Test for accuracy of perfect curves

osu.Game.Rulesets.Osu.Tests/Editor/TestSliderScaling.cs

@@ -3,8 +3,10 @@
 
 #nullable disable
 
+using System;
 using System.Linq;
 using NUnit.Framework;
+using osu.Framework.Graphics.Primitives;
 using osu.Framework.Testing;
 using osu.Framework.Utils;
 using osu.Game.Beatmaps;
@@ -72,48 +74,119 @@ namespace osu.Game.Rulesets.Osu.Tests.Editor
         private void moveMouse(Vector2 pos) =>
             AddStep($"move mouse to {pos}", () => InputManager.MoveMouseTo(playfield.ToScreenSpace(pos)));
     }
+
     [TestFixture]
     public class TestSliderNearLinearScaling
     {
+        private readonly Random rng = new Random(1337);
+
         [Test]
         public void TestScalingSliderFlat()
         {
-            Slider sliderPerfect = new Slider
+            SliderPath sliderPathPerfect = new SliderPath(
-            {
+            [
-                Position = new Vector2(300),
+                new PathControlPoint(new Vector2(0), PathType.PERFECT_CURVE),
-                Path = new SliderPath(
+                new PathControlPoint(new Vector2(50, 25)),
-                    [
+                new PathControlPoint(new Vector2(25, 100)),
-                        new PathControlPoint(new Vector2(0), PathType.PERFECT_CURVE),
+            ]);
-                        new PathControlPoint(new Vector2(50, 25)),
-                        new PathControlPoint(new Vector2(25, 100)),
-                    ])
-            };
 
-            Slider sliderBezier = new Slider
+            SliderPath sliderPathBezier = new SliderPath(
-            {
+            [
-                Position = new Vector2(300),
+                new PathControlPoint(new Vector2(0), PathType.BEZIER),
-                Path = new SliderPath(
+                new PathControlPoint(new Vector2(50, 25)),
-                    [
+                new PathControlPoint(new Vector2(25, 100)),
-                        new PathControlPoint(new Vector2(0), PathType.BEZIER),
+            ]);
-                        new PathControlPoint(new Vector2(50, 25)),
-                        new PathControlPoint(new Vector2(25, 100)),
-                    ])
-            };
 
-            scaleSlider(sliderPerfect, new Vector2(0.000001f, 1));
+            scaleSlider(sliderPathPerfect, new Vector2(0.000001f, 1));
-            scaleSlider(sliderBezier, new Vector2(0.000001f, 1));
+            scaleSlider(sliderPathBezier, new Vector2(0.000001f, 1));
 
             for (int i = 0; i < 100; i++)
             {
-                Assert.True(Precision.AlmostEquals(sliderPerfect.Path.PositionAt(i / 100.0f), sliderBezier.Path.PositionAt(i / 100.0f)));
+                Assert.True(Precision.AlmostEquals(sliderPathPerfect.PositionAt(i / 100.0f), sliderPathBezier.PositionAt(i / 100.0f)));
             }
         }
 
-        private void scaleSlider(Slider slider, Vector2 scale)
+        [Test]
+        public void TestPerfectCurveMatchesTheoretical()
         {
-            for (int i = 0; i < slider.Path.ControlPoints.Count; i++)
+            for (int i = 0; i < 20000; i++)
             {
-                slider.Path.ControlPoints[i].Position *= scale;
+                //Only test points that are in the screen's bounds
+                float p1X = 640.0f * (float)rng.NextDouble();
+                float p2X = 640.0f * (float)rng.NextDouble();
+
+                float p1Y = 480.0f * (float)rng.NextDouble();
+                float p2Y = 480.0f * (float)rng.NextDouble();
+                SliderPath sliderPathPerfect = new SliderPath(
+                [
+                    new PathControlPoint(new Vector2(0, 0), PathType.PERFECT_CURVE),
+                    new PathControlPoint(new Vector2(p1X, p1Y)),
+                    new PathControlPoint(new Vector2(p2X, p2Y)),
+                ]);
+
+                assertMatchesPerfectCircle(sliderPathPerfect);
+
+                scaleSlider(sliderPathPerfect, new Vector2(0.00001f, 1));
+
+                assertMatchesPerfectCircle(sliderPathPerfect);
+            }
+        }
+
+        private void assertMatchesPerfectCircle(SliderPath path)
+        {
+            if (path.ControlPoints.Count != 3)
+                return;
+
+            //Replication of PathApproximator.CircularArcToPiecewiseLinear
+            CircularArcProperties circularArcProperties = new CircularArcProperties(path.ControlPoints.Select(x => x.Position).ToArray());
+
+            if (!circularArcProperties.IsValid)
+                return;
+
+            //Addresses cases where circularArcProperties.ThetaRange>0.5
+            //Occurs in code in PathControlPointVisualiser.ensureValidPathType
+            RectangleF boundingBox = PathApproximator.CircularArcBoundingBox(path.ControlPoints.Select(x => x.Position).ToArray());
+            if (boundingBox.Width >= 640 || boundingBox.Height >= 480)
+                return;
+
+            int subpoints = (2f * circularArcProperties.Radius <= 0.1f) ? 2 : Math.Max(2, (int)Math.Ceiling(circularArcProperties.ThetaRange / (2.0 * Math.Acos(1f - 0.1f / circularArcProperties.Radius))));
+
+            //ignore cases where subpoints is int.MaxValue, result will be garbage
+            //as well, having this many subpoints will cause an out of memory error, so can't happen during normal useage
+            if (subpoints == int.MaxValue)
+                return;
+
+            for (int i = 0; i < Math.Min(subpoints, 100); i++)
+            {
+                float progress = (float)rng.NextDouble();
+
+                //To avoid errors from interpolating points, ensure we check only positions that would be subpoints.
+                progress = (float)Math.Ceiling(progress * (subpoints - 1)) / (subpoints - 1);
+
+                //Special case - if few subpoints, ensure checking every single one rather than randomly
+                if (subpoints < 100)
+                    progress = i / (float)(subpoints - 1);
+
+                //edge points cause issue with interpolation, so ignore the last two points and first
+                if (progress == 0.0f || progress >= (subpoints - 2) / (float)(subpoints - 1))
+                    continue;
+
+                double theta = circularArcProperties.ThetaStart + circularArcProperties.Direction * progress * circularArcProperties.ThetaRange;
+                Vector2 vector = new Vector2((float)Math.Cos(theta), (float)Math.Sin(theta)) * circularArcProperties.Radius;
+
+                Assert.True(Precision.AlmostEquals(circularArcProperties.Centre + vector, path.PositionAt(progress), 0.01f),
+                    "A perfect circle with points " + string.Join(", ", path.ControlPoints.Select(x => x.Position)) + " and radius" + circularArcProperties.Radius + "from SliderPath does not almost equal a theoretical perfect circle with " + subpoints + " subpoints"
+                    + ": " + (circularArcProperties.Centre + vector) + " - " + path.PositionAt(progress)
+                    + " = " + (circularArcProperties.Centre + vector - path.PositionAt(progress))
+                );
+            }
+        }
+
+        private void scaleSlider(SliderPath path, Vector2 scale)
+        {
+            for (int i = 0; i < path.ControlPoints.Count; i++)
+            {
+                path.ControlPoints[i].Position *= scale;
             }
         }
     }