feat(rendering): add Frustum with AABB intersection test

Rendering/Frustum.cs

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+using OpenTK.Mathematics;
+
+namespace VoxelEngine.Rendering;
+
+// View-frustum for culling chunk AABBs. Built from a world→clip matrix in this
+// engine's row-vector convention (clip = worldPos * view * projection, matching
+// the chunk vertex shader). Planes point inward; a point is inside when it is on
+// the positive side of all six.
+public readonly struct Frustum
+{
+    // Each Vector4 is (a, b, c, d) for plane a*x + b*y + c*z + d = 0, normalized.
+    private readonly Vector4 _left, _right, _bottom, _top, _near, _far;
+
+    private Frustum(Vector4 l, Vector4 r, Vector4 b, Vector4 t, Vector4 n, Vector4 f)
+    {
+        this._left = l; this._right = r; this._bottom = b;
+        this._top = t; this._near = n; this._far = f;
+    }
+
+    // `vp` maps a world-space row vector p to clip space via p * vp. In that
+    // convention clip.x = p · column0, clip.w = p · column3, etc., so each plane
+    // is a combination of vp's columns (Gribb–Hartmann, row-vector form).
+    public static Frustum FromViewProjection(Matrix4 vp)
+    {
+        Vector4 c0 = vp.Column0, c1 = vp.Column1, c2 = vp.Column2, c3 = vp.Column3;
+        return new Frustum(
+            Normalize(c3 + c0),  // left:   clip.w + clip.x >= 0
+            Normalize(c3 - c0),  // right:  clip.w - clip.x >= 0
+            Normalize(c3 + c1),  // bottom: clip.w + clip.y >= 0
+            Normalize(c3 - c1),  // top:    clip.w - clip.y >= 0
+            Normalize(c3 + c2),  // near:   clip.w + clip.z >= 0 (GL NDC z in [-1,1])
+            Normalize(c3 - c2)); // far:    clip.w - clip.z >= 0
+    }
+
+    // True if the axis-aligned box [min,max] is at least partially inside.
+    public bool Intersects(Vector3 min, Vector3 max)
+    {
+        return InsideOrCrossing(this._left, min, max)
+            && InsideOrCrossing(this._right, min, max)
+            && InsideOrCrossing(this._bottom, min, max)
+            && InsideOrCrossing(this._top, min, max)
+            && InsideOrCrossing(this._near, min, max)
+            && InsideOrCrossing(this._far, min, max);
+    }
+
+    // The box is fully outside a plane only if its most-positive vertex (the
+    // corner farthest along the plane normal) is still behind the plane.
+    private static bool InsideOrCrossing(Vector4 plane, Vector3 min, Vector3 max)
+    {
+        float px = plane.X >= 0 ? max.X : min.X;
+        float py = plane.Y >= 0 ? max.Y : min.Y;
+        float pz = plane.Z >= 0 ? max.Z : min.Z;
+        return plane.X * px + plane.Y * py + plane.Z * pz + plane.W >= 0f;
+    }
+
+    private static Vector4 Normalize(Vector4 p)
+    {
+        float len = new Vector3(p.X, p.Y, p.Z).Length;
+        return len > 0f ? p / len : p;
+    }
+}

VoxelEngine.Tests/FrustumTests.cs

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+using OpenTK.Mathematics;
+using VoxelEngine.Rendering;
+using Xunit;
+
+namespace VoxelEngine.Tests;
+
+public class FrustumTests
+{
+    // Camera at the origin, default yaw -90° → looks down -Z.
+    private static Frustum MakeFrustum()
+    {
+        var cam = new Camera(new Vector3(0, 0, 0), 16f / 9f);
+        return Frustum.FromViewProjection(cam.GetViewMatrix() * cam.GetProjectionMatrix());
+    }
+
+    [Fact]
+    public void AABBInFront_IsVisible()
+    {
+        var f = MakeFrustum();
+        Assert.True(f.Intersects(new Vector3(-2, -2, -22), new Vector3(2, 2, -18)));
+    }
+
+    [Fact]
+    public void AABBBehindCamera_IsCulled()
+    {
+        var f = MakeFrustum();
+        Assert.False(f.Intersects(new Vector3(-2, -2, 18), new Vector3(2, 2, 22)));
+    }
+
+    [Fact]
+    public void AABBStraddlingCamera_Intersects()
+    {
+        var f = MakeFrustum();
+        Assert.True(f.Intersects(new Vector3(-2, -2, -5), new Vector3(2, 2, 5)));
+    }
+
+    [Fact]
+    public void AABBFarToTheSide_IsCulled()
+    {
+        var f = MakeFrustum();
+        // Far along +X at a depth in front of the camera — outside horizontal FOV.
+        Assert.False(f.Intersects(new Vector3(1000, -2, -5), new Vector3(1004, 2, -1)));
+    }
+}