Use minimum enclosing circle as selection centre for scale and rotate

osu.Game.Benchmarks/BenchmarkGeometryUtils.cs

@@ -0,0 +1,29 @@
+// Copyright (c) ppy Pty Ltd <[email protected]>. Licensed under the MIT Licence.
+// See the LICENCE file in the repository root for full licence text.
+
+using BenchmarkDotNet.Attributes;
+using osu.Framework.Utils;
+using osu.Game.Utils;
+using osuTK;
+
+namespace osu.Game.Benchmarks
+{
+    public class BenchmarkGeometryUtils : BenchmarkTest
+    {
+        [Params(100, 1000, 2000, 4000, 8000, 10000)]
+        public int N;
+
+        private Vector2[] points = null!;
+
+        public override void SetUp()
+        {
+            points = new Vector2[N];
+
+            for (int i = 0; i < points.Length; ++i)
+                points[i] = new Vector2(RNG.Next(512), RNG.Next(384));
+        }
+
+        [Benchmark]
+        public void MinimumEnclosingCircle() => GeometryUtils.MinimumEnclosingCircle(points);
+    }
+}

osu.Game.Rulesets.Osu/Edit/OsuSelectionRotationHandler.cs

@@ -47,7 +47,6 @@ private void updateState()
 
         private OsuHitObject[]? objectsInRotation;
 
-        private Vector2? defaultOrigin;
         private Dictionary<OsuHitObject, Vector2>? originalPositions;
         private Dictionary<IHasPath, Vector2[]>? originalPathControlPointPositions;
 
@@ -61,7 +60,7 @@ public override void Begin()
             changeHandler?.BeginChange();
 
             objectsInRotation = selectedMovableObjects.ToArray();
-            defaultOrigin = GeometryUtils.GetSurroundingQuad(objectsInRotation).Centre;
+            DefaultOrigin = GeometryUtils.MinimumEnclosingCircle(objectsInRotation).Item1;
             originalPositions = objectsInRotation.ToDictionary(obj => obj, obj => obj.Position);
             originalPathControlPointPositions = objectsInRotation.OfType<IHasPath>().ToDictionary(
                 obj => obj,
@@ -73,9 +72,9 @@ public override void Update(float rotation, Vector2? origin = null)
             if (!OperationInProgress.Value)
                 throw new InvalidOperationException($"Cannot {nameof(Update)} a rotate operation without calling {nameof(Begin)} first!");
 
-            Debug.Assert(objectsInRotation != null && originalPositions != null && originalPathControlPointPositions != null && defaultOrigin != null);
+            Debug.Assert(objectsInRotation != null && originalPositions != null && originalPathControlPointPositions != null && DefaultOrigin != null);
 
-            Vector2 actualOrigin = origin ?? defaultOrigin.Value;
+            Vector2 actualOrigin = origin ?? DefaultOrigin.Value;
 
             foreach (var ho in objectsInRotation)
             {
@@ -103,7 +102,7 @@ public override void Commit()
             objectsInRotation = null;
             originalPositions = null;
             originalPathControlPointPositions = null;
-            defaultOrigin = null;
+            DefaultOrigin = null;
         }
 
         private IEnumerable<OsuHitObject> selectedMovableObjects => selectedItems.Cast<OsuHitObject>()

osu.Game.Rulesets.Osu/Edit/OsuSelectionScaleHandler.cs

@@ -84,10 +84,10 @@ public override void Begin()
             OriginalSurroundingQuad = objectsInScale.Count == 1 && objectsInScale.First().Key is Slider slider
                 ? GeometryUtils.GetSurroundingQuad(slider.Path.ControlPoints.Select(p => slider.Position + p.Position))
                 : GeometryUtils.GetSurroundingQuad(objectsInScale.Keys);
-            defaultOrigin = OriginalSurroundingQuad.Value.Centre;
             originalConvexHull = objectsInScale.Count == 1 && objectsInScale.First().Key is Slider slider2
                 ? GeometryUtils.GetConvexHull(slider2.Path.ControlPoints.Select(p => slider2.Position + p.Position))
                 : GeometryUtils.GetConvexHull(objectsInScale.Keys);
+            defaultOrigin = GeometryUtils.MinimumEnclosingCircle(originalConvexHull).Item1;
         }
 
         public override void Update(Vector2 scale, Vector2? origin = null, Axes adjustAxis = Axes.Both, float axisRotation = 0)

osu.Game.Tests/Utils/GeometryUtilsTest.cs

@@ -29,5 +29,23 @@ public void TestConvexHull(int[] values, int[] expected)
 
             Assert.That(hull, Is.EquivalentTo(expectedPoints));
         }
+
+        [TestCase(new int[] { }, 0, 0, 0)]
+        [TestCase(new[] { 0, 0 }, 0, 0, 0)]
+        [TestCase(new[] { 0, 0, 1, 1, 1, -1, 2, 0 }, 1, 0, 1)]
+        [TestCase(new[] { 0, 0, 1, 1, 1, -1, 2, 0, 1, 0 }, 1, 0, 1)]
+        [TestCase(new[] { 0, 0, 1, 1, 2, -1, 2, 0, 1, 0, 4, 10 }, 3, 4.5f, 5.5901699f)]
+        public void TestMinimumEnclosingCircle(int[] values, float x, float y, float r)
+        {
+            var points = new Vector2[values.Length / 2];
+            for (int i = 0; i < values.Length; i += 2)
+                points[i / 2] = new Vector2(values[i], values[i + 1]);
+
+            (var centre, float radius) = GeometryUtils.MinimumEnclosingCircle(points);
+
+            Assert.That(centre.X, Is.EqualTo(x).Within(0.0001));
+            Assert.That(centre.Y, Is.EqualTo(y).Within(0.0001));
+            Assert.That(radius, Is.EqualTo(r).Within(0.0001));
+        }
     }
 }

osu.Game.Tests/Visual/Editing/TestSceneComposeSelectBox.cs

@@ -84,6 +84,7 @@ public override void Begin()
 
                 targetContainer = getTargetContainer();
                 initialRotation = targetContainer!.Rotation;
+                DefaultOrigin = ToLocalSpace(targetContainer.ToScreenSpace(Vector2.Zero));
 
                 base.Begin();
             }

osu.Game/Overlays/SkinEditor/SkinSelectionRotationHandler.cs

@@ -46,7 +46,6 @@ private void updateState()
 
         private Drawable[]? objectsInRotation;
 
-        private Vector2? defaultOrigin;
         private Dictionary<Drawable, float>? originalRotations;
         private Dictionary<Drawable, Vector2>? originalPositions;
 
@@ -60,7 +59,7 @@ public override void Begin()
             objectsInRotation = selectedItems.Cast<Drawable>().ToArray();
             originalRotations = objectsInRotation.ToDictionary(d => d, d => d.Rotation);
             originalPositions = objectsInRotation.ToDictionary(d => d, d => d.ToScreenSpace(d.OriginPosition));
-            defaultOrigin = GeometryUtils.GetSurroundingQuad(objectsInRotation.SelectMany(d => d.ScreenSpaceDrawQuad.GetVertices().ToArray())).Centre;
+            DefaultOrigin = GeometryUtils.GetSurroundingQuad(objectsInRotation.SelectMany(d => d.ScreenSpaceDrawQuad.GetVertices().ToArray())).Centre;
 
             base.Begin();
         }
@@ -70,7 +69,7 @@ public override void Update(float rotation, Vector2? origin = null)
             if (objectsInRotation == null)
                 throw new InvalidOperationException($"Cannot {nameof(Update)} a rotate operation without calling {nameof(Begin)} first!");
 
-            Debug.Assert(originalRotations != null && originalPositions != null && defaultOrigin != null);
+            Debug.Assert(originalRotations != null && originalPositions != null && DefaultOrigin != null);
 
             if (objectsInRotation.Length == 1 && origin == null)
             {
@@ -79,7 +78,7 @@ public override void Update(float rotation, Vector2? origin = null)
                 return;
             }
 
-            var actualOrigin = origin ?? defaultOrigin.Value;
+            var actualOrigin = origin ?? DefaultOrigin.Value;
 
             foreach (var drawableItem in objectsInRotation)
             {
@@ -100,7 +99,7 @@ public override void Commit()
             objectsInRotation = null;
             originalPositions = null;
             originalRotations = null;
-            defaultOrigin = null;
+            DefaultOrigin = null;
 
             base.Commit();
         }

osu.Game/Overlays/SkinEditor/SkinSelectionScaleHandler.cs

@@ -67,7 +67,7 @@ public override void Begin()
 
             objectsInScale = selectedItems.Cast<Drawable>().ToDictionary(d => d, d => new OriginalDrawableState(d));
             OriginalSurroundingQuad = ToLocalSpace(GeometryUtils.GetSurroundingQuad(objectsInScale.SelectMany(d => d.Key.ScreenSpaceDrawQuad.GetVertices().ToArray())));
-            defaultOrigin = OriginalSurroundingQuad.Value.Centre;
+            defaultOrigin = ToLocalSpace(GeometryUtils.MinimumEnclosingCircle(objectsInScale.SelectMany(d => d.Key.ScreenSpaceDrawQuad.GetVertices().ToArray())).Item1);
 
             isFlippedX = false;
             isFlippedY = false;

osu.Game/Screens/Edit/Compose/Components/SelectionBoxRotationHandle.cs

@@ -77,6 +77,8 @@ protected override void OnDrag(DragEvent e)
         {
             base.OnDrag(e);
 
+            if (rotationHandler == null || !rotationHandler.OperationInProgress.Value) return;
+
             rawCumulativeRotation += convertDragEventToAngleOfRotation(e);
 
             applyRotation(shouldSnap: e.ShiftPressed);
@@ -113,9 +115,11 @@ protected override void OnDragEnd(DragEndEvent e)
 
         private float convertDragEventToAngleOfRotation(DragEvent e)
         {
-            // Adjust coordinate system to the center of SelectionBox
-            float startAngle = MathF.Atan2(e.LastMousePosition.Y - selectionBox.DrawHeight / 2, e.LastMousePosition.X - selectionBox.DrawWidth / 2);
-            float endAngle = MathF.Atan2(e.MousePosition.Y - selectionBox.DrawHeight / 2, e.MousePosition.X - selectionBox.DrawWidth / 2);
+            // Adjust coordinate system to the center of the selection
+            Vector2 center = selectionBox.ToLocalSpace(rotationHandler!.ToScreenSpace(rotationHandler!.DefaultOrigin!.Value));
+
+            float startAngle = MathF.Atan2(e.LastMousePosition.Y - center.Y, e.LastMousePosition.X - center.X);
+            float endAngle = MathF.Atan2(e.MousePosition.Y - center.Y, e.MousePosition.X - center.X);
 
             return (endAngle - startAngle) * 180 / MathF.PI;
         }

osu.Game/Screens/Edit/Compose/Components/SelectionRotationHandler.cs

@@ -13,7 +13,7 @@ namespace osu.Game.Screens.Edit.Compose.Components
     public partial class SelectionRotationHandler : Component
     {
         /// <summary>
-        /// Whether there is any ongoing scale operation right now.
+        /// Whether there is any ongoing rotation operation right now.
         /// </summary>
         public Bindable<bool> OperationInProgress { get; private set; } = new BindableBool();
 
@@ -27,6 +27,12 @@ public partial class SelectionRotationHandler : Component
         /// </summary>
         public Bindable<bool> CanRotateAroundPlayfieldOrigin { get; private set; } = new BindableBool();
 
+        /// <summary>
+        /// Implementation-defined origin point to rotate around when no explicit origin is provided.
+        /// This field is only assigned during a rotation operation.
+        /// </summary>
+        public Vector2? DefaultOrigin { get; protected set; }
+
         /// <summary>
         /// Performs a single, instant, atomic rotation operation.
         /// </summary>

osu.Game/Utils/GeometryUtils.cs

@@ -6,6 +6,7 @@
 using System.Linq;
 using osu.Framework.Graphics;
 using osu.Framework.Graphics.Primitives;
+using osu.Framework.Utils;
 using osu.Game.Rulesets.Objects.Types;
 using osuTK;
 
@@ -218,5 +219,158 @@ private static IEnumerable<Vector2> enumerateStartAndEndPositions(IEnumerable<IH
 
                 return new[] { h.Position };
             });
+
+        #region Welzl helpers
+
+        // Function to check whether a point lies inside or on the boundaries of the circle
+        private static bool isInside((Vector2 Centre, float Radius) c, Vector2 p)
+        {
+            return Precision.AlmostBigger(c.Radius, Vector2.Distance(c.Centre, p));
+        }
+
+        // Function to return a unique circle that intersects three points
+        private static (Vector2, float) circleFrom(Vector2 a, Vector2 b, Vector2 c)
+        {
+            if (Precision.AlmostEquals(0, (b.Y - a.Y) * (c.X - a.X) - (b.X - a.X) * (c.Y - a.Y)))
+                return circleFrom(a, b);
+
+            // See: https://en.wikipedia.org/wiki/Circumcircle#Cartesian_coordinates
+            float d = 2 * (a.X * (b - c).Y + b.X * (c - a).Y + c.X * (a - b).Y);
+            float aSq = a.LengthSquared;
+            float bSq = b.LengthSquared;
+            float cSq = c.LengthSquared;
+
+            var centre = new Vector2(
+                aSq * (b - c).Y + bSq * (c - a).Y + cSq * (a - b).Y,
+                aSq * (c - b).X + bSq * (a - c).X + cSq * (b - a).X) / d;
+
+            return (centre, Vector2.Distance(a, centre));
+        }
+
+        // Function to return the smallest circle that intersects 2 points
+        private static (Vector2, float) circleFrom(Vector2 a, Vector2 b)
+        {
+            var centre = (a + b) / 2.0f;
+            return (centre, Vector2.Distance(a, b) / 2.0f);
+        }
+
+        // Function to check whether a circle encloses the given points
+        private static bool isValidCircle((Vector2, float) c, List<Vector2> points)
+        {
+            // Iterating through all the points to check whether the points lie inside the circle or not
+            foreach (Vector2 p in points)
+            {
+                if (!isInside(c, p)) return false;
+            }
+
+            return true;
+        }
+
+        // Function to return the minimum enclosing circle for N <= 3
+        private static (Vector2, float) minCircleTrivial(List<Vector2> points)
+        {
+            if (points.Count > 3)
+                throw new ArgumentException("Number of points must be at most 3", nameof(points));
+
+            switch (points.Count)
+            {
+                case 0:
+                    return (new Vector2(0, 0), 0);
+
+                case 1:
+                    return (points[0], 0);
+
+                case 2:
+                    return circleFrom(points[0], points[1]);
+            }
+
+            // To check if MEC can be determined by 2 points only
+            for (int i = 0; i < 3; i++)
+            {
+                for (int j = i + 1; j < 3; j++)
+                {
+                    var c = circleFrom(points[i], points[j]);
+
+                    if (isValidCircle(c, points))
+                        return c;
+                }
+            }
+
+            return circleFrom(points[0], points[1], points[2]);
+        }
+
+        #endregion
+
+        /// <summary>
+        /// Function to find the minimum enclosing circle for a collection of points.
+        /// </summary>
+        /// <returns>A tuple containing the circle centre and radius.</returns>
+        public static (Vector2, float) MinimumEnclosingCircle(IEnumerable<Vector2> points)
+        {
+            // Using Welzl's algorithm to find the minimum enclosing circle
+            // https://www.geeksforgeeks.org/minimum-enclosing-circle-using-welzls-algorithm/
+            List<Vector2> p = points.ToList();
+
+            var stack = new Stack<(Vector2?, int)>();
+            var r = new List<Vector2>(3);
+            (Vector2, float) d = (Vector2.Zero, 0);
+
+            stack.Push((null, p.Count));
+
+            while (stack.Count > 0)
+            {
+                // `n` represents the number of points in P that are not yet processed.
+                // `point` represents the point that was randomly picked to process.
+                (Vector2? point, int n) = stack.Pop();
+
+                if (!point.HasValue)
+                {
+                    // Base case when all points processed or |R| = 3
+                    if (n == 0 || r.Count == 3)
+                    {
+                        d = minCircleTrivial(r);
+                        continue;
+                    }
+
+                    // Pick a random point randomly
+                    int idx = RNG.Next(n);
+                    point = p[idx];
+
+                    // Put the picked point at the end of P since it's more efficient than
+                    // deleting from the middle of the list
+                    (p[idx], p[n - 1]) = (p[n - 1], p[idx]);
+
+                    // Schedule processing of p after we get the MEC circle d from the set of points P - {p}
+                    stack.Push((point, n));
+                    // Get the MEC circle d from the set of points P - {p}
+                    stack.Push((null, n - 1));
+                }
+                else
+                {
+                    // If d contains p, return d
+                    if (isInside(d, point.Value))
+                        continue;
+
+                    // Remove points from R that were added in a deeper recursion
+                    // |R| = |P| - |stack| - n
+                    int removeCount = r.Count - (p.Count - stack.Count - n);
+                    r.RemoveRange(r.Count - removeCount, removeCount);
+
+                    // Otherwise, must be on the boundary of the MEC
+                    r.Add(point.Value);
+                    // Return the MEC for P - {p} and R U {p}
+                    stack.Push((null, n - 1));
+                }
+            }
+
+            return d;
+        }
+
+        /// <summary>
+        /// Function to find the minimum enclosing circle for a collection of hit objects.
+        /// </summary>
+        /// <returns>A tuple containing the circle centre and radius.</returns>
+        public static (Vector2, float) MinimumEnclosingCircle(IEnumerable<IHasPosition> hitObjects) =>
+            MinimumEnclosingCircle(enumerateStartAndEndPositions(hitObjects));
     }
 }