rect_bounder_test.go

// Copyright 2017 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"
	"testing"

	"github.com/golang/geo/r1"
	"github.com/golang/geo/r3"
	"github.com/golang/geo/s1"
)

func rectBoundForPoints(a, b Point) Rect {
	bounder := NewRectBounder()
	bounder.AddPoint(a)
	bounder.AddPoint(b)
	return bounder.RectBound()
}

func TestRectBounderMaxLatitudeSimple(t *testing.T) {
	cubeLat := math.Asin(1 / math.Sqrt(3)) // 35.26 degrees
	cubeLatRect := Rect{r1.IntervalFromPoint(-cubeLat).AddPoint(cubeLat),
		s1.IntervalFromEndpoints(-math.Pi/4, math.Pi/4)}

	tests := []struct {
		a, b Point
		want Rect
	}{
		// Check cases where the min/max latitude is attained at a vertex.
		{
			a:    Point{r3.Vector{X: 1, Y: 1, Z: 1}},
			b:    Point{r3.Vector{X: 1, Y: -1, Z: -1}},
			want: cubeLatRect,
		},
		{
			a:    Point{r3.Vector{X: 1, Y: -1, Z: 1}},
			b:    Point{r3.Vector{X: 1, Y: 1, Z: -1}},
			want: cubeLatRect,
		},
	}

	for _, test := range tests {
		if got := rectBoundForPoints(test.a, test.b); !rectsApproxEqual(got, test.want, rectErrorLat, rectErrorLng) {
			t.Errorf("RectBounder for points (%v, %v) near max lat failed: got %v, want %v", test.a, test.b, got, test.want)
		}
	}
}

func TestRectBounderMaxLatitudeEdgeInterior(t *testing.T) {
	// Check cases where the min/max latitude occurs in the edge interior.
	// These tests expect the result to be pretty close to the middle of the
	// allowable error range (i.e., by adding 0.5 * kRectError).

	tests := []struct {
		got  float64
		want float64
	}{
		// Max latitude, CW edge
		{
			math.Pi/4 + 0.5*rectErrorLat,
			rectBoundForPoints(Point{r3.Vector{X: 1, Y: 1, Z: 1}}, Point{r3.Vector{X: 1, Y: -1, Z: 1}}).Lat.Hi,
		},
		// Min latitude, CW edge
		{
			-math.Pi/4 - 0.5*rectErrorLat,
			rectBoundForPoints(Point{r3.Vector{X: 1, Y: -1, Z: -1}}, Point{r3.Vector{X: -1, Y: -1, Z: -1}}).Lat.Lo,
		},
		// Max latitude, CCW edge
		{
			math.Pi/4 + 0.5*rectErrorLat,
			rectBoundForPoints(Point{r3.Vector{X: 1, Y: -1, Z: 1}}, Point{r3.Vector{X: 1, Y: 1, Z: 1}}).Lat.Hi,
		},
		// Min latitude, CCW edge
		{
			-math.Pi/4 - 0.5*rectErrorLat,
			rectBoundForPoints(Point{r3.Vector{X: -1, Y: 1, Z: -1}}, Point{r3.Vector{X: -1, Y: -1, Z: -1}}).Lat.Lo,
		},

		// Check cases where the edge passes through one of the poles.
		{
			math.Pi / 2,
			rectBoundForPoints(Point{r3.Vector{X: .3, Y: .4, Z: 1}}, Point{r3.Vector{X: -.3, Y: -.4, Z: 1}}).Lat.Hi,
		},
		{
			-math.Pi / 2,
			rectBoundForPoints(Point{r3.Vector{X: .3, Y: .4, Z: -1}}, Point{r3.Vector{X: -.3, Y: -.4, Z: -1}}).Lat.Lo,
		},
	}

	for _, test := range tests {
		if !float64Eq(test.got, test.want) {
			t.Errorf("RectBound for max lat on interior of edge failed; got %v want %v", test.got, test.want)
		}
	}
}

func TestRectBounderMaxLatitudeRandom(t *testing.T) {
	// Check that the maximum latitude of edges is computed accurately to within
	// 3 * dblEpsilon (the expected maximum error). We concentrate on maximum
	// latitudes near the equator and north pole since these are the extremes.

	for i := 0; i < 100; i++ {
		// Construct a right-handed coordinate frame (U,V,W) such that U points
		// slightly above the equator, V points at the equator, and W is slightly
		// offset from the north pole.
		u := randomPoint()
		u.Z = dblEpsilon * 1e-6 * math.Pow(1e12, randomFloat64())

		u = Point{u.Normalize()}
		v := Point{PointFromCoords(0, 0, 1).PointCross(u).Normalize()}
		w := Point{u.PointCross(v).Normalize()}

		// Construct a line segment AB that passes through U, and check that the
		// maximum latitude of this segment matches the latitude of U.
		a := Point{u.Sub(v.Mul(randomFloat64())).Normalize()}
		b := Point{u.Add(v.Mul(randomFloat64())).Normalize()}
		abBound := rectBoundForPoints(a, b)
		if !float64Near(latitude(u).Radians(), abBound.Lat.Hi, rectErrorLat) {
			t.Errorf("bound for line AB not near enough to the latitude of point %v. got %v, want %v",
				u, latitude(u).Radians(), abBound.Lat.Hi)
		}

		// Construct a line segment CD that passes through W, and check that the
		// maximum latitude of this segment matches the latitude of W.
		c := Point{w.Sub(v.Mul(randomFloat64())).Normalize()}
		d := Point{w.Add(v.Mul(randomFloat64())).Normalize()}
		cdBound := rectBoundForPoints(c, d)
		if !float64Near(latitude(w).Radians(), cdBound.Lat.Hi, rectErrorLat) {
			t.Errorf("bound for line CD not near enough to the lat of point %v. got %v, want %v",
				v, latitude(w).Radians(), cdBound.Lat.Hi)
		}
	}
}

func TestRectBounderExpandForSubregions(t *testing.T) {
	// Test the full and empty bounds.
	if !ExpandForSubregions(FullRect()).IsFull() {
		t.Errorf("Subregion Bound of full rect should be full")
	}
	if !ExpandForSubregions(EmptyRect()).IsEmpty() {
		t.Errorf("Subregion Bound of empty rect should be empty")
	}

	tests := []struct {
		xLat, xLng, yLat, yLng float64
		wantFull               bool
	}{
		// Cases where the bound does not straddle the equator (but almost does),
		// and spans nearly 180 degrees in longitude.
		{3e-16, 0, 1e-14, math.Pi, true},
		{9e-16, 0, 1e-14, math.Pi, false},
		{1e-16, 7e-16, 1e-14, math.Pi, true},
		{3e-16, 14e-16, 1e-14, math.Pi, false},
		{1e-100, 14e-16, 1e-14, math.Pi, true},
		{1e-100, 22e-16, 1e-14, math.Pi, false},
		// Cases where the bound spans at most 90 degrees in longitude, and almost
		// 180 degrees in latitude.  Note that DBL_EPSILON is about 2.22e-16, which
		// implies that the double-precision value just below Pi/2 can be written as
		// (math.Pi/2 - 2e-16).
		{-math.Pi / 2, -1e-15, math.Pi/2 - 7e-16, 0, true},
		{-math.Pi / 2, -1e-15, math.Pi/2 - 30e-16, 0, false},
		{-math.Pi/2 + 4e-16, 0, math.Pi/2 - 2e-16, 1e-7, true},
		{-math.Pi/2 + 30e-16, 0, math.Pi / 2, 1e-7, false},
		{-math.Pi/2 + 4e-16, 0, math.Pi/2 - 4e-16, math.Pi / 2, true},
		{-math.Pi / 2, 0, math.Pi/2 - 30e-16, math.Pi / 2, false},
		// Cases where the bound straddles the equator and spans more than 90
		// degrees in longitude.  These are the cases where the critical distance is
		// between a corner of the bound and the opposite longitudinal edge.  Unlike
		// the cases above, here the bound may contain nearly-antipodal points (to
		// within 3.055 * DBL_EPSILON) even though the latitude and longitude ranges
		// are both significantly less than (math.Pi - 3.055 * DBL_EPSILON).
		{-math.Pi / 2, 0, math.Pi/2 - 1e-8, math.Pi - 1e-7, true},
		{-math.Pi / 2, 0, math.Pi/2 - 1e-7, math.Pi - 1e-7, false},
		{-math.Pi/2 + 1e-12, -math.Pi + 1e-4, math.Pi / 2, 0, true},
		{-math.Pi/2 + 1e-11, -math.Pi + 1e-4, math.Pi / 2, 0, true},
	}

	for _, tc := range tests {
		in := RectFromLatLng(LatLng{s1.Angle(tc.xLat), s1.Angle(tc.xLng)})
		in = in.AddPoint(LatLng{s1.Angle(tc.yLat), s1.Angle(tc.yLng)})
		got := ExpandForSubregions(in)

		// Test that the bound is actually expanded.
		if !got.Contains(in) {
			t.Errorf("Subregion bound of (%f, %f, %f, %f) should contain original rect", tc.xLat, tc.xLng, tc.yLat, tc.yLng)
		}
		if in.Lat == validRectLatRange && in.Lat.ContainsInterval(got.Lat) {
			t.Errorf("Subregion bound of (%f, %f, %f, %f) shouldn't be contained by original rect", tc.xLat, tc.xLng, tc.yLat, tc.yLng)
		}

		// We check the various situations where the bound contains nearly-antipodal points. The tests are organized into pairs
		// where the two bounds are similar except that the first bound meets the nearly-antipodal criteria while the second does not.
		if got.IsFull() != tc.wantFull {
			t.Errorf("Subregion Bound of (%f, %f, %f, %f).IsFull should be %t", tc.xLat, tc.xLng, tc.yLat, tc.yLng, tc.wantFull)
		}
	}

	rectTests := []struct {
		xLat, xLng, yLat, yLng float64
		wantRect               Rect
	}{
		{1.5, -math.Pi / 2, 1.5, math.Pi/2 - 2e-16, Rect{r1.Interval{Lo: 1.5, Hi: 1.5}, s1.FullInterval()}},
		{1.5, -math.Pi / 2, 1.5, math.Pi/2 - 7e-16, Rect{r1.Interval{Lo: 1.5, Hi: 1.5}, s1.Interval{Lo: -math.Pi / 2, Hi: math.Pi/2 - 7e-16}}},
		// Check for cases where the bound is expanded to include one of the poles
		{-math.Pi/2 + 1e-15, 0, -math.Pi/2 + 1e-15, 0, Rect{r1.Interval{Lo: -math.Pi / 2, Hi: -math.Pi/2 + 1e-15}, s1.FullInterval()}},
		{math.Pi/2 - 1e-15, 0, math.Pi/2 - 1e-15, 0, Rect{r1.Interval{Lo: math.Pi/2 - 1e-15, Hi: math.Pi / 2}, s1.FullInterval()}},
	}

	for _, tc := range rectTests {
		// Now we test cases where the bound does not contain nearly-antipodal
		// points, but it does contain points that are approximately 180 degrees
		// apart in latitude.
		in := RectFromLatLng(LatLng{s1.Angle(tc.xLat), s1.Angle(tc.xLng)})
		in = in.AddPoint(LatLng{s1.Angle(tc.yLat), s1.Angle(tc.yLng)})
		got := ExpandForSubregions(in)
		if !rectsApproxEqual(got, tc.wantRect, rectErrorLat, rectErrorLng) {
			t.Errorf("Subregion Bound of (%f, %f, %f, %f) = (%v) should be %v", tc.xLat, tc.xLng, tc.yLat, tc.yLng, got, tc.wantRect)
		}
	}
}

// TODO(roberts): TestRectBounderNearlyIdenticalOrAntipodalPoints(t *testing.T)