Fix bug in mercator y calculation

geo.go

@@ -21,7 +21,7 @@ func semicirclesToRadians(s int32) float64 {
 
 func mercatorMeters(lat, lon float64) (float64, float64) {
 	x := 6_378_137 * lon
-	y := 6_378_137 * math.Log(math.Tan(lat+(math.Pi/4))) / (2 * math.Pi)
+	y := 6_378_137 * math.Log(math.Tan((2*lat+math.Pi)/4))
 	return x, y
 }
 

geo_test.go

@@ -0,0 +1,29 @@
+package main
+
+import (
+	"math"
+	"testing"
+)
+
+func TestMercatorMeters(t *testing.T) {
+	testCases := []struct {
+		lat, lon float64
+	}{
+		{0, 0},
+		{0, -180},
+		{0, 180},
+		{45, 0},
+		{-45, 0},
+		{80, 0},
+		{-80, 0},
+	}
+	for i, testCase := range testCases {
+		x, y := mercatorMeters(degreesToRadians(testCase.lat), degreesToRadians(testCase.lon))
+		if math.IsNaN(x) {
+			t.Fatal("test case", i, "failed: expected x number")
+		}
+		if math.IsNaN(y) {
+			t.Fatal("test case", i, "failed: expected y number")
+		}
+	}
+}