Fix bulbs on Catmull sliders

osu.Game/Rulesets/Objects/SliderPath.cs

@@ -42,6 +42,17 @@ namespace osu.Game.Rulesets.Objects
         private readonly List<double> cumulativeLength = new List<double>();
         private readonly Cached pathCache = new Cached();
 
+        /// <summary>
+        /// Any additional length of the path which was optimised out during piecewise approximation, but should still be considered as part of <see cref="calculatedLength"/>.
+        /// </summary>
+        /// <remarks>
+        /// This is a hack for Catmull paths.
+        /// </remarks>
+        private double optimisedLength;
+
+        /// <summary>
+        /// The final calculated length of the path.
+        /// </summary>
         private double calculatedLength;
 
         private readonly List<int> segmentEnds = new List<int>();
@@ -244,6 +255,7 @@ namespace osu.Game.Rulesets.Objects
         {
             calculatedPath.Clear();
             segmentEnds.Clear();
+            optimisedLength = 0;
 
             if (ControlPoints.Count == 0)
                 return;
@@ -268,7 +280,8 @@ namespace osu.Game.Rulesets.Objects
                     calculatedPath.Add(segmentVertices[0]);
                 else if (segmentVertices.Length > 1)
                 {
-                    List<Vector2> subPath = calculateSubPath(segmentVertices, segmentType);
+                    List<Vector2> subPath = calculateSubPath(segmentVertices, segmentType, ref optimisedLength);
+
                     // Skip the first vertex if it is the same as the last vertex from the previous segment
                     bool skipFirst = calculatedPath.Count > 0 && subPath.Count > 0 && calculatedPath.Last() == subPath[0];
 
@@ -287,7 +300,7 @@ namespace osu.Game.Rulesets.Objects
             }
         }
 
-        private List<Vector2> calculateSubPath(ReadOnlySpan<Vector2> subControlPoints, PathType type)
+        private static List<Vector2> calculateSubPath(ReadOnlySpan<Vector2> subControlPoints, PathType type, ref double optimisedLength)
         {
             switch (type.Type)
             {
@@ -295,6 +308,7 @@ namespace osu.Game.Rulesets.Objects
                     return PathApproximator.LinearToPiecewiseLinear(subControlPoints);
 
                 case SplineType.PerfectCurve:
+                {
                     if (subControlPoints.Length != 3)
                         break;
 
@@ -305,9 +319,55 @@ namespace osu.Game.Rulesets.Objects
                         break;
 
                     return subPath;
+                }
 
                 case SplineType.Catmull:
-                    return PathApproximator.CatmullToPiecewiseLinear(subControlPoints);
+                {
+                    List<Vector2> subPath = PathApproximator.CatmullToPiecewiseLinear(subControlPoints);
+
+                    // At draw time, osu!stable optimises paths by only keeping piecewise segments that are 6px apart.
+                    // For the most part we don't care about this optimisation, and its additional heuristics are hard to reproduce in every implementation.
+                    //
+                    // However, it matters for Catmull paths which form "bulbs" around sequential knots with identical positions,
+                    // so we'll apply a very basic form of the optimisation here and return a length representing the optimised portion.
+                    // The returned length is important so that the optimisation doesn't cause the path to get extended to match the value of ExpectedDistance.
+
+                    List<Vector2> optimisedPath = new List<Vector2>(subPath.Count);
+
+                    Vector2? lastStart = null;
+                    double lengthRemovedSinceStart = 0;
+
+                    for (int i = 0; i < subPath.Count; i++)
+                    {
+                        if (lastStart == null)
+                        {
+                            optimisedPath.Add(subPath[i]);
+                            lastStart = subPath[i];
+                            continue;
+                        }
+
+                        Debug.Assert(i > 0);
+
+                        double distFromStart = Vector2.Distance(lastStart.Value, subPath[i]);
+                        lengthRemovedSinceStart += Vector2.Distance(subPath[i - 1], subPath[i]);
+
+                        // See PathApproximator.catmull_detail.
+                        const int catmull_detail = 50;
+                        const int catmull_segment_length = catmull_detail * 2;
+
+                        // Either 6px from the start, the last vertex at every knot, or the end of the path.
+                        if (distFromStart > 6 || (i + 1) % catmull_segment_length == 0 || i == subPath.Count - 1)
+                        {
+                            optimisedPath.Add(subPath[i]);
+                            optimisedLength += lengthRemovedSinceStart - distFromStart;
+
+                            lastStart = null;
+                            lengthRemovedSinceStart = 0;
+                        }
+                    }
+
+                    return optimisedPath;
+                }
             }
 
             return PathApproximator.BSplineToPiecewiseLinear(subControlPoints, type.Degree ?? subControlPoints.Length);
@@ -315,7 +375,7 @@ namespace osu.Game.Rulesets.Objects
 
         private void calculateLength()
         {
-            calculatedLength = 0;
+            calculatedLength = optimisedLength;
             cumulativeLength.Clear();
             cumulativeLength.Add(0);