Merge pull request #76 from syncromatics/master

Add functions to calculate points based on distance and bearing

Author: paulmach

geo/distance.go

@@ -69,3 +69,50 @@ func Midpoint(p, p2 orb.Point) orb.Point {
 
 	return r
 }
+
+// PointAtBearingAndDistance returns the point at the given bearing and distance in meters from the point
+func PointAtBearingAndDistance(p orb.Point, bearing, distance float64) orb.Point {
+	aLat := deg2rad(p[1])
+	aLon := deg2rad(p[0])
+
+	bearingRadians := deg2rad(bearing)
+
+	distanceRatio := distance / orb.EarthRadius
+	bLat := math.Asin(math.Sin(aLat)*math.Cos(distanceRatio) + math.Cos(aLat)*math.Sin(distanceRatio)*math.Cos(bearingRadians))
+	bLon := aLon + math.Atan2(math.Sin(bearingRadians)*math.Sin(distanceRatio)*math.Cos(aLat), math.Cos(distanceRatio)-math.Sin(aLat)*math.Sin(bLat))
+
+	r := orb.Point{
+		rad2deg(bLon),
+		rad2deg(bLat),
+	}
+
+	return r
+}
+
+func PointAtDistanceAlongLine(ls orb.LineString, distance float64) (orb.Point, float64) {
+	if len(ls) == 0 {
+		panic("empty LineString")
+	}
+
+	if distance < 0 || len(ls) == 1 {
+		return ls[0], 0.0
+	}
+
+	travelled := 0.0
+	i := 1
+	var from, to orb.Point
+	for ; i < len(ls); i++ {
+		from = ls[i-1]
+		to = ls[i]
+		actualSegmentDistance := DistanceHaversine(from, to)
+		expectedSegmentDistance := distance - travelled
+		if expectedSegmentDistance < actualSegmentDistance {
+			bearing := Bearing(from, to)
+			return PointAtBearingAndDistance(from, bearing, expectedSegmentDistance), bearing
+		}
+		travelled += actualSegmentDistance
+	}
+
+	bearing := Bearing(from, to)
+	return to, bearing
+}

geo/distance_test.go

@@ -89,3 +89,112 @@ func TestMidpoint(t *testing.T) {
 		t.Errorf("expected %v, got %v", answer, m)
 	}
 }
+
+func TestPointAtBearingAndDistance(t *testing.T) {
+	expected := orb.Point{-0.841153, 52.68179432}
+	bearing := 127.373
+	distance := 85194.89
+	actual := PointAtBearingAndDistance(orb.Point{-1.8444, 53.1506}, bearing, distance)
+
+	if d := DistanceHaversine(actual, expected); d > 1 {
+		t.Errorf("expected %v, got %v (%vm away)", expected, actual, d)
+	}
+}
+func TestMidpointAgainstPointAtBearingAndDistance(t *testing.T) {
+	a := orb.Point{-1.8444, 53.1506}
+	b := orb.Point{0.1406, 52.2047}
+	bearing := Bearing(a, b)
+	distance := DistanceHaversine(a, b)
+	acceptableTolerance := 1e-06 // unit is meters
+
+	p1 := PointAtBearingAndDistance(a, bearing, distance/2)
+	p2 := Midpoint(a, b)
+
+	if d := DistanceHaversine(p1, p2); d > acceptableTolerance {
+		t.Errorf("expected %v to be within %vm of %v", p1, acceptableTolerance, p2)
+	}
+}
+
+func TestPointAtDistanceAlongLineWithEmptyLineString(t *testing.T) {
+	defer func() {
+		if r := recover(); r == nil {
+			t.Errorf("PointAtDistanceAlongLine did not panic")
+		}
+	}()
+
+	line := orb.LineString{}
+	PointAtDistanceAlongLine(line, 90000)
+}
+
+func TestPointAtDistanceAlongLineWithSinglePoint(t *testing.T) {
+	expectedPoint := orb.Point{-1.8444, 53.1506}
+	line := orb.LineString{
+		expectedPoint,
+	}
+	actualPoint, actualBearing := PointAtDistanceAlongLine(line, 90000)
+
+	if actualPoint != expectedPoint {
+		t.Errorf("expected %v but got %v", expectedPoint, actualPoint)
+	}
+	if actualBearing != 0.0 {
+		t.Errorf("expected %v but got %v", actualBearing, 0.0)
+	}
+}
+
+func TestPointAtDistanceAlongLineWithMinimalPoints(t *testing.T) {
+	expected := orb.Point{-0.841153, 52.68179432}
+	acceptableDistanceTolerance := 1.0 // unit is meters
+	line := orb.LineString{
+		orb.Point{-1.8444, 53.1506},
+		orb.Point{0.1406, 52.2047},
+	}
+	acceptableBearingTolerance := 0.01 // unit is degrees
+	expectedBearing := Bearing(line[0], line[1])
+	actual, actualBearing := PointAtDistanceAlongLine(line, 85194.89)
+
+	if d := DistanceHaversine(expected, actual); d > acceptableDistanceTolerance {
+		t.Errorf("expected %v to be within %vm of %v (%vm away)", actual, acceptableDistanceTolerance, expected, d)
+	}
+	if b := math.Abs(actualBearing - expectedBearing); b > acceptableBearingTolerance {
+		t.Errorf("expected bearing %v to be within %v degrees of %v", actualBearing, acceptableBearingTolerance, expectedBearing)
+	}
+}
+
+func TestPointAtDistanceAlongLineWithMultiplePoints(t *testing.T) {
+	expected := orb.Point{-0.78526, 52.65506}
+	acceptableTolerance := 1.0 // unit is meters
+	line := orb.LineString{
+		orb.Point{-1.8444, 53.1506},
+		orb.Point{-0.8411, 52.6817},
+		orb.Point{0.1406, 52.2047},
+	}
+	acceptableBearingTolerance := 0.01 // unit is degrees
+	expectedBearing := Bearing(line[1], line[2])
+	actualPoint, actualBearing := PointAtDistanceAlongLine(line, 90000)
+
+	if d := DistanceHaversine(expected, actualPoint); d > acceptableTolerance {
+		t.Errorf("expected %v to be within %vm of %v (%vm away)", expected, acceptableTolerance, actualPoint, d)
+	}
+	if b := math.Abs(actualBearing - expectedBearing); b > acceptableBearingTolerance {
+		t.Errorf("expected bearing %v to be within %v degrees of %v", actualBearing, acceptableBearingTolerance, expectedBearing)
+	}
+}
+
+func TestPointAtDistanceAlongLinePastEndOfLine(t *testing.T) {
+	expected := orb.Point{0.1406, 52.2047}
+	line := orb.LineString{
+		orb.Point{-1.8444, 53.1506},
+		orb.Point{-0.8411, 52.6817},
+		expected,
+	}
+	acceptableBearingTolerance := 0.01 // unit is degrees
+	expectedBearing := Bearing(line[1], line[2])
+	actualPoint, actualBearing := PointAtDistanceAlongLine(line, 200000)
+
+	if actualPoint != expected {
+		t.Errorf("expected %v but got %v", expected, actualPoint)
+	}
+	if b := math.Abs(actualBearing - expectedBearing); b > acceptableBearingTolerance {
+		t.Errorf("expected bearing %v to be within %v degrees of %v", actualBearing, acceptableBearingTolerance, expectedBearing)
+	}
+}