diff --git a/src/Collision/Fixed/SpatialHash2D.cs b/src/Collision/Fixed/SpatialHash2D.cs
index 2a3a33a..7b7ceda 100644
--- a/src/Collision/Fixed/SpatialHash2D.cs
+++ b/src/Collision/Fixed/SpatialHash2D.cs
@@ -28,7 +28,7 @@ namespace MoonWorks.Collision.Fixed
 
 		private (int, int) Hash(Vector2 position)
 		{
-			return ((int) Fix64.Floor(position.X / cellSize), (int) Fix64.Floor(position.Y / cellSize));
+			return ((int) (position.X / cellSize), (int) (position.Y / cellSize));
 		}
 
 		/// <summary>
diff --git a/src/Math/Fixed/Fix64.cs b/src/Math/Fixed/Fix64.cs
index d7c6820..c21d9ad 100644
--- a/src/Math/Fixed/Fix64.cs
+++ b/src/Math/Fixed/Fix64.cs
@@ -30,6 +30,9 @@ namespace MoonWorks.Math.Fixed
 		const int LUT_SIZE = (int)(PI_OVER_2 >> 15);
 		static readonly Fix64 LutInterval = (Fix64)(LUT_SIZE - 1) / PiOver2;
 
+		public bool IsFractional => (RawValue & 0x00000000FFFFFFFF) != 0;
+		public bool IsIntegral => (RawValue & 0x00000000FFFFFFFF) == 0;
+
 		private Fix64(long value)
 		{
 			RawValue = value;
@@ -95,8 +98,7 @@ namespace MoonWorks.Math.Fixed
         /// </summary>
 		public static Fix64 Ceiling(Fix64 value)
 		{
-			var hasFractionalPart = (value.RawValue & 0x00000000FFFFFFFF) != 0;
-			return hasFractionalPart ? Floor(value) + One : value;
+			return value.IsFractional ? Floor(value) + One : value;
 		}
 
         /// <summary>
@@ -697,12 +699,12 @@ namespace MoonWorks.Math.Fixed
 
 		public static bool operator >(Fix64 x, int y)
 		{
-			return ((int) x) > y;
+			return x > ((Fix64) y);
 		}
 
 		public static bool operator <(Fix64 x, int y)
 		{
-			return ((int) x) < y;
+			return x < ((Fix64) y);
 		}
 
 		public static bool operator >=(Fix64 x, Fix64 y)
@@ -717,12 +719,12 @@ namespace MoonWorks.Math.Fixed
 
 		public static bool operator >=(Fix64 x, int y)
 		{
-			return ((int) x) >= y;
+			return x >= ((Fix64) y);
 		}
 
 		public static bool operator <=(Fix64 x, int y)
 		{
-			return ((int) x) <= y;
+			return x <= ((Fix64) y);
 		}
 
 		// Casting
diff --git a/src/Math/Fixed/Transform2D.cs b/src/Math/Fixed/Transform2D.cs
index bbb9cfc..9a61c35 100644
--- a/src/Math/Fixed/Transform2D.cs
+++ b/src/Math/Fixed/Transform2D.cs
@@ -6,7 +6,21 @@ namespace MoonWorks.Math.Fixed
 		public Fix64 Rotation { get; }
 		public Vector2 Scale { get; }
 
-		public Matrix3x2 TransformMatrix { get; }
+		private bool transformMatrixCalculated = false;
+		private Matrix3x2 transformMatrix = Matrix3x2.Identity;
+		public Matrix3x2 TransformMatrix
+		{
+			get
+			{
+				if (!transformMatrixCalculated)
+				{
+					transformMatrix = CreateTransformMatrix(Position, Rotation, Scale);
+					transformMatrixCalculated = true;
+				}
+
+				return transformMatrix;
+			}
+		}
 
 		public bool IsAxisAligned => Rotation % Fix64.PiOver2 == Fix64.Zero;
 		public bool IsUniformScale => Scale.X == Scale.Y;
@@ -18,7 +32,6 @@ namespace MoonWorks.Math.Fixed
 			Position = Vector2.Zero;
 			Rotation = Fix64.Zero;
 			Scale = Vector2.One;
-			TransformMatrix = CreateTransformMatrix(Position, Rotation, Scale);
 		}
 
 		public Transform2D(Vector2 position)
@@ -26,7 +39,6 @@ namespace MoonWorks.Math.Fixed
 			Position = position;
 			Rotation = Fix64.Zero;
 			Scale = Vector2.One;
-			TransformMatrix = CreateTransformMatrix(Position, Rotation, Scale);
 		}
 
 		public Transform2D(Vector2 position, Fix64 rotation)
@@ -34,7 +46,6 @@ namespace MoonWorks.Math.Fixed
 			Position = position;
 			Rotation = rotation;
 			Scale = Vector2.One;
-			TransformMatrix = CreateTransformMatrix(Position, Rotation, Scale);
 		}
 
 		public Transform2D(Vector2 position, Fix64 rotation, Vector2 scale)
@@ -42,7 +53,6 @@ namespace MoonWorks.Math.Fixed
 			Position = position;
 			Rotation = rotation;
 			Scale = scale;
-			TransformMatrix = CreateTransformMatrix(Position, Rotation, Scale);
 		}
 
 		public Transform2D Compose(Transform2D other)
diff --git a/src/Math/Fixed/Vector2.cs b/src/Math/Fixed/Vector2.cs
index ced8b76..c261554 100644
--- a/src/Math/Fixed/Vector2.cs
+++ b/src/Math/Fixed/Vector2.cs
@@ -218,6 +218,14 @@ namespace MoonWorks.Math.Fixed
 			return Fix64.Atan2(Y, X);
 		}
 
+		/// <summary>
+		/// Returns this Vector2 with the fractional components cut off.
+		/// </summary>
+		public Vector2 Truncated()
+		{
+			return new Vector2((int) X, (int) Y);
+		}
+
 		/// <summary>
 		/// Returns a <see cref="String"/> representation of this <see cref="Vector2"/> in the format:
 		/// {X:[<see cref="X"/>] Y:[<see cref="Y"/>]}