(test.point)
		if !poly.ContainsPoint(pt) {
			t.Errorf("%v.ContainsPoint(%v) = false, want true", test.polygon, test.point)
		}
	}
}

// Given a pair of polygons where A contains B, check that various identities
// involving union, intersection, and difference operations hold true.
func testPolygonOneNestedPair(t *testing.T, a, b *Polygon) {
	if !a.Contains(b) {
		t.Errorf("%v.Contains(%v) = false, want true", a, b)
	}
	if got, want := a.Intersects(b), !b.IsEmpty(); got != want {
		t.Errorf("%v.Intersects(%v) = %v, want %v", a, b, got, want)
	}
	if got, want := b.Intersects(a), !b.IsEmpty(); got != want {
		t.Errorf("%v.Intersects(%v) = %v, want %v", b, a, got, want)
	}

	// TODO(roberts): Add the remaining checks related to construction
	// via union, intersection, and difference.
}

// Given a pair of disjoint polygons A and B, check that various identities
// involving union, intersection, and difference operations hold true.
func testPolygonOneDisjointPair(t *testing.T, a, b *Polygon) {
	if a.Intersects(b) {
		t.Errorf("%v.Intersects(%v) = true, want false", a, b)
	}
	if b.Intersects(a) {
		t.Errorf("%v.Intersects(%v) = true, want false", b, a)
	}
	if got, want := a.Contains(b), b.IsEmpty(); got != want {
		t.Errorf("%v.Contains(%v) = %v, want %v", b, a, got, want)
	}

	if got, want := b.Contains(a), a.IsEmpty(); got != want {
		t.Errorf("%v.Contains(%v) = %v, want %v", b, a, got, want)
	}

	// TODO(roberts): Add the remaining checks related to construction
	// via builder, union, intersection, and difference.
}

// Given polygons A and B whose union covers the sphere, check that various
// identities involving union, intersection, and difference hold true.
func testPolygonOneCoveringPair(t *testing.T, a, b *Polygon) {
	if got, want := a.Contains(b), a.IsFull(); got != want {
		t.Errorf("%v.Contains(%v) = %v, want %v", a, b, got, want)
	}
	if got, want := b.Contains(a), b.IsFull(); got != want {
		t.Errorf("%v.Contains(%v) = %v, want %v", a, b, got, want)
	}
	// TODO(roberts): Add the remaining checks related to construction via union

}

// Given polygons A and B such that both A and its complement intersect both B
// and its complement, check that various identities involving union,
// intersection, and difference hold true.
func testPolygonOneOverlappingPair(t *testing.T, a, b *Polygon) {
	if a.Contains(b) {
		t.Errorf("%v.Contains(%v) = true, want false", a, b)
	}
	if b.Contains(a) {
		t.Errorf("%v.Contains(%v) = true, want false", b, a)
	}
	if !a.Intersects(b) {
		t.Errorf("%v.Intersects(%v) = false, want true", a, b)
	}

	// TODO(roberts): Add the remaining checks related to construction
	// via builder, union, intersection, and difference.
}

// Given a pair of polygons where A contains B, test various identities
// involving A, B, and their complements.
func testPolygonNestedPair(t *testing.T, a, b *Polygon) {
	// TODO(roberts): Uncomment once complement is completed
	// a1 := InitToComplement(a)
	// b1 := InitToComplement(b)

	testPolygonOneNestedPair(t, a, b)
	// testPolygonOneNestedPair(t, b1, a1)
	// testPolygonOneDisjointPair(t, a1, b)
	// testPolygonOneCoveringPair(t, a, b1)
}

// Given a pair of disjoint polygons A and B, test various identities
// involving A, B, and their complements.
func testPolygonDisjointPair(t *testing.T, a, b *Polygon) {
	// TODO(roberts): Uncomment once complement is completed
	// a1 := InitToComplement(a)
	// b1 := InitToComplement(b)

	testPolygonOneDisjointPair(t, a, b)
	// testPolygonOneCoveringPair(t, a1, b1)
	// testPolygonOneNestedPair(t, a1, b)
	// testPolygonOneNestedPair(t, b1, a)
}

// Given polygons A and B such that both A and its complement intersect both B
// and its complement, test various identities involving these four polygons.
func testPolygonOverlappingPair(t *testing.T, a, b *Polygon) {
	// TODO(roberts): Uncomment once complement is completed
	// a1 := InitToComplement(a);
	// b1 := InitToComplement(b);

	testPolygonOneOverlappingPair(t, a, b)
	// testPolygonOneOverlappingPair(t, a1, b1);
	// testPolygonOneOverlappingPair(t, a1, b);
	// testPolygonOneOverlappingPair(t, a, b1);
}

// Test identities that should hold for any pair of polygons A, B and their
// complements.
func testPolygonComplements(t *testing.T, a, b *Polygon) {
	// TODO(roberts): Uncomment once complement is completed
	// a1 := InitToComplement(a);
	// b1 := InitToComplement(b);

	// testOneComplementPair(t, a, a1, b, b1)
	// testOneComplementPair(t, a1, a, b, b1)
	// testOneComplementPair(t, a, a1, b1, b)
	// testOneComplementPair(t, a1, a, b1, b)

	// TODO(roberts): Add the checks related to construction via union, etc.
}

func testPolygonDestructiveUnion(t *testing.T, a, b *Polygon) {
	// TODO(roberts): Add the checks related to construction via union, etc.
}

func TestPolygonRelations(t *testing.T) {
	tests := []struct {
		a, b       *Polygon
		contains   bool // A contains B
		contained  bool // B contains A
		intersects bool // A and B intersect
	}{
		{
			a:          near01Polygon,
			b:          emptyPolygon,
			contains:   true,
			contained:  false,
			intersects: false,
		},
		{
			a:          near01Polygon,
			b:          near01Polygon,
			contains:   true,
			contained:  true,
			intersects: true,
		},
		{
			a:          fullPolygon,
			b:          near01Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          near01Polygon,
			b:          near30Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          near01Polygon,
			b:          near23Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          near01Polygon,
			b:          near0231Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          near01Polygon,
			b:          near023H1Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          near30Polygon,
			b:          near23Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          near30Polygon,
			b:          near0231Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          near30Polygon,
			b:          near023H1Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          near23Polygon,
			b:          near0231Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          near23Polygon,
			b:          near023H1Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          near0231Polygon,
			b:          near023H1Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},

		{
			a:          far01Polygon,
			b:          far21Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          far01Polygon,
			b:          far231Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          far01Polygon,
			b:          far2H0Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          far01Polygon,
			b:          far2H013Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          far21Polygon,
			b:          far231Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          far21Polygon,
			b:          far2H0Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          far21Polygon,
			b:          far2H013Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          far231Polygon,
			b:          far2H0Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          far231Polygon,
			b:          far2H013Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          far2H0Polygon,
			b:          far2H013Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},

		{
			a:          south0abPolygon,
			b:          south2Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          south0abPolygon,
			b:          south20b1Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          south0abPolygon,
			b:          south2H1Polygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          south0abPolygon,
			b:          south20bH0acPolygon,
			contains:   false,
			contained:  true,
			intersects: true,
		},
		{
			a:          south2Polygon,
			b:          south20b1Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          south2Polygon,
			b:          south2H1Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          south2Polygon,
			b:          south20bH0acPolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          south20b1Polygon,
			b:          south2H1Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          south20b1Polygon,
			b:          south20bH0acPolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          south2H1Polygon,
			b:          south20bH0acPolygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},

		{
			a:          nf1N10F2S10abcPolygon,
			b:          nf2N2F210S210abPolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          nf1N10F2S10abcPolygon,
			b:          near23Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          nf1N10F2S10abcPolygon,
			b:          far21Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          nf1N10F2S10abcPolygon,
			b:          south0abPolygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          nf1N10F2S10abcPolygon,
			b:          f32n0Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},

		{
			a:          nf2N2F210S210abPolygon,
			b:          near01Polygon,
			contains:   false,
			contained:  false,
			intersects: false,
		},
		{
			a:          nf2N2F210S210abPolygon,
			b:          far01Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          nf2N2F210S210abPolygon,
			b:          south20b1Polygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          nf2N2F210S210abPolygon,
			b:          south0abPolygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          nf2N2F210S210abPolygon,
			b:          n32s0bPolygon,
			contains:   true,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1Polygon,
			b:          cross2Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1SideHolePolygon,
			b:          cross2Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1CenterHolePolygon,
			b:          cross2Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1Polygon,
			b:          cross2SideHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1Polygon,
			b:          cross2CenterHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1SideHolePolygon,
			b:          cross2SideHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1CenterHolePolygon,
			b:          cross2SideHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1SideHolePolygon,
			b:          cross2CenterHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          cross1CenterHolePolygon,
			b:          cross2CenterHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		// These cases, when either polygon has a hole, test a different code path
		// from the other cases.
		{
			a:          overlap1Polygon,
			b:          overlap2Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1SideHolePolygon,
			b:          overlap2Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1CenterHolePolygon,
			b:          overlap2Polygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1Polygon,
			b:          overlap2SideHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1Polygon,
			b:          overlap2CenterHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1SideHolePolygon,
			b:          overlap2SideHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1CenterHolePolygon,
			b:          overlap2SideHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1SideHolePolygon,
			b:          overlap2CenterHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
		{
			a:          overlap1CenterHolePolygon,
			b:          overlap2CenterHolePolygon,
			contains:   false,
			contained:  false,
			intersects: true,
		},
	}

	for i, test := range tests {
		if got := test.a.Contains(test.b); got != test.contains {
			t.Errorf("%d. %v.Contains(%v) = %v, want %v", i, test.a, test.b, got, test.contains)
		}

		if got := test.b.Contains(test.a); got != test.contained {
			t.Errorf("%d. %v.Contains(%v) = %v, want %v", i, test.b, test.a, got, test.contained)
		}

		if got := test.a.Intersects(test.b); got != test.intersects {
			t.Errorf("%v.Intersects(%v) = %v, want %v", test.a, test.b, got, test.intersects)
		}

		if test.contains {
			testPolygonNestedPair(t, test.a, test.b)
		}
		if test.contained {
			testPolygonNestedPair(t, test.b, test.a)
		}
		if !test.intersects {
			testPolygonDisjointPair(t, test.a, test.b)
		}
		if test.intersects && (!test.contains && !test.contained) {
			testPolygonOverlappingPair(t, test.a, test.b)
		}
		testPolygonDestructiveUnion(t, test.a, test.b)
		testPolygonComplements(t, test.a, test.b)
	}

	testPolygonNestedPair(t, emptyPolygon, emptyPolygon)
	testPolygonNestedPair(t, fullPolygon, emptyPolygon)
	testPolygonNestedPair(t, fullPolygon, fullPolygon)
}

func TestPolygonArea(t *testing.T) {
	tests := []struct {
		have *Polygon
		want float64
	}{
		{have: emptyPolygon, want: 0},
		{have: fullPolygon, want: 4 * math.Pi},
		{have: southHemiPolygon, want: 2 * math.Pi},
		{have: farSouthHemiPolygon, want: math.Pi},
		{
			// compare the polygon of two shells to the sum of its loops.
			have: makePolygon(loopCross1SideHole+loopCrossCenterHole, true),
			// the strings for the loops contain ';' so copy and paste without it
			want: makeLoop("-1.5:0.5, -1.2:0.5, -1.2:-0.5, -1.5:-0.5").Area() +
				makeLoop("-0.5:0.5, 0.5:0.5, 0.5:-0.5, -0.5:-0.5").Area(),
		},
		{
			// test that polygon with a shell and a hole matches its loop parts.
			have: makePolygon(loopCross1+loopCrossCenterHole, true),
			// the strings for the loops contain ';' so copy and paste without it
			want: makeLoop("-2:1, -1:1, 1:1, 2:1, 2:-1, 1:-1, -1:-1, -2:-1").Area() -
				makeLoop("-0.5:0.5, 0.5:0.5, 0.5:-0.5, -0.5:-0.5").Area(),
		},
	}

	for _, test := range tests {
		if got := test.have.Area(); !float64Eq(got, test.want) {
			t.Errorf("%v.Area() = %v, want %v", test.have, got, test.want)
		}
	}
}

func TestPolygonCentroid(t *testing.T) {
	tests := []struct {
		have *Polygon
		want Point
	}{
		{have: emptyPolygon, want: Point{}},
		{have: fullPolygon, want: Point{}},
		{
			// compare the polygon of two shells to the sum of its loops.
			have: makePolygon(loopCross1SideHole+loopCrossCenterHole, true),
			// the strings for the loops contain ';' so copy and paste without it
			want: Point{
				makeLoop("-1.5:0.5, -1.2:0.5, -1.2:-0.5, -1.5:-0.5").Centroid().Add(
					makeLoop("-0.5:0.5, 0.5:0.5, 0.5:-0.5, -0.5:-0.5").Centroid().Vector)},
		},
		{
			// test that polygon with a shell and a hole matches its loop parts.
			have: makePolygon(loopCross1+loopCrossCenterHole, true),
			// the strings for the loops contain ';' so copy and paste without it
			want: Point{
				makeLoop("-2:1, -1:1, 1:1, 2:1, 2:-1, 1:-1, -1:-1, -2:-1").Centroid().Sub(
					makeLoop("-0.5:0.5, 0.5:0.5, 0.5:-0.5, -0.5:-0.5").Centroid().Vector)},
		},
	}

	for _, test := range tests {
		if got := test.have.Centroid(); got.Cmp(test.want.Vector) != 0 {
			t.Errorf("%v.Centroid() = %v, want %v", test.have, got, test.want)
		}
	}
}

func TestPolygonInvert(t *testing.T) {
	origin := PointFromLatLng(LatLngFromDegrees(0, 0))
	pt := PointFromLatLng(LatLngFromDegrees(30, 30))
	p := PolygonFromLoops([]*Loop{
		RegularLoop(origin, 1000/earthRadiusKm, 100),
	})

	if p.ContainsPoint(pt) {
		t.Errorf("polygon contains point outside itself")
	}

	p.Invert()
	if !p.ContainsPoint(pt) {
		t.Errorf("inverted polygon does not contain point that is inside itself")
	}
}

// TODO(roberts): Remaining Tests
// TestInit
// TestMultipleInit
// TestInitSingleLoop
// TestCellConstructorAndContains
// TestOverlapFractions
// TestOriginNearPole
// TestTestApproxContainsAndDisjoint
// TestOneLoopPolygonShape
// TestSeveralLoopPolygonShape
// TestManyLoopPolygonShape
// TestPointInBigLoop
// TestOperations
// TestIntersectionSnapFunction
// TestIntersectionPreservesLoopOrder
// TestLoopPointers
// TestBug1 - Bug14
// TestPolylineIntersection
// TestSplitting
// TestInitToCellUnionBorder
// TestUnionWithAmbgiuousCrossings
// TestInitToSloppySupportsEmptyPolygons
// TestInitToSnappedDoesNotRotateVertices
// TestInitToSnappedWithSnapLevel
// TestInitToSnappedIsValid_A
// TestInitToSnappedIsValid_B
// TestInitToSnappedIsValid_C
// TestInitToSnappedIsValid_D
// TestProject
// TestDistance
//
// PolygonSimplifier
//   TestNoSimplification
//   TestSimplifiedLoopSelfIntersects
//   TestNoSimplificationManyLoops
//   TestTinyLoopDisappears
//   TestStraightLinesAreSimplified
//   TestEdgeSplitInManyPieces
//   TestEdgesOverlap
//   TestLargeRegularPolygon
//
// InitToSimplifiedInCell
//   TestPointsOnCellBoundaryKept
//   TestPointsInsideCellSimplified
//   TestCellCornerKept
//   TestNarrowStripRemoved
//   TestNarrowGapRemoved
//   TestCloselySpacedEdgeVerticesKept
//   TestPolylineAssemblyBug