fix(physics): #32 L.2c precipice edge-slide context

Port the first retail precipice-slide slice from named retail/ACE: terrain and BSP walkable hits now preserve polygon vertices, failed step-down edges back-probe to rediscover the walkable polygon, and edge-slide can run precipice/cliff slide instead of only hard-stopping.

Adds pseudocode anchors plus regression coverage for terrain polygon context and loaded-terrain boundary edge-slide.

Co-authored-by: Codex <codex@openai.com>

src/AcDream.Core/Physics/TerrainSurface.cs

@@ -1,7 +1,13 @@
 using System;
+using System.Numerics;
 
 namespace AcDream.Core.Physics;
 
+public readonly record struct TerrainSurfacePolygon(
+    float Z,
+    Vector3 Normal,
+    Vector3[] Vertices);
+
 /// <summary>
 /// Outdoor terrain height resolver for a single landblock. Performs
 /// per-triangle barycentric Z interpolation matching the visual terrain
@@ -250,6 +256,72 @@ public sealed class TerrainSurface
         return (z, normal);
     }
 
+    /// <summary>
+    /// Sample the terrain triangle at (localX, localY), including the three
+    /// local-space vertices that bound the sampled point. Edge-slide needs
+    /// these vertices so the retail crossed-edge test can identify which edge
+    /// the sphere left when a step-down probe fails.
+    /// </summary>
+    public TerrainSurfacePolygon SampleSurfacePolygon(float localX, float localY)
+    {
+        float fx = Math.Clamp(localX / CellSize, 0f, CellsPerSide - 0.001f);
+        float fy = Math.Clamp(localY / CellSize, 0f, CellsPerSide - 0.001f);
+        int cx = Math.Clamp((int)fx, 0, CellsPerSide - 1);
+        int cy = Math.Clamp((int)fy, 0, CellsPerSide - 1);
+
+        float tx = fx - cx;
+        float ty = fy - cy;
+
+        float hBL = _z[cx,     cy    ];
+        float hBR = _z[cx + 1, cy    ];
+        float hTR = _z[cx + 1, cy + 1];
+        float hTL = _z[cx,     cy + 1];
+
+        bool splitSWtoNE = IsSplitSWtoNE(_landblockX, (uint)cx, _landblockY, (uint)cy);
+
+        Vector3 bl = new(cx * CellSize,       cy * CellSize,       hBL);
+        Vector3 br = new((cx + 1) * CellSize, cy * CellSize,       hBR);
+        Vector3 tr = new((cx + 1) * CellSize, (cy + 1) * CellSize, hTR);
+        Vector3 tl = new(cx * CellSize,       (cy + 1) * CellSize, hTL);
+
+        float z;
+        Vector3[] vertices;
+
+        if (splitSWtoNE)
+        {
+            if (tx > ty)
+            {
+                z = hBL + (hBR - hBL) * tx + (hTR - hBR) * ty;
+                vertices = new[] { bl, br, tr };
+            }
+            else
+            {
+                z = hBL + (hTR - hTL) * tx + (hTL - hBL) * ty;
+                vertices = new[] { bl, tr, tl };
+            }
+        }
+        else
+        {
+            if (tx + ty <= 1f)
+            {
+                z = hBL + (hBR - hBL) * tx + (hTL - hBL) * ty;
+                vertices = new[] { bl, br, tl };
+            }
+            else
+            {
+                z = hTR + (hTL - hTR) * (1f - tx) + (hBR - hTR) * (1f - ty);
+                vertices = new[] { br, tr, tl };
+            }
+        }
+
+        var normal = Vector3.Normalize(
+            Vector3.Cross(vertices[1] - vertices[0], vertices[2] - vertices[0]));
+        if (normal.Z < 0f)
+            normal = -normal;
+
+        return new TerrainSurfacePolygon(z, normal, vertices);
+    }
+
     /// <summary>
     /// Retail per-point water depth in meters — the amount the character's
     /// feet are allowed to sink below the contact plane before the