types/geo: add geo.Point and its associated units (#16583)

Package geo provides functionality to represent and process
geographical locations on a sphere. The main type, geo.Point,
represents a pair of latitude and longitude coordinates.

Updates tailscale/corp#29968

Signed-off-by: Simon Law <[email protected]>

types/geo/doc.go

@@ -0,0 +1,6 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+// Package geo provides functionality to represent and process geographical
+// locations on a spherical Earth.
+package geo

types/geo/point.go

@@ -0,0 +1,279 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package geo
+
+import (
+	"encoding/binary"
+	"errors"
+	"fmt"
+	"math"
+	"strconv"
+)
+
+// ErrBadPoint indicates that the point is malformed.
+var ErrBadPoint = errors.New("not a valid point")
+
+// Point represents a pair of latitude and longitude coordinates.
+type Point struct {
+	lat Degrees
+	// lng180 is the longitude offset by +180° so the zero value is invalid
+	// and +0+0/ is Point{lat: +0.0, lng180: +180.0}.
+	lng180 Degrees
+}
+
+// MakePoint returns a Point representing a given latitude and longitude on
+// a WGS 84 ellipsoid. The Coordinate Reference System is EPSG:4326.
+// Latitude is wrapped to [-90°, +90°] and longitude to (-180°, +180°].
+func MakePoint(latitude, longitude Degrees) Point {
+	lat, lng := float64(latitude), float64(longitude)
+
+	switch {
+	case math.IsNaN(lat) || math.IsInf(lat, 0):
+		// don’t wrap
+	case lat < -90 || lat > 90:
+		// Latitude wraps by flipping the longitude
+		lat = math.Mod(lat, 360.0)
+		switch {
+		case lat == 0.0:
+			lat = 0.0 // -0.0 == 0.0, but -0° is not valid
+		case lat < -270.0:
+			lat = +360.0 + lat
+		case lat < -90.0:
+			lat = -180.0 - lat
+			lng += 180.0
+		case lat > +270.0:
+			lat = -360.0 + lat
+		case lat > +90.0:
+			lat = +180.0 - lat
+			lng += 180.0
+		}
+	}
+
+	switch {
+	case lat == -90.0 || lat == +90.0:
+		// By convention, the north and south poles have longitude 0°.
+		lng = 0
+	case math.IsNaN(lng) || math.IsInf(lng, 0):
+		// don’t wrap
+	case lng <= -180.0 || lng > 180.0:
+		// Longitude wraps around normally
+		lng = math.Mod(lng, 360.0)
+		switch {
+		case lng == 0.0:
+			lng = 0.0 // -0.0 == 0.0, but -0° is not valid
+		case lng <= -180.0:
+			lng = +360.0 + lng
+		case lng > +180.0:
+			lng = -360.0 + lng
+		}
+	}
+
+	return Point{
+		lat:    Degrees(lat),
+		lng180: Degrees(lng + 180.0),
+	}
+}
+
+// Valid reports if p is a valid point.
+func (p Point) Valid() bool {
+	return !p.IsZero()
+}
+
+// LatLng reports the latitude and longitude.
+func (p Point) LatLng() (lat, lng Degrees, err error) {
+	if p.IsZero() {
+		return 0 * Degree, 0 * Degree, ErrBadPoint
+	}
+	return p.lat, p.lng180 - 180.0*Degree, nil
+}
+
+// LatLng reports the latitude and longitude in float64. If err is nil, then lat
+// and lng will never both be 0.0 to disambiguate between an empty struct and
+// Null Island (0° 0°).
+func (p Point) LatLngFloat64() (lat, lng float64, err error) {
+	dlat, dlng, err := p.LatLng()
+	if err != nil {
+		return 0.0, 0.0, err
+	}
+	if dlat == 0.0 && dlng == 0.0 {
+		// dlng must survive conversion to float32.
+		dlng = math.SmallestNonzeroFloat32
+	}
+	return float64(dlat), float64(dlng), err
+}
+
+// SphericalAngleTo returns the angular distance from p to q, calculated on a
+// spherical Earth.
+func (p Point) SphericalAngleTo(q Point) (Radians, error) {
+	pLat, pLng, pErr := p.LatLng()
+	qLat, qLng, qErr := q.LatLng()
+	switch {
+	case pErr != nil && qErr != nil:
+		return 0.0, fmt.Errorf("spherical distance from %v to %v: %w", p, q, errors.Join(pErr, qErr))
+	case pErr != nil:
+		return 0.0, fmt.Errorf("spherical distance from %v: %w", p, pErr)
+	case qErr != nil:
+		return 0.0, fmt.Errorf("spherical distance to %v: %w", q, qErr)
+	}
+	// The spherical law of cosines is accurate enough for close points when
+	// using float64.
+	//
+	// The haversine formula is an alternative, but it is poorly behaved
+	// when points are on opposite sides of the sphere.
+	rLat, rLng := float64(pLat.Radians()), float64(pLng.Radians())
+	sLat, sLng := float64(qLat.Radians()), float64(qLng.Radians())
+	cosA := math.Sin(rLat)*math.Sin(sLat) +
+		math.Cos(rLat)*math.Cos(sLat)*math.Cos(rLng-sLng)
+	return Radians(math.Acos(cosA)), nil
+}
+
+// DistanceTo reports the great-circle distance between p and q, in meters.
+func (p Point) DistanceTo(q Point) (Distance, error) {
+	r, err := p.SphericalAngleTo(q)
+	if err != nil {
+		return 0, err
+	}
+	return DistanceOnEarth(r.Turns()), nil
+}
+
+// String returns a space-separated pair of latitude and longitude, in decimal
+// degrees. Positive latitudes are in the northern hemisphere, and positive
+// longitudes are east of the prime meridian. If p was not initialized, this
+// will return "nowhere".
+func (p Point) String() string {
+	lat, lng, err := p.LatLng()
+	if err != nil {
+		if err == ErrBadPoint {
+			return "nowhere"
+		}
+		panic(err)
+	}
+
+	return lat.String() + " " + lng.String()
+}
+
+// AppendBinary implements [encoding.BinaryAppender]. The output consists of two
+// float32s in big-endian byte order: latitude and longitude offset by 180°.
+// If p is not a valid, the output will be an 8-byte zero value.
+func (p Point) AppendBinary(b []byte) ([]byte, error) {
+	end := binary.BigEndian
+	b = end.AppendUint32(b, math.Float32bits(float32(p.lat)))
+	b = end.AppendUint32(b, math.Float32bits(float32(p.lng180)))
+	return b, nil
+}
+
+// MarshalBinary implements [encoding.BinaryMarshaller]. The output matches that
+// of calling [Point.AppendBinary].
+func (p Point) MarshalBinary() ([]byte, error) {
+	var b [8]byte
+	return p.AppendBinary(b[:0])
+}
+
+// UnmarshalBinary implements [encoding.BinaryUnmarshaler]. It expects input
+// that was formatted by [Point.AppendBinary]: in big-endian byte order, a
+// float32 representing latitude followed by a float32 representing longitude
+// offset by 180°. If latitude and longitude fall outside valid ranges, then
+// an error is returned.
+func (p *Point) UnmarshalBinary(data []byte) error {
+	if len(data) < 8 { // Two uint32s are 8 bytes long
+		return fmt.Errorf("%w: not enough data: %q", ErrBadPoint, data)
+	}
+
+	end := binary.BigEndian
+	lat := Degrees(math.Float32frombits(end.Uint32(data[0:])))
+	if lat < -90*Degree || lat > 90*Degree {
+		return fmt.Errorf("%w: latitude outside [-90°, +90°]: %s", ErrBadPoint, lat)
+	}
+	lng180 := Degrees(math.Float32frombits(end.Uint32(data[4:])))
+	if lng180 != 0 && (lng180 < 0*Degree || lng180 > 360*Degree) {
+		// lng180 == 0 is OK: the zero value represents invalid points.
+		lng := lng180 - 180*Degree
+		return fmt.Errorf("%w: longitude outside (-180°, +180°]: %s", ErrBadPoint, lng)
+	}
+
+	p.lat = lat
+	p.lng180 = lng180
+	return nil
+}
+
+// AppendText implements [encoding.TextAppender]. The output is a point
+// formatted as OGC Well-Known Text, as "POINT (longitude latitude)" where
+// longitude and latitude are in decimal degrees. If p is not valid, the output
+// will be "POINT EMPTY".
+func (p Point) AppendText(b []byte) ([]byte, error) {
+	if p.IsZero() {
+		b = append(b, []byte("POINT EMPTY")...)
+		return b, nil
+	}
+
+	lat, lng, err := p.LatLng()
+	if err != nil {
+		return b, err
+	}
+
+	b = append(b, []byte("POINT (")...)
+	b = strconv.AppendFloat(b, float64(lng), 'f', -1, 64)
+	b = append(b, ' ')
+	b = strconv.AppendFloat(b, float64(lat), 'f', -1, 64)
+	b = append(b, ')')
+	return b, nil
+}
+
+// MarshalText implements [encoding.TextMarshaller]. The output matches that
+// of calling [Point.AppendText].
+func (p Point) MarshalText() ([]byte, error) {
+	var b [8]byte
+	return p.AppendText(b[:0])
+}
+
+// MarshalUint64 produces the same output as MashalBinary, encoded in a uint64.
+func (p Point) MarshalUint64() (uint64, error) {
+	b, err := p.MarshalBinary()
+	return binary.NativeEndian.Uint64(b), err
+}
+
+// UnmarshalUint64 expects input formatted by MarshalUint64.
+func (p *Point) UnmarshalUint64(v uint64) error {
+	b := binary.NativeEndian.AppendUint64(nil, v)
+	return p.UnmarshalBinary(b)
+}
+
+// IsZero reports if p is the zero value.
+func (p Point) IsZero() bool {
+	return p == Point{}
+}
+
+// EqualApprox reports if p and q are approximately equal: that is the absolute
+// difference of both latitude and longitude are less than tol. If tol is
+// negative, then tol defaults to a reasonably small number (10⁻⁵). If tol is
+// zero, then p and q must be exactly equal.
+func (p Point) EqualApprox(q Point, tol float64) bool {
+	if tol == 0 {
+		return p == q
+	}
+
+	if p.IsZero() && q.IsZero() {
+		return true
+	} else if p.IsZero() || q.IsZero() {
+		return false
+	}
+
+	plat, plng, err := p.LatLng()
+	if err != nil {
+		panic(err)
+	}
+	qlat, qlng, err := q.LatLng()
+	if err != nil {
+		panic(err)
+	}
+
+	if tol < 0 {
+		tol = 1e-5
+	}
+
+	dlat := float64(plat) - float64(qlat)
+	dlng := float64(plng) - float64(qlng)
+	return ((dlat < 0 && -dlat < tol) || (dlat >= 0 && dlat < tol)) &&
+		((dlng < 0 && -dlng < tol) || (dlng >= 0 && dlng < tol))
+}

types/geo/point_test.go

@@ -0,0 +1,541 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package geo_test
+
+import (
+	"fmt"
+	"math"
+	"testing"
+	"testing/quick"
+
+	"tailscale.com/types/geo"
+)
+
+func TestPointZero(t *testing.T) {
+	var zero geo.Point
+
+	if got := zero.IsZero(); !got {
+		t.Errorf("IsZero() got %t", got)
+	}
+
+	if got := zero.Valid(); got {
+		t.Errorf("Valid() got %t", got)
+	}
+
+	wantErr := geo.ErrBadPoint.Error()
+	if _, _, err := zero.LatLng(); err.Error() != wantErr {
+		t.Errorf("LatLng() err %q, want %q", err, wantErr)
+	}
+
+	wantStr := "nowhere"
+	if got := zero.String(); got != wantStr {
+		t.Errorf("String() got %q, want %q", got, wantStr)
+	}
+
+	wantB := []byte{0, 0, 0, 0, 0, 0, 0, 0}
+	if b, err := zero.MarshalBinary(); err != nil {
+		t.Errorf("MarshalBinary() err %q, want nil", err)
+	} else if string(b) != string(wantB) {
+		t.Errorf("MarshalBinary got %q, want %q", b, wantB)
+	}
+
+	wantI := uint64(0x00000000)
+	if i, err := zero.MarshalUint64(); err != nil {
+		t.Errorf("MarshalUint64() err %q, want nil", err)
+	} else if i != wantI {
+		t.Errorf("MarshalUint64 got %v, want %v", i, wantI)
+	}
+}
+
+func TestPoint(t *testing.T) {
+	for _, tt := range []struct {
+		name       string
+		lat        geo.Degrees
+		lng        geo.Degrees
+		wantLat    geo.Degrees
+		wantLng    geo.Degrees
+		wantString string
+		wantText   string
+	}{
+		{
+			name:       "null-island",
+			lat:        +0.0,
+			lng:        +0.0,
+			wantLat:    +0.0,
+			wantLng:    +0.0,
+			wantString: "+0° +0°",
+			wantText:   "POINT (0 0)",
+		},
+		{
+			name:       "north-pole",
+			lat:        +90.0,
+			lng:        +0.0,
+			wantLat:    +90.0,
+			wantLng:    +0.0,
+			wantString: "+90° +0°",
+			wantText:   "POINT (0 90)",
+		},
+		{
+			name:       "south-pole",
+			lat:        -90.0,
+			lng:        +0.0,
+			wantLat:    -90.0,
+			wantLng:    +0.0,
+			wantString: "-90° +0°",
+			wantText:   "POINT (0 -90)",
+		},
+		{
+			name:       "north-pole-weird-longitude",
+			lat:        +90.0,
+			lng:        +1.0,
+			wantLat:    +90.0,
+			wantLng:    +0.0,
+			wantString: "+90° +0°",
+			wantText:   "POINT (0 90)",
+		},
+		{
+			name:       "south-pole-weird-longitude",
+			lat:        -90.0,
+			lng:        +1.0,
+			wantLat:    -90.0,
+			wantLng:    +0.0,
+			wantString: "-90° +0°",
+			wantText:   "POINT (0 -90)",
+		},
+		{
+			name:       "almost-north",
+			lat:        +89.0,
+			lng:        +0.0,
+			wantLat:    +89.0,
+			wantLng:    +0.0,
+			wantString: "+89° +0°",
+			wantText:   "POINT (0 89)",
+		},
+		{
+			name:       "past-north",
+			lat:        +91.0,
+			lng:        +0.0,
+			wantLat:    +89.0,
+			wantLng:    +180.0,
+			wantString: "+89° +180°",
+			wantText:   "POINT (180 89)",
+		},
+		{
+			name:       "almost-south",
+			lat:        -89.0,
+			lng:        +0.0,
+			wantLat:    -89.0,
+			wantLng:    +0.0,
+			wantString: "-89° +0°",
+			wantText:   "POINT (0 -89)",
+		},
+		{
+			name:       "past-south",
+			lat:        -91.0,
+			lng:        +0.0,
+			wantLat:    -89.0,
+			wantLng:    +180.0,
+			wantString: "-89° +180°",
+			wantText:   "POINT (180 -89)",
+		},
+		{
+			name:       "antimeridian-north",
+			lat:        +180.0,
+			lng:        +0.0,
+			wantLat:    +0.0,
+			wantLng:    +180.0,
+			wantString: "+0° +180°",
+			wantText:   "POINT (180 0)",
+		},
+		{
+			name:       "antimeridian-south",
+			lat:        -180.0,
+			lng:        +0.0,
+			wantLat:    +0.0,
+			wantLng:    +180.0,
+			wantString: "+0° +180°",
+			wantText:   "POINT (180 0)",
+		},
+		{
+			name:       "almost-antimeridian-north",
+			lat:        +179.0,
+			lng:        +0.0,
+			wantLat:    +1.0,
+			wantLng:    +180.0,
+			wantString: "+1° +180°",
+			wantText:   "POINT (180 1)",
+		},
+		{
+			name:       "past-antimeridian-north",
+			lat:        +181.0,
+			lng:        +0.0,
+			wantLat:    -1.0,
+			wantLng:    +180.0,
+			wantString: "-1° +180°",
+			wantText:   "POINT (180 -1)",
+		},
+		{
+			name:       "almost-antimeridian-south",
+			lat:        -179.0,
+			lng:        +0.0,
+			wantLat:    -1.0,
+			wantLng:    +180.0,
+			wantString: "-1° +180°",
+			wantText:   "POINT (180 -1)",
+		},
+		{
+			name:       "past-antimeridian-south",
+			lat:        -181.0,
+			lng:        +0.0,
+			wantLat:    +1.0,
+			wantLng:    +180.0,
+			wantString: "+1° +180°",
+			wantText:   "POINT (180 1)",
+		},
+		{
+			name:       "circumnavigate-north",
+			lat:        +360.0,
+			lng:        +1.0,
+			wantLat:    +0.0,
+			wantLng:    +1.0,
+			wantString: "+0° +1°",
+			wantText:   "POINT (1 0)",
+		},
+		{
+			name:       "circumnavigate-south",
+			lat:        -360.0,
+			lng:        +1.0,
+			wantLat:    +0.0,
+			wantLng:    +1.0,
+			wantString: "+0° +1°",
+			wantText:   "POINT (1 0)",
+		},
+		{
+			name:       "almost-circumnavigate-north",
+			lat:        +359.0,
+			lng:        +1.0,
+			wantLat:    -1.0,
+			wantLng:    +1.0,
+			wantString: "-1° +1°",
+			wantText:   "POINT (1 -1)",
+		},
+		{
+			name:       "past-circumnavigate-north",
+			lat:        +361.0,
+			lng:        +1.0,
+			wantLat:    +1.0,
+			wantLng:    +1.0,
+			wantString: "+1° +1°",
+			wantText:   "POINT (1 1)",
+		},
+		{
+			name:       "almost-circumnavigate-south",
+			lat:        -359.0,
+			lng:        +1.0,
+			wantLat:    +1.0,
+			wantLng:    +1.0,
+			wantString: "+1° +1°",
+			wantText:   "POINT (1 1)",
+		},
+		{
+			name:       "past-circumnavigate-south",
+			lat:        -361.0,
+			lng:        +1.0,
+			wantLat:    -1.0,
+			wantLng:    +1.0,
+			wantString: "-1° +1°",
+			wantText:   "POINT (1 -1)",
+		},
+		{
+			name:       "antimeridian-east",
+			lat:        +0.0,
+			lng:        +180.0,
+			wantLat:    +0.0,
+			wantLng:    +180.0,
+			wantString: "+0° +180°",
+			wantText:   "POINT (180 0)",
+		},
+		{
+			name:       "antimeridian-west",
+			lat:        +0.0,
+			lng:        -180.0,
+			wantLat:    +0.0,
+			wantLng:    +180.0,
+			wantString: "+0° +180°",
+			wantText:   "POINT (180 0)",
+		},
+		{
+			name:       "almost-antimeridian-east",
+			lat:        +0.0,
+			lng:        +179.0,
+			wantLat:    +0.0,
+			wantLng:    +179.0,
+			wantString: "+0° +179°",
+			wantText:   "POINT (179 0)",
+		},
+		{
+			name:       "past-antimeridian-east",
+			lat:        +0.0,
+			lng:        +181.0,
+			wantLat:    +0.0,
+			wantLng:    -179.0,
+			wantString: "+0° -179°",
+			wantText:   "POINT (-179 0)",
+		},
+		{
+			name:       "almost-antimeridian-west",
+			lat:        +0.0,
+			lng:        -179.0,
+			wantLat:    +0.0,
+			wantLng:    -179.0,
+			wantString: "+0° -179°",
+			wantText:   "POINT (-179 0)",
+		},
+		{
+			name:       "past-antimeridian-west",
+			lat:        +0.0,
+			lng:        -181.0,
+			wantLat:    +0.0,
+			wantLng:    +179.0,
+			wantString: "+0° +179°",
+			wantText:   "POINT (179 0)",
+		},
+		{
+			name:       "montreal",
+			lat:        +45.508888,
+			lng:        -73.561668,
+			wantLat:    +45.508888,
+			wantLng:    -73.561668,
+			wantString: "+45.508888° -73.561668°",
+			wantText:   "POINT (-73.561668 45.508888)",
+		},
+		{
+			name:       "canada",
+			lat:        57.550480044655636,
+			lng:        -98.41680517868062,
+			wantLat:    57.550480044655636,
+			wantLng:    -98.41680517868062,
+			wantString: "+57.550480044655636° -98.41680517868062°",
+			wantText:   "POINT (-98.41680517868062 57.550480044655636)",
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			p := geo.MakePoint(tt.lat, tt.lng)
+
+			lat, lng, err := p.LatLng()
+			if !approx(lat, tt.wantLat) {
+				t.Errorf("MakePoint: lat %v, want %v", lat, tt.wantLat)
+			}
+			if !approx(lng, tt.wantLng) {
+				t.Errorf("MakePoint: lng %v, want %v", lng, tt.wantLng)
+			}
+			if err != nil {
+				t.Fatalf("LatLng: err %q, expected nil", err)
+			}
+
+			if got := p.String(); got != tt.wantString {
+				t.Errorf("String: got %q, wantString %q", got, tt.wantString)
+			}
+
+			txt, err := p.MarshalText()
+			if err != nil {
+				t.Errorf("Text: err %q, expected nil", err)
+			} else if string(txt) != tt.wantText {
+				t.Errorf("Text: got %q, wantText %q", txt, tt.wantText)
+			}
+
+			b, err := p.MarshalBinary()
+			if err != nil {
+				t.Fatalf("MarshalBinary: err %q, expected nil", err)
+			}
+
+			var q geo.Point
+			if err := q.UnmarshalBinary(b); err != nil {
+				t.Fatalf("UnmarshalBinary: err %q, expected nil", err)
+			}
+			if !q.EqualApprox(p, -1) {
+				t.Errorf("UnmarshalBinary: roundtrip failed: %#v != %#v", q, p)
+			}
+
+			i, err := p.MarshalUint64()
+			if err != nil {
+				t.Fatalf("MarshalUint64: err %q, expected nil", err)
+			}
+
+			var r geo.Point
+			if err := r.UnmarshalUint64(i); err != nil {
+				t.Fatalf("UnmarshalUint64: err %r, expected nil", err)
+			}
+			if !q.EqualApprox(r, -1) {
+				t.Errorf("UnmarshalUint64: roundtrip failed: %#v != %#v", r, p)
+			}
+		})
+	}
+}
+
+func TestPointMarshalBinary(t *testing.T) {
+	roundtrip := func(p geo.Point) error {
+		b, err := p.MarshalBinary()
+		if err != nil {
+			return fmt.Errorf("marshal: %v", err)
+		}
+		var q geo.Point
+		if err := q.UnmarshalBinary(b); err != nil {
+			return fmt.Errorf("unmarshal: %v", err)
+		}
+		if q != p {
+			return fmt.Errorf("%#v != %#v", q, p)
+		}
+		return nil
+	}
+
+	t.Run("nowhere", func(t *testing.T) {
+		var nowhere geo.Point
+		if err := roundtrip(nowhere); err != nil {
+			t.Errorf("roundtrip: %v", err)
+		}
+	})
+
+	t.Run("quick-check", func(t *testing.T) {
+		f := func(lat geo.Degrees, lng geo.Degrees) (ok bool) {
+			pt := geo.MakePoint(lat, lng)
+			if err := roundtrip(pt); err != nil {
+				t.Errorf("roundtrip: %v", err)
+			}
+			return !t.Failed()
+		}
+		if err := quick.Check(f, nil); err != nil {
+			t.Error(err)
+		}
+	})
+}
+
+func TestPointMarshalUint64(t *testing.T) {
+	t.Skip("skip")
+	roundtrip := func(p geo.Point) error {
+		i, err := p.MarshalUint64()
+		if err != nil {
+			return fmt.Errorf("marshal: %v", err)
+		}
+		var q geo.Point
+		if err := q.UnmarshalUint64(i); err != nil {
+			return fmt.Errorf("unmarshal: %v", err)
+		}
+		if q != p {
+			return fmt.Errorf("%#v != %#v", q, p)
+		}
+		return nil
+	}
+
+	t.Run("nowhere", func(t *testing.T) {
+		var nowhere geo.Point
+		if err := roundtrip(nowhere); err != nil {
+			t.Errorf("roundtrip: %v", err)
+		}
+	})
+
+	t.Run("quick-check", func(t *testing.T) {
+		f := func(lat geo.Degrees, lng geo.Degrees) (ok bool) {
+			if err := roundtrip(geo.MakePoint(lat, lng)); err != nil {
+				t.Errorf("roundtrip: %v", err)
+			}
+			return !t.Failed()
+		}
+		if err := quick.Check(f, nil); err != nil {
+			t.Error(err)
+		}
+	})
+}
+
+func TestPointSphericalAngleTo(t *testing.T) {
+	const earthRadius = 6371.000 // volumetric mean radius (km)
+	const kmToRad = 1 / earthRadius
+	for _, tt := range []struct {
+		name    string
+		x       geo.Point
+		y       geo.Point
+		want    geo.Radians
+		wantErr string
+	}{
+		{
+			name: "same-point-null-island",
+			x:    geo.MakePoint(0, 0),
+			y:    geo.MakePoint(0, 0),
+			want: 0.0 * geo.Radian,
+		},
+		{
+			name: "same-point-north-pole",
+			x:    geo.MakePoint(+90, 0),
+			y:    geo.MakePoint(+90, +90),
+			want: 0.0 * geo.Radian,
+		},
+		{
+			name: "same-point-south-pole",
+			x:    geo.MakePoint(-90, 0),
+			y:    geo.MakePoint(-90, -90),
+			want: 0.0 * geo.Radian,
+		},
+		{
+			name: "north-pole-to-south-pole",
+			x:    geo.MakePoint(+90, 0),
+			y:    geo.MakePoint(-90, -90),
+			want: math.Pi * geo.Radian,
+		},
+		{
+			name: "toronto-to-montreal",
+			x:    geo.MakePoint(+43.6532, -79.3832),
+			y:    geo.MakePoint(+45.5019, -73.5674),
+			want: 504.26 * kmToRad * geo.Radian,
+		},
+		{
+			name: "sydney-to-san-francisco",
+			x:    geo.MakePoint(-33.8727, +151.2057),
+			y:    geo.MakePoint(+37.7749, -122.4194),
+			want: 11948.18 * kmToRad * geo.Radian,
+		},
+		{
+			name: "new-york-to-paris",
+			x:    geo.MakePoint(+40.7128, -74.0060),
+			y:    geo.MakePoint(+48.8575, +2.3514),
+			want: 5837.15 * kmToRad * geo.Radian,
+		},
+		{
+			name: "seattle-to-tokyo",
+			x:    geo.MakePoint(+47.6061, -122.3328),
+			y:    geo.MakePoint(+35.6764, +139.6500),
+			want: 7700.00 * kmToRad * geo.Radian,
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			got, err := tt.x.SphericalAngleTo(tt.y)
+			if tt.wantErr == "" && err != nil {
+				t.Fatalf("err %q, expected nil", err)
+			}
+			if tt.wantErr != "" && (err == nil || err.Error() != tt.wantErr) {
+				t.Fatalf("err %q, expected %q", err, tt.wantErr)
+			}
+			if tt.wantErr != "" {
+				return
+			}
+
+			if !approx(got, tt.want) {
+				t.Errorf("x to y: got %v, want %v", got, tt.want)
+			}
+
+			// Distance should be commutative
+			got, err = tt.y.SphericalAngleTo(tt.x)
+			if err != nil {
+				t.Fatalf("err %q, expected nil", err)
+			}
+			if !approx(got, tt.want) {
+				t.Errorf("y to x: got %v, want %v", got, tt.want)
+			}
+			t.Logf("x to y: %v km", got/kmToRad)
+		})
+	}
+}
+
+func approx[T ~float64](x, y T) bool {
+	return math.Abs(float64(x)-float64(y)) <= 1e-5
+}

types/geo/quantize.go

@@ -0,0 +1,106 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package geo
+
+import (
+	"math"
+	"sync"
+)
+
+// MinSeparation is the minimum separation between two points after quantizing.
+// [Point.Quantize] guarantees that two points will either be snapped to exactly
+// the same point, which conflates multiple positions together, or that the two
+// points will be far enough apart that successfully performing most reverse
+// lookups would be highly improbable.
+const MinSeparation = 50_000 * Meter
+
+// Latitude
+var (
+	// numSepsEquatorToPole is the number of separations between a point on
+	// the equator to a point on a pole, that satisfies [minPointSep]. In
+	// other words, the number of separations between 0° and +90° degrees
+	// latitude.
+	numSepsEquatorToPole = int(math.Floor(float64(
+		earthPolarCircumference / MinSeparation / 4)))
+
+	// latSep is the number of degrees between two adjacent latitudinal
+	// points. In other words, the next point going straight north of
+	// 0° would be latSep°.
+	latSep = Degrees(90.0 / float64(numSepsEquatorToPole))
+)
+
+// snapToLat returns the number of the nearest latitudinal separation to
+// lat. A positive result is north of the equator, a negative result is south,
+// and zero is the equator itself. For example, a result of -1 would mean a
+// point that is [latSep] south of the equator.
+func snapToLat(lat Degrees) int {
+	return int(math.Round(float64(lat / latSep)))
+}
+
+// lngSep is a lookup table for the number of degrees between two adjacent
+// longitudinal separations. where the index corresponds to the absolute value
+// of the latitude separation. The first value corresponds to the equator and
+// the last value corresponds to the separation before the pole. There is no
+// value for the pole itself, because longitude has no meaning there.
+//
+// [lngSep] is calculated on init, which is so quick and will be used so often
+// that the startup cost is negligible.
+var lngSep = sync.OnceValue(func() []Degrees {
+	lut := make([]Degrees, numSepsEquatorToPole)
+
+	// i ranges from the equator to a pole
+	for i := range len(lut) {
+		// lat ranges from [0°, 90°], because the southern hemisphere is
+		// a reflection of the northern one.
+		lat := Degrees(i) * latSep
+		ratio := math.Cos(float64(lat.Radians()))
+		circ := Distance(ratio) * earthEquatorialCircumference
+		num := int(math.Floor(float64(circ / MinSeparation)))
+		// We define lut[0] as 0°, lut[len(lut)] to be the north pole,
+		// which means -lut[len(lut)] is the south pole.
+		lut[i] = Degrees(360.0 / float64(num))
+	}
+	return lut
+})
+
+// snapToLatLng returns the number of the nearest latitudinal separation to lat,
+// and the nearest longitudinal separation to lng.
+func snapToLatLng(lat, lng Degrees) (Degrees, Degrees) {
+	latN := snapToLat(lat)
+
+	// absolute index into lngSep
+	n := latN
+	if n < 0 {
+		n = -latN
+	}
+
+	lngSep := lngSep()
+	if n < len(lngSep) {
+		sep := lngSep[n]
+		lngN := int(math.Round(float64(lng / sep)))
+		return Degrees(latN) * latSep, Degrees(lngN) * sep
+	}
+	if latN < 0 { // south pole
+		return -90 * Degree, 0 * Degree
+	} else { // north pole
+		return +90 * Degree, 0 * Degree
+	}
+}
+
+// Quantize returns a new [Point] after throwing away enough location data in p
+// so that it would be difficult to distinguish a node among all the other nodes
+// in its general vicinity. One caveat is that if there’s only one point in an
+// obscure location, someone could triangulate the node using additional data.
+//
+// This method is stable: given the same p, it will always return the same
+// result. It is equivalent to snapping to points on Earth that are at least
+// [MinSeparation] apart.
+func (p Point) Quantize() Point {
+	if p.IsZero() {
+		return p
+	}
+
+	lat, lng := snapToLatLng(p.lat, p.lng180-180)
+	return MakePoint(lat, lng)
+}

types/geo/quantize_test.go

@@ -0,0 +1,130 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package geo_test
+
+import (
+	"testing"
+	"testing/quick"
+
+	"tailscale.com/types/geo"
+)
+
+func TestPointAnonymize(t *testing.T) {
+	t.Run("nowhere", func(t *testing.T) {
+		var zero geo.Point
+		p := zero.Quantize()
+		want := zero.Valid()
+		if got := p.Valid(); got != want {
+			t.Fatalf("zero.Valid %t, want %t", got, want)
+		}
+	})
+
+	t.Run("separation", func(t *testing.T) {
+		// Walk from the south pole to the north pole and check that each
+		// point on the latitude is approximately MinSeparation apart.
+		const southPole = -90 * geo.Degree
+		const northPole = 90 * geo.Degree
+		const dateLine = 180 * geo.Degree
+
+		llat := southPole
+		for lat := llat; lat <= northPole; lat += 0x1p-4 {
+			last := geo.MakePoint(llat, 0)
+			cur := geo.MakePoint(lat, 0)
+			anon := cur.Quantize()
+			switch l, g, err := anon.LatLng(); {
+			case err != nil:
+				t.Fatal(err)
+			case lat == southPole:
+				// initialize llng, to the first snapped longitude
+				llat = l
+				goto Lng
+			case g != 0:
+				t.Fatalf("%v is west or east of %v", anon, last)
+			case l < llat:
+				t.Fatalf("%v is south of %v", anon, last)
+			case l == llat:
+				continue
+			case l > llat:
+				switch dist, err := last.DistanceTo(anon); {
+				case err != nil:
+					t.Fatal(err)
+				case dist == 0.0:
+					continue
+				case dist < geo.MinSeparation:
+					t.Logf("lat=%v last=%v cur=%v anon=%v", lat, last, cur, anon)
+					t.Fatalf("%v is too close to %v", anon, last)
+				default:
+					llat = l
+				}
+			}
+
+		Lng:
+			llng := dateLine
+			for lng := llng; lng <= dateLine && lng >= -dateLine; lng -= 0x1p-3 {
+				last := geo.MakePoint(llat, llng)
+				cur := geo.MakePoint(lat, lng)
+				anon := cur.Quantize()
+				switch l, g, err := anon.LatLng(); {
+				case err != nil:
+					t.Fatal(err)
+				case lng == dateLine:
+					// initialize llng, to the first snapped longitude
+					llng = g
+					continue
+				case l != llat:
+					t.Fatalf("%v is north or south of %v", anon, last)
+				case g != llng:
+					const tolerance = geo.MinSeparation * 0x1p-9
+					switch dist, err := last.DistanceTo(anon); {
+					case err != nil:
+						t.Fatal(err)
+					case dist < tolerance:
+						continue
+					case dist < (geo.MinSeparation - tolerance):
+						t.Logf("lat=%v lng=%v last=%v cur=%v anon=%v", lat, lng, last, cur, anon)
+						t.Fatalf("%v is too close to %v: %v", anon, last, dist)
+					default:
+						llng = g
+					}
+
+				}
+			}
+		}
+		if llat == southPole {
+			t.Fatal("llat never incremented")
+		}
+	})
+
+	t.Run("quick-check", func(t *testing.T) {
+		f := func(lat, lng geo.Degrees) bool {
+			p := geo.MakePoint(lat, lng)
+			q := p.Quantize()
+			t.Logf("quantize %v = %v", p, q)
+
+			lat, lng, err := q.LatLng()
+			if err != nil {
+				t.Errorf("err %v, want nil", err)
+				return !t.Failed()
+			}
+
+			if lat < -90*geo.Degree || lat > 90*geo.Degree {
+				t.Errorf("lat outside [-90°, +90°]: %v", lat)
+			}
+			if lng < -180*geo.Degree || lng > 180*geo.Degree {
+				t.Errorf("lng outside [-180°, +180°], %v", lng)
+			}
+
+			if dist, err := p.DistanceTo(q); err != nil {
+				t.Error(err)
+			} else if dist > (geo.MinSeparation * 2) {
+				t.Errorf("moved too far: %v", dist)
+			}
+
+			return !t.Failed()
+		}
+		if err := quick.Check(f, nil); err != nil {
+			t.Fatal(err)
+		}
+	})
+}

types/geo/units.go

@@ -0,0 +1,191 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package geo
+
+import (
+	"math"
+	"strconv"
+	"strings"
+	"unicode"
+)
+
+const (
+	Degree Degrees  = 1
+	Radian Radians  = 1
+	Turn   Turns    = 1
+	Meter  Distance = 1
+)
+
+// Degrees represents a latitude or longitude, in decimal degrees.
+type Degrees float64
+
+// ParseDegrees parses s as decimal degrees.
+func ParseDegrees(s string) (Degrees, error) {
+	s = strings.TrimSuffix(s, "°")
+	f, err := strconv.ParseFloat(s, 64)
+	return Degrees(f), err
+}
+
+// MustParseDegrees parses s as decimal degrees, but panics on error.
+func MustParseDegrees(s string) Degrees {
+	d, err := ParseDegrees(s)
+	if err != nil {
+		panic(err)
+	}
+	return d
+}
+
+// String implements the [Stringer] interface. The output is formatted in
+// decimal degrees, prefixed by either the appropriate + or - sign, and suffixed
+// by a ° degree symbol.
+func (d Degrees) String() string {
+	b, _ := d.AppendText(nil)
+	b = append(b, []byte("°")...)
+	return string(b)
+}
+
+// AppendText implements [encoding.TextAppender]. The output is formatted in
+// decimal degrees, prefixed by either the appropriate + or - sign.
+func (d Degrees) AppendText(b []byte) ([]byte, error) {
+	b = d.AppendZeroPaddedText(b, 0)
+	return b, nil
+}
+
+// AppendZeroPaddedText appends d formatted as decimal degrees to b. The number of
+// integer digits will be zero-padded to nint.
+func (d Degrees) AppendZeroPaddedText(b []byte, nint int) []byte {
+	n := float64(d)
+
+	if math.IsInf(n, 0) || math.IsNaN(n) {
+		return strconv.AppendFloat(b, n, 'f', -1, 64)
+	}
+
+	sign := byte('+')
+	if math.Signbit(n) {
+		sign = '-'
+		n = -n
+	}
+	b = append(b, sign)
+
+	pad := nint - 1
+	for nn := n / 10; nn >= 1 && pad > 0; nn /= 10 {
+		pad--
+	}
+	for range pad {
+		b = append(b, '0')
+	}
+	return strconv.AppendFloat(b, n, 'f', -1, 64)
+}
+
+// Radians converts d into radians.
+func (d Degrees) Radians() Radians {
+	return Radians(d * math.Pi / 180.0)
+}
+
+// Turns converts d into a number of turns.
+func (d Degrees) Turns() Turns {
+	return Turns(d / 360.0)
+}
+
+// Radians represents a latitude or longitude, in radians.
+type Radians float64
+
+// ParseRadians parses s as radians.
+func ParseRadians(s string) (Radians, error) {
+	s = strings.TrimSuffix(s, "rad")
+	s = strings.TrimRightFunc(s, unicode.IsSpace)
+	f, err := strconv.ParseFloat(s, 64)
+	return Radians(f), err
+}
+
+// MustParseRadians parses s as radians, but panics on error.
+func MustParseRadians(s string) Radians {
+	r, err := ParseRadians(s)
+	if err != nil {
+		panic(err)
+	}
+	return r
+}
+
+// String implements the [Stringer] interface.
+func (r Radians) String() string {
+	return strconv.FormatFloat(float64(r), 'f', -1, 64) + " rad"
+}
+
+// Degrees converts r into decimal degrees.
+func (r Radians) Degrees() Degrees {
+	return Degrees(r * 180.0 / math.Pi)
+}
+
+// Turns converts r into a number of turns.
+func (r Radians) Turns() Turns {
+	return Turns(r / 2 / math.Pi)
+}
+
+// Turns represents a number of complete revolutions around a sphere.
+type Turns float64
+
+// String implements the [Stringer] interface.
+func (o Turns) String() string {
+	return strconv.FormatFloat(float64(o), 'f', -1, 64)
+}
+
+// Degrees converts t into decimal degrees.
+func (o Turns) Degrees() Degrees {
+	return Degrees(o * 360.0)
+}
+
+// Radians converts t into radians.
+func (o Turns) Radians() Radians {
+	return Radians(o * 2 * math.Pi)
+}
+
+// Distance represents a great-circle distance in meters.
+type Distance float64
+
+// ParseDistance parses s as distance in meters.
+func ParseDistance(s string) (Distance, error) {
+	s = strings.TrimSuffix(s, "m")
+	s = strings.TrimRightFunc(s, unicode.IsSpace)
+	f, err := strconv.ParseFloat(s, 64)
+	return Distance(f), err
+}
+
+// MustParseDistance parses s as distance in meters, but panics on error.
+func MustParseDistance(s string) Distance {
+	d, err := ParseDistance(s)
+	if err != nil {
+		panic(err)
+	}
+	return d
+}
+
+// String implements the [Stringer] interface.
+func (d Distance) String() string {
+	return strconv.FormatFloat(float64(d), 'f', -1, 64) + "m"
+}
+
+// DistanceOnEarth converts t turns into the great-circle distance, in meters.
+func DistanceOnEarth(t Turns) Distance {
+	return Distance(t) * EarthMeanCircumference
+}
+
+// Earth Fact Sheet
+// https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
+const (
+	// EarthMeanRadius is the volumetric mean radius of the Earth.
+	EarthMeanRadius = 6_371_000 * Meter
+	// EarthMeanCircumference is the volumetric mean circumference of the Earth.
+	EarthMeanCircumference = 2 * math.Pi * EarthMeanRadius
+
+	// earthEquatorialRadius is the equatorial radius of the Earth.
+	earthEquatorialRadius = 6_378_137 * Meter
+	// earthEquatorialCircumference is the equatorial circumference of the Earth.
+	earthEquatorialCircumference = 2 * math.Pi * earthEquatorialRadius
+
+	// earthPolarRadius is the polar radius of the Earth.
+	earthPolarRadius = 6_356_752 * Meter
+	// earthPolarCircumference is the polar circumference of the Earth.
+	earthPolarCircumference = 2 * math.Pi * earthPolarRadius
+)

types/geo/units_test.go

@@ -0,0 +1,395 @@
+// Copyright (c) Tailscale Inc & AUTHORS
+// SPDX-License-Identifier: BSD-3-Clause
+
+package geo_test
+
+import (
+	"math"
+	"strings"
+	"testing"
+
+	"tailscale.com/types/geo"
+)
+
+func TestDegrees(t *testing.T) {
+	for _, tt := range []struct {
+		name      string
+		degs      geo.Degrees
+		wantStr   string
+		wantText  string
+		wantPad   string
+		wantRads  geo.Radians
+		wantTurns geo.Turns
+	}{
+		{
+			name:      "zero",
+			degs:      0.0 * geo.Degree,
+			wantStr:   "+0°",
+			wantText:  "+0",
+			wantPad:   "+000",
+			wantRads:  0.0 * geo.Radian,
+			wantTurns: 0 * geo.Turn,
+		},
+		{
+			name:      "quarter-turn",
+			degs:      90.0 * geo.Degree,
+			wantStr:   "+90°",
+			wantText:  "+90",
+			wantPad:   "+090",
+			wantRads:  0.5 * math.Pi * geo.Radian,
+			wantTurns: 0.25 * geo.Turn,
+		},
+		{
+			name:      "half-turn",
+			degs:      180.0 * geo.Degree,
+			wantStr:   "+180°",
+			wantText:  "+180",
+			wantPad:   "+180",
+			wantRads:  1.0 * math.Pi * geo.Radian,
+			wantTurns: 0.5 * geo.Turn,
+		},
+		{
+			name:      "full-turn",
+			degs:      360.0 * geo.Degree,
+			wantStr:   "+360°",
+			wantText:  "+360",
+			wantPad:   "+360",
+			wantRads:  2.0 * math.Pi * geo.Radian,
+			wantTurns: 1.0 * geo.Turn,
+		},
+		{
+			name:      "negative-zero",
+			degs:      geo.MustParseDegrees("-0.0"),
+			wantStr:   "-0°",
+			wantText:  "-0",
+			wantPad:   "-000",
+			wantRads:  0 * geo.Radian * -1,
+			wantTurns: 0 * geo.Turn * -1,
+		},
+		{
+			name:      "small-degree",
+			degs:      -1.2003 * geo.Degree,
+			wantStr:   "-1.2003°",
+			wantText:  "-1.2003",
+			wantPad:   "-001.2003",
+			wantRads:  -0.020949187011687936 * geo.Radian,
+			wantTurns: -0.0033341666666666663 * geo.Turn,
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := tt.degs.String(); got != tt.wantStr {
+				t.Errorf("String got %q, want %q", got, tt.wantStr)
+			}
+
+			d, err := geo.ParseDegrees(tt.wantStr)
+			if err != nil {
+				t.Fatalf("ParseDegrees err %q, want nil", err.Error())
+			}
+			if d != tt.degs {
+				t.Errorf("ParseDegrees got %q, want %q", d, tt.degs)
+			}
+
+			b, err := tt.degs.AppendText(nil)
+			if err != nil {
+				t.Fatalf("AppendText err %q, want nil", err.Error())
+			}
+			if string(b) != tt.wantText {
+				t.Errorf("AppendText got %q, want %q", b, tt.wantText)
+			}
+
+			b = tt.degs.AppendZeroPaddedText(nil, 3)
+			if string(b) != tt.wantPad {
+				t.Errorf("AppendZeroPaddedText got %q, want %q", b, tt.wantPad)
+			}
+
+			r := tt.degs.Radians()
+			if r != tt.wantRads {
+				t.Errorf("Radian got %v, want %v", r, tt.wantRads)
+			}
+			if d := r.Degrees(); d != tt.degs { // Roundtrip
+				t.Errorf("Degrees got %v, want %v", d, tt.degs)
+			}
+
+			o := tt.degs.Turns()
+			if o != tt.wantTurns {
+				t.Errorf("Turns got %v, want %v", o, tt.wantTurns)
+			}
+		})
+	}
+}
+
+func TestRadians(t *testing.T) {
+	for _, tt := range []struct {
+		name      string
+		rads      geo.Radians
+		wantStr   string
+		wantText  string
+		wantDegs  geo.Degrees
+		wantTurns geo.Turns
+	}{
+		{
+			name:      "zero",
+			rads:      0.0 * geo.Radian,
+			wantStr:   "0 rad",
+			wantDegs:  0.0 * geo.Degree,
+			wantTurns: 0 * geo.Turn,
+		},
+		{
+			name:      "quarter-turn",
+			rads:      0.5 * math.Pi * geo.Radian,
+			wantStr:   "1.5707963267948966 rad",
+			wantDegs:  90.0 * geo.Degree,
+			wantTurns: 0.25 * geo.Turn,
+		},
+		{
+			name:      "half-turn",
+			rads:      1.0 * math.Pi * geo.Radian,
+			wantStr:   "3.141592653589793 rad",
+			wantDegs:  180.0 * geo.Degree,
+			wantTurns: 0.5 * geo.Turn,
+		},
+		{
+			name:      "full-turn",
+			rads:      2.0 * math.Pi * geo.Radian,
+			wantStr:   "6.283185307179586 rad",
+			wantDegs:  360.0 * geo.Degree,
+			wantTurns: 1.0 * geo.Turn,
+		},
+		{
+			name:      "negative-zero",
+			rads:      geo.MustParseRadians("-0"),
+			wantStr:   "-0 rad",
+			wantDegs:  0 * geo.Degree * -1,
+			wantTurns: 0 * geo.Turn * -1,
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := tt.rads.String(); got != tt.wantStr {
+				t.Errorf("String got %q, want %q", got, tt.wantStr)
+			}
+
+			r, err := geo.ParseRadians(tt.wantStr)
+			if err != nil {
+				t.Fatalf("ParseDegrees err %q, want nil", err.Error())
+			}
+			if r != tt.rads {
+				t.Errorf("ParseDegrees got %q, want %q", r, tt.rads)
+			}
+
+			d := tt.rads.Degrees()
+			if d != tt.wantDegs {
+				t.Errorf("Degrees got %v, want %v", d, tt.wantDegs)
+			}
+			if r := d.Radians(); r != tt.rads { // Roundtrip
+				t.Errorf("Radians got %v, want %v", r, tt.rads)
+			}
+
+			o := tt.rads.Turns()
+			if o != tt.wantTurns {
+				t.Errorf("Turns got %v, want %v", o, tt.wantTurns)
+			}
+		})
+	}
+}
+
+func TestTurns(t *testing.T) {
+	for _, tt := range []struct {
+		name     string
+		turns    geo.Turns
+		wantStr  string
+		wantText string
+		wantDegs geo.Degrees
+		wantRads geo.Radians
+	}{
+		{
+			name:     "zero",
+			turns:    0.0,
+			wantStr:  "0",
+			wantDegs: 0.0 * geo.Degree,
+			wantRads: 0 * geo.Radian,
+		},
+		{
+			name:     "quarter-turn",
+			turns:    0.25,
+			wantStr:  "0.25",
+			wantDegs: 90.0 * geo.Degree,
+			wantRads: 0.5 * math.Pi * geo.Radian,
+		},
+		{
+			name:     "half-turn",
+			turns:    0.5,
+			wantStr:  "0.5",
+			wantDegs: 180.0 * geo.Degree,
+			wantRads: 1.0 * math.Pi * geo.Radian,
+		},
+		{
+			name:     "full-turn",
+			turns:    1.0,
+			wantStr:  "1",
+			wantDegs: 360.0 * geo.Degree,
+			wantRads: 2.0 * math.Pi * geo.Radian,
+		},
+		{
+			name:     "negative-zero",
+			turns:    geo.Turns(math.Copysign(0, -1)),
+			wantStr:  "-0",
+			wantDegs: 0 * geo.Degree * -1,
+			wantRads: 0 * geo.Radian * -1,
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := tt.turns.String(); got != tt.wantStr {
+				t.Errorf("String got %q, want %q", got, tt.wantStr)
+			}
+
+			d := tt.turns.Degrees()
+			if d != tt.wantDegs {
+				t.Errorf("Degrees got %v, want %v", d, tt.wantDegs)
+			}
+			if o := d.Turns(); o != tt.turns { // Roundtrip
+				t.Errorf("Turns got %v, want %v", o, tt.turns)
+			}
+
+			r := tt.turns.Radians()
+			if r != tt.wantRads {
+				t.Errorf("Turns got %v, want %v", r, tt.wantRads)
+			}
+		})
+	}
+}
+
+func TestDistance(t *testing.T) {
+	for _, tt := range []struct {
+		name    string
+		dist    geo.Distance
+		wantStr string
+	}{
+		{
+			name:    "zero",
+			dist:    0.0 * geo.Meter,
+			wantStr: "0m",
+		},
+		{
+			name:    "random",
+			dist:    4 * geo.Meter,
+			wantStr: "4m",
+		},
+		{
+			name:    "light-second",
+			dist:    299_792_458 * geo.Meter,
+			wantStr: "299792458m",
+		},
+		{
+			name:    "planck-length",
+			dist:    1.61625518e-35 * geo.Meter,
+			wantStr: "0.0000000000000000000000000000000000161625518m",
+		},
+		{
+			name:    "negative-zero",
+			dist:    geo.Distance(math.Copysign(0, -1)),
+			wantStr: "-0m",
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			if got := tt.dist.String(); got != tt.wantStr {
+				t.Errorf("String got %q, want %q", got, tt.wantStr)
+			}
+
+			r, err := geo.ParseDistance(tt.wantStr)
+			if err != nil {
+				t.Fatalf("ParseDegrees err %q, want nil", err.Error())
+			}
+			if r != tt.dist {
+				t.Errorf("ParseDegrees got %q, want %q", r, tt.dist)
+			}
+		})
+	}
+}
+
+func TestDistanceOnEarth(t *testing.T) {
+	for _, tt := range []struct {
+		name    string
+		here    geo.Point
+		there   geo.Point
+		want    geo.Distance
+		wantErr string
+	}{
+		{
+			name:    "no-points",
+			here:    geo.Point{},
+			there:   geo.Point{},
+			wantErr: "not a valid point",
+		},
+		{
+			name:    "not-here",
+			here:    geo.Point{},
+			there:   geo.MakePoint(0, 0),
+			wantErr: "not a valid point",
+		},
+		{
+			name:    "not-there",
+			here:    geo.MakePoint(0, 0),
+			there:   geo.Point{},
+			wantErr: "not a valid point",
+		},
+		{
+			name:  "null-island",
+			here:  geo.MakePoint(0, 0),
+			there: geo.MakePoint(0, 0),
+			want:  0 * geo.Meter,
+		},
+		{
+			name:  "equator-to-south-pole",
+			here:  geo.MakePoint(0, 0),
+			there: geo.MakePoint(-90, 0),
+			want:  geo.EarthMeanCircumference / 4,
+		},
+		{
+			name:  "north-pole-to-south-pole",
+			here:  geo.MakePoint(+90, 0),
+			there: geo.MakePoint(-90, 0),
+			want:  geo.EarthMeanCircumference / 2,
+		},
+		{
+			name:  "meridian-to-antimeridian",
+			here:  geo.MakePoint(0, 0),
+			there: geo.MakePoint(0, -180),
+			want:  geo.EarthMeanCircumference / 2,
+		},
+		{
+			name:  "positive-to-negative-antimeridian",
+			here:  geo.MakePoint(0, 180),
+			there: geo.MakePoint(0, -180),
+			want:  0 * geo.Meter,
+		},
+		{
+			name:  "toronto-to-montreal",
+			here:  geo.MakePoint(+43.70011, -79.41630),
+			there: geo.MakePoint(+45.50884, -73.58781),
+			want:  503_200 * geo.Meter,
+		},
+		{
+			name:  "montreal-to-san-francisco",
+			here:  geo.MakePoint(+45.50884, -73.58781),
+			there: geo.MakePoint(+37.77493, -122.41942),
+			want:  4_082_600 * geo.Meter,
+		},
+	} {
+		t.Run(tt.name, func(t *testing.T) {
+			got, err := tt.here.DistanceTo(tt.there)
+			if tt.wantErr == "" && err != nil {
+				t.Fatalf("err %q, want nil", err)
+			}
+			if tt.wantErr != "" && !strings.Contains(err.Error(), tt.wantErr) {
+				t.Fatalf("err %q, want %q", err, tt.wantErr)
+			}
+
+			approx := func(x, y geo.Distance) bool {
+				return math.Abs(float64(x)-float64(y)) <= 10
+			}
+			if !approx(got, tt.want) {
+				t.Fatalf("got %v, want %v", got, tt.want)
+			}
+		})
+	}
+}