zzre: Add ToZZRotationVector as roundtrip to ToZZRotation

zzre.core.tests/math/TestMath.cs

@@ -0,0 +1,53 @@
+using System;
+using System.Collections;
+using System.Collections.Generic;
+using System.Numerics;
+using NUnit.Framework;
+
+namespace zzre.core.tests.math;
+
+[TestFixture]
+public class TestMath
+{
+    [Test]
+    public void TestRoundtrip()
+    {
+        foreach (var dir in GenerateUniformPoints())
+        {
+            var dirQuat = dir.ToZZRotation();
+            var roundtripDir = dirQuat.ToZZRotationVector();
+            var dirLength = dir.Length();
+            var roundtripDirLength = roundtripDir.Length();
+            var acosAngle = Vector3.Dot(dir, roundtripDir) / (dirLength * roundtripDirLength);
+            // We still occasionally get values slightly outside -1 to 1. Is this a problem in game too?
+            acosAngle = Math.Clamp(acosAngle, -1, 1);
+            var roundtripAngle = Math.Acos(acosAngle) * MathEx.RadToDeg;
+
+            Assert.That(dir.Length(), Is.EqualTo(1.0f).Within(1).Percent);
+            Assert.That(roundtripDir.Length(), Is.EqualTo(1.0f).Within(1).Percent);
+            Assert.That(roundtripAngle, Is.EqualTo(0).Within(0.1), $"For {dir}");
+        }
+    }
+
+    private const int PointCount = 10000;
+    public static IEnumerable<Vector3> GenerateUniformPoints()
+    {
+        // TODO: Move uniform sphere point generator to NumericsExtensions
+        // (and test that everything still works after that change)
+
+        var random = new Random(42);
+        for (int i = 0; i < PointCount; i++)
+        {
+            // from https://corysimon.github.io/articles/uniformdistn-on-sphere/
+            double theta = 2 * Math.PI * random.NextDouble();
+            double phi = Math.Acos(1 - 2 * random.NextDouble());
+            double sinTheta = Math.Sin(theta), cosTheta = Math.Cos(theta);
+            double sinPhi = Math.Sin(phi), cosPhi = Math.Cos(phi);
+            var vec = new Vector3(
+                (float)(sinPhi * cosTheta),
+                (float)(sinPhi * sinTheta),
+                (float)(cosPhi));
+            yield return vec;
+        }
+    }
+}

zzre.core/math/ZZIOExtensions.cs

@@ -20,6 +20,9 @@ public static void CopyFromNumerics(this ref FColor c, Vector4 v)
     public static Quaternion ToZZRotation(this Vector3 v) =>
         Quaternion.Conjugate(Quaternion.CreateFromRotationMatrix(Matrix4x4.CreateLookAt(Vector3.Zero, v * -1f, Vector3.UnitY)));
 
+    public static Vector3 ToZZRotationVector(this Quaternion rotation) =>
+        Vector3.Transform(-Vector3.UnitZ, rotation) * -1f;
+
     public static RgbaByte ToVeldrid(this IColor c) => new(c.r, c.g, c.b, c.a);
     public static RgbaFloat ToVeldrid(this FColor c) => new(c.r, c.g, c.b, c.a);
     public static FColor ToFColor(this Vector4 v) => new(v.X, v.Y, v.Z, v.W);