Improve precision for BoundingBox.Transform with Transform

Source/Engine/Core/Math/BoundingBox.cpp

@@ -129,30 +129,28 @@ void BoundingBox::Transform(const BoundingBox& box, const Matrix& matrix, Boundi
     const auto zb = backward * box.Maximum.Z;
 
     const auto translation = matrix.GetTranslation();
-    result = BoundingBox(
-        Vector3::Min(xa, xb) + Vector3::Min(ya, yb) + Vector3::Min(za, zb) + translation,
-        Vector3::Max(xa, xb) + Vector3::Max(ya, yb) + Vector3::Max(za, zb) + translation);
-
-    /*
-    // Get box corners
-    Vector3 corners[8];
-    box.GetCorners(corners);
-
-    // Transform them
-    for (int32 i = 0; i < 8; i++)
-    {
-        corners[i] = Vector3::Transform(corners[i], matrix);
-    }
-
-    // Construct box from the points
-    result = FromPoints(corners, 8);
-    */
+    const auto min = Vector3::Min(xa, xb) + Vector3::Min(ya, yb) + Vector3::Min(za, zb) + translation;
+    const auto max = Vector3::Max(xa, xb) + Vector3::Max(ya, yb) + Vector3::Max(za, zb) + translation;
+    result = BoundingBox(min, max);
 }
 
 void BoundingBox::Transform(const BoundingBox& box, const ::Transform& transform, BoundingBox& result)
 {
-    // TODO: optimize it and support large worlds without using Matrix
-    Matrix matrix;
-    transform.GetWorld(matrix);
-    Transform(box, matrix, result);
+    // Reference: http://dev.theomader.com/transform-bounding-boxes/
+
+    const auto right = transform.GetRight();
+    const auto xa = right * box.Minimum.X;
+    const auto xb = right * box.Maximum.X;
+
+    const auto up = transform.GetUp();
+    const auto ya = up * box.Minimum.Y;
+    const auto yb = up * box.Maximum.Y;
+
+    const auto backward = transform.GetBackward();
+    const auto za = backward * box.Minimum.Z;
+    const auto zb = backward * box.Maximum.Z;
+
+    const auto min = Vector3::Min(xa, xb) + Vector3::Min(ya, yb) + Vector3::Min(za, zb) + transform.Translation;
+    const auto max = Vector3::Max(xa, xb) + Vector3::Max(ya, yb) + Vector3::Max(za, zb) + transform.Translation;
+    result = BoundingBox(min, max);
 }

Source/Engine/Core/Math/BoundingBox.cs

@@ -454,24 +454,48 @@ namespace FlaxEngine
             var zb = backward * box.Maximum.Z;
 
             var translation = transform.TranslationVector;
-            result = new BoundingBox(
-                                     Vector3.Min(xa, xb) + Vector3.Min(ya, yb) + Vector3.Min(za, zb) + translation,
-                                     Vector3.Max(xa, xb) + Vector3.Max(ya, yb) + Vector3.Max(za, zb) + translation);
+            var min = Vector3.Min(xa, xb) + Vector3.Min(ya, yb) + Vector3.Min(za, zb) + translation;
+            var max = Vector3.Max(xa, xb) + Vector3.Max(ya, yb) + Vector3.Max(za, zb) + translation;
+            result = new BoundingBox(min, max);
+        }
 
-            /*
-            // Get box corners
-            var corners = new Vector3[8];
-            box.GetCorners(corners);
+        /// <summary>
+        /// Transforms bounding box using the given transformation matrix.
+        /// </summary>
+        /// <param name="box">The bounding box to transform.</param>
+        /// <param name="transform">The transformation matrix.</param>
+        /// <returns>The result of the transformation.</returns>
+        public static BoundingBox Transform(BoundingBox box, Transform transform)
+        {
+            Transform(ref box, ref transform, out BoundingBox result);
+            return result;
+        }
 
-            // Transform them
-            for (int i = 0; i < 8; i++)
-            {
-                Vector3.Transform(ref corners[i], ref transform, out corners[i]);
-            }
+        /// <summary>
+        /// Transforms bounding box using the given transformation.
+        /// </summary>
+        /// <param name="box">The bounding box to transform.</param>
+        /// <param name="transform">The transformation.</param>
+        /// <param name="result">The result of the transformation.</param>
+        public static void Transform(ref BoundingBox box, ref Transform transform, out BoundingBox result)
+        {
+            // Reference: http://dev.theomader.com/transform-bounding-boxes/
 
-            // Construct box from the points
-            FromPoints(corners, out result);
-            */
+            Double3 right = transform.Right;
+            var xa = right * box.Minimum.X;
+            var xb = right * box.Maximum.X;
+
+            Double3 up = transform.Up;
+            var ya = up * box.Minimum.Y;
+            var yb = up * box.Maximum.Y;
+
+            Double3 backward = transform.Backward;
+            var za = backward * box.Minimum.Z;
+            var zb = backward * box.Maximum.Z;
+
+            var min = Vector3.Min(xa, xb) + Vector3.Min(ya, yb) + Vector3.Min(za, zb) + transform.Translation;
+            var max = Vector3.Max(xa, xb) + Vector3.Max(ya, yb) + Vector3.Max(za, zb) + transform.Translation;
+            result = new BoundingBox(min, max);
         }
 
         /// <summary>