diff --git a/MapControl/Shared/TransverseMercatorProjection.cs b/MapControl/Shared/TransverseMercatorProjection.cs
index 6b03f70e..a4e1eeca 100644
--- a/MapControl/Shared/TransverseMercatorProjection.cs
+++ b/MapControl/Shared/TransverseMercatorProjection.cs
@@ -14,9 +14,15 @@ namespace MapControl
     /// </summary>
     public class TransverseMercatorProjection : MapProjection
     {
-        private readonly double[] alpha = new double[3]; // α_j
-        private readonly double[] beta = new double[3];  // β_j
-        private readonly double[] delta = new double[3]; // δ_j
+        private double a1; // α1
+        private double a2; // α2
+        private double a3; // α3
+        private double b1; // β1
+        private double b2; // β2
+        private double b3; // β3
+        private double d1; // δ1
+        private double d2; // δ2
+        private double d3; // δ3
         private double f1; // A / a
         private double f2; // 2 * sqrt(n) / (1+n)
 
@@ -26,26 +32,20 @@ namespace MapControl
             set
             {
                 field = value;
-                // n, n^2, n^3
                 var n = field / (2d - field);
-                var n2 = n * n;
-                var n3 = n * n2;
-                // A / a
-                f1 = (1d + n2 / 4d + n2 * n2 / 64d) / (1d + n);
-                // 2 * sqrt(n) / (1+n)
+                var nn = n * n;
+                var nnn = n * nn;
+                a1 = n / 2d - nn * 2d / 3d + nnn * 5d / 16d;
+                a2 = nn * 13d / 48d - nnn * 3d / 5d;
+                a3 = nnn * 61d / 240d;
+                b1 = n / 2d - nn * 2d / 3d + nnn * 37d / 96d;
+                b2 = nn / 48d + nnn / 15d;
+                b3 = nnn * 17d / 480d;
+                d1 = n * 2d - nn * 2d / 3d - nnn * 2d;
+                d2 = nn * 7d / 3d - nnn * 8d / 5d;
+                d3 = nnn * 56d / 15d;
+                f1 = (1d + nn / 4d + nn * nn / 64d) / (1d + n);
                 f2 = 2d * Math.Sqrt(n) / (1d + n);
-                // α_j
-                alpha[0] = n / 2d - n2 * 2d / 3d + n3 * 5d / 16d;
-                alpha[1] = n2 * 13d / 48d - n3 * 3d / 5d;
-                alpha[2] = n3 * 61d / 240d;
-                // β_j
-                beta[0] = n / 2d - n2 * 2d / 3d + n3 * 37d / 96d;
-                beta[1] = n2 / 48d + n3 / 15d;
-                beta[2] = n3 * 17d / 480d;
-                // δ_j
-                delta[0] = n * 2d - n2 * 2d / 3d - n3 * 2d;
-                delta[1] = n2 * 7d / 3d - n3 * 8d / 5d;
-                delta[2] = n3 * 56d / 15d;
             }
         }
 
@@ -63,7 +63,7 @@ namespace MapControl
 
         public override Point RelativeScale(double latitude, double longitude)
         {
-            return new Point(ScaleFactor, ScaleFactor);
+            return new Point(ScaleFactor, ScaleFactor); // sufficiently precise
         }
 
         public override Point? LocationToMap(double latitude, double longitude)
@@ -73,7 +73,7 @@ namespace MapControl
 #else
             static double Atanh(double x) => Math.Atanh(x);
 #endif
-            // k_0 * A
+            // k0 * A
             var k0A = ScaleFactor * EquatorialRadius * f1;
             // φ
             var phi = latitude * Math.PI / 180d;
@@ -88,14 +88,14 @@ namespace MapControl
             var eta_ = Atanh(Math.Sin(lambda) / Math.Sqrt(1d + t * t));
             // ξ
             var xi = xi_
-                + alpha[0] * Math.Sin(2d * xi_) * Math.Cosh(2d * eta_)
-                + alpha[1] * Math.Sin(4d * xi_) * Math.Cosh(4d * eta_)
-                + alpha[2] * Math.Sin(6d * xi_) * Math.Cosh(6d * eta_);
+                + a1 * Math.Sin(2d * xi_) * Math.Cosh(2d * eta_)
+                + a2 * Math.Sin(4d * xi_) * Math.Cosh(4d * eta_)
+                + a3 * Math.Sin(6d * xi_) * Math.Cosh(6d * eta_);
             // η
             var eta = eta_
-                + alpha[0] * Math.Cos(2d * xi_) * Math.Sinh(2d * eta_)
-                + alpha[1] * Math.Cos(4d * xi_) * Math.Sinh(4d * eta_)
-                + alpha[2] * Math.Cos(6d * xi_) * Math.Sinh(6d * eta_);
+                + a1 * Math.Cos(2d * xi_) * Math.Sinh(2d * eta_)
+                + a2 * Math.Cos(4d * xi_) * Math.Sinh(4d * eta_)
+                + a3 * Math.Cos(6d * xi_) * Math.Sinh(6d * eta_);
 
             return new Point(
                 k0A * eta + FalseEasting,
@@ -104,7 +104,7 @@ namespace MapControl
 
         public override Location MapToLocation(double x, double y)
         {
-            // k_0 * A
+            // k0 * A
             var k0A = ScaleFactor * EquatorialRadius * f1;
             // ξ
             var xi = (y - FalseNorthing) / k0A;
@@ -112,21 +112,21 @@ namespace MapControl
             var eta = (x - FalseEasting) / k0A;
             // ξ'
             var xi_ = xi
-                - beta[0] * Math.Sin(2d * xi) * Math.Cosh(2d * eta)
-                - beta[1] * Math.Sin(4d * xi) * Math.Cosh(4d * eta)
-                - beta[2] * Math.Sin(6d * xi) * Math.Cosh(6d * eta);
+                - b1 * Math.Sin(2d * xi) * Math.Cosh(2d * eta)
+                - b2 * Math.Sin(4d * xi) * Math.Cosh(4d * eta)
+                - b3 * Math.Sin(6d * xi) * Math.Cosh(6d * eta);
             // η'
             var eta_ = eta
-                - beta[0] * Math.Cos(2d * xi) * Math.Sinh(2d * eta)
-                - beta[1] * Math.Cos(4d * xi) * Math.Sinh(4d * eta)
-                - beta[2] * Math.Cos(6d * xi) * Math.Sinh(6d * eta);
+                - b1 * Math.Cos(2d * xi) * Math.Sinh(2d * eta)
+                - b2 * Math.Cos(4d * xi) * Math.Sinh(4d * eta)
+                - b3 * Math.Cos(6d * xi) * Math.Sinh(6d * eta);
             // χ
             var chi = Math.Asin(Math.Sin(xi_) / Math.Cosh(eta_));
             // φ
             var phi = chi
-                + delta[0] * Math.Sin(2d * chi)
-                + delta[1] * Math.Sin(4d * chi)
-                + delta[2] * Math.Sin(6d * chi);
+                + d1 * Math.Sin(2d * chi)
+                + d2 * Math.Sin(4d * chi)
+                + d3 * Math.Sin(6d * chi);
             // λ - λ0
             var lambda = Math.Atan(Math.Sinh(eta_) / Math.Cos(xi_));