fix(motion): project anim root motion onto terrain plane (slope staircase)

Grounded player remotes were showing a ~5 Hz Z staircase when running
up/down slopes — the rate of server UpdatePositions. Body Z stayed flat
between UPs, then ramped over ~100ms during the queue-active chase to
each new server position, then went flat again until the next UP.

Diagnosis (no diagnostic needed — the math is unambiguous):
PositionManager.ComputeOffset has two modes via
InterpolationManager.AdjustOffset:

  - Queue active (body chasing a waypoint): returns
    `(head − body) / dist × min(catchUpSpeed × dt, dist)`. 3D direction,
    Z follows server's reported Z naturally.
  - Queue empty / head-reached (within DESIRED_DISTANCE = 0.05m of the
    most recent UP): returns Vector3.Zero. ComputeOffset falls back to
    `seqVel × dt rotated into world` — pure animation root motion. Every
    locomotion cycle bakes Z=0 in body-local, so the world result has
    Z=0 too. XY advances at the running pace; Z stays at the last UP.

For a runner at maxSpeed ≈ 4 m/s with catchUpSpeed = 2× = 8 m/s and
server UPs at ~5 Hz, body covers ~0.8m per UP, chases for ~100ms
(queue-active 3D path, Z ramps), then sits in seqVel-only mode for
~100ms (Z flat) until the next UP. Visible as a 5 Hz Z staircase.

Fix mirrors retail's CTransition::adjust_offset contact-plane projection
(named-retail acclient_2013_pseudo_c.txt:272296-272346) for grounded
motion, applied at the queue-empty boundary instead of inside the sweep:

  PositionManager.ComputeOffset gains an optional Vector3? terrainNormal.
  When the seqVel-only fallback runs AND a non-trivial terrain normal is
  supplied, project rootMotionWorld onto the plane:

      result = rootMotionWorld − N × dot(rootMotionWorld, N)

  Anim XY motion gains a corresponding Z component proportional to slope
  angle × forward speed, so body Z follows the terrain mesh between UPs.
  No-op on flat ground (N ≈ +Z, dot ≈ 0); cannot regress L.3 M2's
  flat-ground verification.

GameWindow.TickAnimations grounded-remote path samples
PhysicsEngine.SampleTerrainNormal at the body's current XY each tick
and passes it to ComputeOffset. SampleTerrainNormal is a thin public
wrapper over the existing internal SampleTerrainWalkable that returns
just the plane normal (no need to expose the internal sample shape).

Diagnostic: ACDREAM_SLOPE_DIAG=1 prints a per-tick [SLOPE] line with
guid, body Z before/after, offset, queue active flag, and the sampled
plane Nz so we can grep before/after the fix and confirm Z changes
continuously between UPs on slopes.

Tests: PositionManagerTests gains two cases:
  - slope projection: 30° east-tilted plane, body running due east at
    4 m/s for 1s → expect (3.0, 0, −1.732) (descends along slope, not
    flat). Math: dot(seqVel, N) = 2.0 → result = (4,0,0) − (0.5,0,0.866)
    × 2.0 = (3.0, 0, −1.732).
  - flat-ground no-op: N = +Z, expect identical Y-only motion as the
    pre-fix behavior.

Build green. 357 pass / 6 pre-existing fail (same set as ec59a08;
verified by stashing this change). The pre-existing
`ComputeOffset_BothActive_Combined` failure reflects an outdated
additive-design test docstring; the M2 commit (40d88b9) deliberately
changed the implementation to REPLACE semantics to fix the prior
3×-server-pace overshoot.

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

src/AcDream.App/Rendering/GameWindow.cs

@@ -6149,15 +6149,42 @@ public sealed class GameWindow : IDisposable
                     //     velocity, keeping legs and body pace synchronized.
                     //   - Blip-to-tail (tail − body) when fail_count > 3.
                     float maxSpeed = rm.Motion.GetMaxSpeed();
+                    // Slope-staircase fix (2026-05-05): sample terrain normal
+                    // at the body's current XY so PositionManager can project
+                    // the seqVel-only fallback onto the local slope. Without
+                    // this, the queue-empty interval between UPs left Z flat
+                    // (anim cycles bake Z=0 body-local) — visible ~5 Hz
+                    // staircase when a remote runs up/down hills. The
+                    // projection is a no-op on flat ground.
+                    System.Numerics.Vector3? terrainNormal = _physicsEngine.SampleTerrainNormal(
+                        rm.Body.Position.X, rm.Body.Position.Y);
+
+                    System.Numerics.Vector3 bodyPosBefore = rm.Body.Position;
                     System.Numerics.Vector3 offset = rm.Position.ComputeOffset(
                         dt: (double)dt,
                         currentBodyPosition: rm.Body.Position,
                         seqVel: seqVel,
                         ori: rm.Body.Orientation,
                         interp: rm.Interp,
-                        maxSpeed: maxSpeed);
+                        maxSpeed: maxSpeed,
+                        terrainNormal: terrainNormal);
                     rm.Body.Position += offset;
 
+                    // Slope-staircase diagnostic — gated on ACDREAM_SLOPE_DIAG=1.
+                    // Prints per-tick body Z trajectory + queue state + projected
+                    // offset.Z so we can grep before/after the fix and confirm Z
+                    // changes continuously between UPs on slopes (no flat
+                    // intervals followed by snaps).
+                    if (System.Environment.GetEnvironmentVariable("ACDREAM_SLOPE_DIAG") == "1")
+                    {
+                        bool queueActive = rm.Interp.IsActive;
+                        float nz = terrainNormal?.Z ?? 1.0f;
+                        System.Console.WriteLine(
+                            $"[SLOPE] guid={serverGuid:X8} bodyZ={bodyPosBefore.Z:F3}->{rm.Body.Position.Z:F3} "
+                            + $"offset=({offset.X:F3},{offset.Y:F3},{offset.Z:F3}) "
+                            + $"queue={queueActive} cpN.Z={nz:F3}");
+                    }
+
                     // Step 2.5: angular velocity → body orientation. Prefer
                     // ObservedOmega (set explicitly in OnLiveMotionUpdated from
                     // the wire's TurnCommand + signed TurnSpeed) over the

src/AcDream.Core/Physics/PhysicsEngine.cs

@@ -169,6 +169,21 @@ public sealed class PhysicsEngine
         return null;
     }
 
+    /// <summary>
+    /// Public surface for callers that only need the local terrain plane
+    /// normal at a world-space XY (e.g., the grounded-remote tick path
+    /// projecting anim root motion onto the slope to avoid the staircase
+    /// between server position updates). Returns null when no registered
+    /// landblock covers the point. Mirrors the plane component of
+    /// <see cref="SampleTerrainWalkable"/> without exposing the internal
+    /// <c>TerrainWalkableSample</c> shape.
+    /// </summary>
+    public Vector3? SampleTerrainNormal(float worldX, float worldY)
+    {
+        var sample = SampleTerrainWalkable(worldX, worldY);
+        return sample?.Plane.Normal;
+    }
+
     /// <summary>
     /// Sample the outdoor terrain walkable triangle at the given world-space
     /// XY position. This carries the same plane as <see cref="SampleTerrainPlane"/>

src/AcDream.Core/Physics/PositionManager.cs

@@ -34,13 +34,28 @@ public sealed class PositionManager
     /// <param name="ori">Body orientation; used to rotate seqVel from body-local to world.</param>
     /// <param name="interp">The remote's InterpolationManager (for AdjustOffset call).</param>
     /// <param name="maxSpeed">From <c>MotionInterpreter.GetMaxSpeed()</c> — passed to AdjustOffset for the catch-up clamp.</param>
+    /// <param name="terrainNormal">
+    /// Optional local terrain plane normal at the body's current XY. When
+    /// supplied AND the queue-empty / head-reached fallback path runs, the
+    /// world-space anim root motion is projected onto the plane so XY motion
+    /// produces a corresponding Z change on slopes. Without this, the
+    /// fallback advances XY at the locomotion cycle's pace but leaves Z at
+    /// the last UP's reported Z — visible as a ~5 Hz staircase on slopes
+    /// (the rate of server UpdatePositions). Mirrors retail's
+    /// <c>CTransition::adjust_offset</c> contact-plane projection
+    /// (named-retail acclient_2013_pseudo_c.txt:272296-272346) for grounded
+    /// motion, applied here at the queue-empty boundary instead of inside
+    /// the sweep. Pass <c>null</c> on flat ground / when no terrain sample
+    /// is available — projection is a no-op when normal == +Z.
+    /// </param>
     public Vector3 ComputeOffset(
         double dt,
         Vector3 currentBodyPosition,
         Vector3 seqVel,
         Quaternion ori,
         InterpolationManager interp,
-        float maxSpeed)
+        float maxSpeed,
+        Vector3? terrainNormal = null)
     {
         // Retail-faithful per-frame combiner. Mirrors
         // CPhysicsObj::UpdatePositionInternal (acclient @ 0x00512c30) +
@@ -71,6 +86,23 @@ public sealed class PositionManager
             return correction;
 
         Vector3 rootMotionLocal = seqVel * (float)dt;
-        return Vector3.Transform(rootMotionLocal, ori);
+        Vector3 rootMotionWorld = Vector3.Transform(rootMotionLocal, ori);
+
+        // Slope projection (queue-empty fallback only). Locomotion cycles
+        // bake Z=0 in body-local, so without projection the body's Z stays
+        // at the last UP's reported value while XY advances at the running
+        // pace — visible ~5 Hz staircase between UPs on hills. Projecting
+        // the world-space anim motion onto the local terrain plane gives
+        // it a Z component proportional to slope × forward speed, so the
+        // body follows the terrain mesh smoothly. No-op on flat ground
+        // (normal ≈ +Z, dot ≈ 0) so it can't regress the M2 flat-ground
+        // verification.
+        if (terrainNormal.HasValue && terrainNormal.Value.Z > 0.01f)
+        {
+            Vector3 N = terrainNormal.Value;
+            float into = Vector3.Dot(rootMotionWorld, N);
+            rootMotionWorld -= N * into;
+        }
+        return rootMotionWorld;
     }
 }