feat(camera): wire RetailChaseCamera Update() + tunables + state

Adds the per-frame Update(playerPos, yaw, velocity, dt) entrypoint
that composes the math primitives into a renderable View matrix +
PlayerTranslucency. State: 5-frame velocity ring, damped eye + forward
unit vector, first-frame snap flag, mouse-filter shared state.
Public surface: Distance/Pitch/YawOffset/PivotHeight tunables,
AdjustDistance/Pitch (with clamps), FilterMouseDelta entry, View +
Position + PlayerTranslucency outputs. 5 new integration tests, all
pass; total RetailChaseCamera test count 25.

Also folds in two minor cleanups from the Task 2 code review:
- AverageVelocity uses ring.Length instead of hardcoded 5
- Basis_NearVerticalHeading test asserts orthogonality of right & up

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

tests/AcDream.App.Tests/Rendering/RetailChaseCameraTests.cs

@@ -1,6 +1,7 @@
 using System;
 using System.Numerics;
 using AcDream.App.Rendering;
+using AcDream.Core.Rendering;
 using Xunit;
 
 namespace AcDream.App.Tests.Rendering;
@@ -84,6 +85,7 @@ public class RetailChaseCameraTests
 
         Assert.Equal(1f, right.Length(), 5);
         Assert.Equal(1f, up.Length(),    5);
+        Assert.Equal(0f, Vector3.Dot(right, up), 5);
     }
 
     // ── Velocity ring & averaging ────────────────────────────────────
@@ -265,4 +267,89 @@ public class RetailChaseCameraTests
         Assert.Equal(1f, RetailChaseCamera.ComputeTranslucency(distance: 0.10f),  5);
         Assert.Equal(1f, RetailChaseCamera.ComputeTranslucency(distance: 0.0f),   5);
     }
+
+    // ── Update() integration ─────────────────────────────────────────
+
+    [Fact]
+    public void FirstUpdate_SnapsToTarget()
+    {
+        var cam = new RetailChaseCamera { Distance = 5f, Pitch = 0f };
+        CameraDiagnostics.AlignToSlope = false;   // deterministic: heading = yaw vec
+
+        cam.Update(
+            playerPosition: new Vector3(10f, 20f, 30f),
+            playerYaw:      0f,             // forward = +X
+            playerVelocity: Vector3.Zero,
+            dt:             1f / 60f);
+
+        // Expected target eye:
+        //   pivot          = (10, 20, 30+1.5=31.5)
+        //   forward (yaw=0)= (1, 0, 0)
+        //   right          = (0, -1, 0) since (1,0,0) × (0,0,1) = (0, -1, 0)
+        //   up             = right × forward = (0,-1,0) × (1,0,0) = (0,0,1)
+        //   viewer_offset  = (0, -5, 0)  (Distance=5, Pitch=0 → -Distance*cos = -5, sin = 0)
+        //   eye = pivot + right*0 + forward*-5 + up*0
+        //       = (10 - 5, 20, 31.5) = (5, 20, 31.5)
+        Assert.Equal(5f,    cam.Position.X, 4);
+        Assert.Equal(20f,   cam.Position.Y, 4);
+        Assert.Equal(31.5f, cam.Position.Z, 4);
+    }
+
+    [Fact]
+    public void SecondUpdate_LerpsTowardTarget()
+    {
+        var cam = new RetailChaseCamera { Distance = 5f, Pitch = 0f };
+        CameraDiagnostics.AlignToSlope         = false;
+        CameraDiagnostics.TranslationStiffness = 0.45f;
+        CameraDiagnostics.RotationStiffness    = 0.45f;
+
+        // First update at origin: dampedEye = (-5, 0, 1.5).
+        cam.Update(Vector3.Zero, playerYaw: 0f, playerVelocity: Vector3.Zero, dt: 1f / 60f);
+        var firstEye = cam.Position;
+
+        // Teleport the player one frame later. Target eye now at (10-5, 0, 1.5) = (5, 0, 1.5).
+        // alpha = 0.45 * (1/60) * 10 = 0.075.
+        // New eye = firstEye + 0.075 * (target - firstEye)
+        //         = (-5,0,1.5) + 0.075 * ((5,0,1.5) - (-5,0,1.5))
+        //         = (-5,0,1.5) + 0.075 * (10,0,0)
+        //         = (-4.25, 0, 1.5)
+        cam.Update(new Vector3(10f, 0f, 0f), playerYaw: 0f, playerVelocity: Vector3.Zero, dt: 1f / 60f);
+
+        Assert.Equal(-4.25f, cam.Position.X, 3);
+        Assert.Equal(0f,     cam.Position.Y, 4);
+        Assert.Equal(1.5f,   cam.Position.Z, 4);
+    }
+
+    [Fact]
+    public void Translucency_PropertyReflectsCurrentDampedDistance()
+    {
+        var cam = new RetailChaseCamera { Distance = 5f, Pitch = 0f, PivotHeight = 1.5f };
+        CameraDiagnostics.AlignToSlope = false;
+
+        // Far from pivot — translucency should be 0.
+        cam.Update(Vector3.Zero, playerYaw: 0f, playerVelocity: Vector3.Zero, dt: 1f / 60f);
+        Assert.Equal(0f, cam.PlayerTranslucency, 5);
+    }
+
+    [Fact]
+    public void AdjustDistance_ClampsToRange()
+    {
+        var cam = new RetailChaseCamera { Distance = 5f };
+        cam.AdjustDistance(-100f);
+        Assert.Equal(RetailChaseCamera.DistanceMin, cam.Distance);
+
+        cam.AdjustDistance(+200f);
+        Assert.Equal(RetailChaseCamera.DistanceMax, cam.Distance);
+    }
+
+    [Fact]
+    public void AdjustPitch_ClampsToRange()
+    {
+        var cam = new RetailChaseCamera { Pitch = 0f };
+        cam.AdjustPitch(-10f);
+        Assert.Equal(RetailChaseCamera.PitchMin, cam.Pitch);
+
+        cam.AdjustPitch(+10f);
+        Assert.Equal(RetailChaseCamera.PitchMax, cam.Pitch);
+    }
 }