chore: Camera3D now uses left handed matrices

Engine.Integration/Engine.Integration.MonoGame/Behaviours/MonoGameCamera3D.cs

@@ -154,17 +154,42 @@ public class MonoGameCamera3D : Behaviour, ICamera3D, IFirstFrameUpdate, ILastFr
         if (!isRecalculationNeeded)
             return;
 
-        Vector3 cameraPosition = Position.ToVector3();
-        View = Matrix.CreateLookAt(
-            cameraPosition,
-            Transform.Forward.ToVector3() + cameraPosition,
-            Transform.Up.ToVector3()
-        );
-        Projection = Matrix.CreatePerspectiveFieldOfView(_fieldOfView, Viewport.AspectRatio, 0.1f, 100f);
-
+        CalculateView();
+        CalculateProjection();
         isRecalculationNeeded = false;
     }
 
+    private void CalculateView()
+    {
+        Vector3 forward = Vector3.Normalize(Transform.Forward.ToVector3());
+        Vector3 up = Vector3.Normalize(Transform.Up.ToVector3());
+        Vector3 right = Vector3.Normalize(Transform.Right.ToVector3());
+        Vector3 position = Position.ToVector3();
+
+        View = new Matrix(
+            right.X, up.X, forward.X, 0,
+            right.Y, up.Y, forward.Y, 0,
+            right.Z, up.Z, forward.Z, 0,
+            -Vector3.Dot(right, position),
+            -Vector3.Dot(up, position),
+            -Vector3.Dot(forward, position),
+            1
+        );
+    }
+
+    private void CalculateProjection()
+    {
+        float yScale = 1f / (float)Math.Tan(_fieldOfView / 2f);
+        float xScale = yScale / Viewport.AspectRatio;
+
+        Projection = new Matrix(
+            xScale, 0, 0, 0,
+            0, yScale, 0, 0,
+            0, 0, _farPlane / (_farPlane - _nearPlane), 1,
+            0, 0, -_nearPlane * _farPlane / (_farPlane - _nearPlane), 0
+        );
+    }
+
     public readonly record struct ViewChangedArguments(Matrix PreviousView);
     public readonly record struct ProjectionChangedArguments(Matrix PreviousProjection);
     public readonly record struct ViewportChangedArguments(Viewport PreviousViewport);