Add MrGameEng.Pathfinding and MrGameEng.Collisions modules

Pathfinding (depends on Core only): GridPathfinder with A* (octile/
Manhattan heuristic), Dijkstra and BFS over a game-implemented
IPathGrid; 4/8 connectivity, diagonals never cut corners. FlowField +
FlowFieldBuilder (multi-source Dijkstra) give crowds O(1) steering per
agent per frame. All buffers are grid-sized once and invalidated by a
generation stamp - repeated queries allocate nothing and clear nothing.

Collisions (Graphics exception: Transform2D, RectF): Collider component
(circle/AABB, offset, two-way layer masks), CollisionWorld - a uniform
spatial hash on flat arrays rebuilt from scratch each tick (O(n) for
movers, zero alloc after warm-up, deterministic pair order), pair
collection, QueryAabb and closest-hit Raycast. scene.UseCollisions()
registers CollisionSystem after movement systems.

30 new tests (string-map mazes, cost weighting, corner cutting, flow
descent; pair/mask/query/raycast). Sample gains a PathfindingScene
('path' console command): click to set the goal, 250 agents follow the
flow field, the A* path is highlighted, colliding agents flash red.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

tests/MrGameEng.Pathfinding.Tests/GridPathfinderTests.cs

@@ -0,0 +1,199 @@
+using Microsoft.Xna.Framework;
+using Xunit;
+
+namespace MrGameEng.Pathfinding.Tests;
+
+public class GridPathfinderTests
+{
+    private static List<Point> Path(IPathGrid grid, Point start, Point goal,
+        PathAlgorithm algorithm = PathAlgorithm.AStar,
+        GridConnectivity connectivity = GridConnectivity.Eight)
+    {
+        var pathfinder = new GridPathfinder(grid, connectivity);
+        var path = new List<Point>();
+        Assert.True(pathfinder.FindPath(start, goal, path, algorithm));
+        return path;
+    }
+
+    private static void AssertValidPath(IPathGrid grid, List<Point> path, Point start, Point goal)
+    {
+        Assert.Equal(start, path[0]);
+        Assert.Equal(goal, path[^1]);
+        for (var i = 0; i < path.Count; i++)
+        {
+            Assert.True(grid.IsPassable(path[i].X, path[i].Y), $"impassable cell {path[i]}");
+            if (i > 0)
+            {
+                var dx = Math.Abs(path[i].X - path[i - 1].X);
+                var dy = Math.Abs(path[i].Y - path[i - 1].Y);
+                Assert.True(dx <= 1 && dy <= 1 && dx + dy > 0, $"non-adjacent step {path[i - 1]} -> {path[i]}");
+            }
+        }
+    }
+
+    [Theory]
+    [InlineData(PathAlgorithm.AStar)]
+    [InlineData(PathAlgorithm.Dijkstra)]
+    [InlineData(PathAlgorithm.BreadthFirst)]
+    public void FindPath_OpenField_StraightLine(PathAlgorithm algorithm)
+    {
+        var grid = new TestGrid(
+            ".....",
+            ".....",
+            ".....");
+
+        var path = Path(grid, new Point(0, 1), new Point(4, 1), algorithm);
+
+        AssertValidPath(grid, path, new Point(0, 1), new Point(4, 1));
+        Assert.Equal(5, path.Count); // прямая, без лишних шагов
+    }
+
+    [Theory]
+    [InlineData(PathAlgorithm.AStar)]
+    [InlineData(PathAlgorithm.Dijkstra)]
+    [InlineData(PathAlgorithm.BreadthFirst)]
+    public void FindPath_WallsForceDetour(PathAlgorithm algorithm)
+    {
+        var grid = new TestGrid(
+            ".....",
+            "####.",
+            ".....");
+
+        var path = Path(grid, new Point(0, 0), new Point(0, 2), algorithm);
+
+        AssertValidPath(grid, path, new Point(0, 0), new Point(0, 2));
+        Assert.Contains(new Point(4, 1), path); // единственный проход
+    }
+
+    [Fact]
+    public void FindPath_NoRoute_ReturnsFalse()
+    {
+        var grid = new TestGrid(
+            ".#.",
+            ".#.",
+            ".#.");
+        var pathfinder = new GridPathfinder(grid);
+        var path = new List<Point>();
+
+        Assert.False(pathfinder.FindPath(new Point(0, 0), new Point(2, 0), path));
+        Assert.Empty(path);
+    }
+
+    [Fact]
+    public void FindPath_StartEqualsGoal_SinglePoint()
+    {
+        var grid = new TestGrid("...");
+
+        var path = Path(grid, new Point(1, 0), new Point(1, 0));
+
+        Assert.Equal([new Point(1, 0)], path);
+    }
+
+    [Fact]
+    public void FindPath_DiagonalNeverCutsCorners()
+    {
+        var grid = new TestGrid(
+            ".#",
+            "#.");
+        var pathfinder = new GridPathfinder(grid, GridConnectivity.Eight);
+        var path = new List<Point>();
+
+        // Диагональ (0,0)->(1,1) зажата стенами — пути нет.
+        Assert.False(pathfinder.FindPath(new Point(0, 0), new Point(1, 1), path));
+    }
+
+    [Fact]
+    public void FindPath_FourConnectivity_NoDiagonalSteps()
+    {
+        var grid = new TestGrid(
+            "...",
+            "...",
+            "...");
+
+        var path = Path(grid, new Point(0, 0), new Point(2, 2), connectivity: GridConnectivity.Four);
+
+        Assert.Equal(5, path.Count); // манхэттен: 4 шага
+        for (var i = 1; i < path.Count; i++)
+        {
+            var dx = Math.Abs(path[i].X - path[i - 1].X);
+            var dy = Math.Abs(path[i].Y - path[i - 1].Y);
+            Assert.Equal(1, dx + dy);
+        }
+    }
+
+    [Theory]
+    [InlineData(PathAlgorithm.AStar)]
+    [InlineData(PathAlgorithm.Dijkstra)]
+    public void FindPath_CostAware_AvoidsExpensiveTerrain(PathAlgorithm algorithm)
+    {
+        // Прямой путь через болото (цена 9) дороже обхода по краю.
+        var grid = new TestGrid(
+            ".....",
+            ".999.",
+            ".....");
+
+        var path = Path(grid, new Point(0, 1), new Point(4, 1), algorithm);
+
+        Assert.DoesNotContain(path, p => grid.Cost(p.X, p.Y) > 1f);
+    }
+
+    [Fact]
+    public void FindPath_BreadthFirst_IgnoresCosts()
+    {
+        var grid = new TestGrid(
+            ".....",
+            ".999.",
+            ".....");
+
+        var path = Path(grid, new Point(0, 1), new Point(4, 1), PathAlgorithm.BreadthFirst);
+
+        Assert.Equal(5, path.Count); // идёт напрямик через дорогие клетки
+    }
+
+    [Fact]
+    public void FindPath_ReusedInstance_GivesCleanResults()
+    {
+        var grid = new TestGrid(
+            ".....",
+            ".###.",
+            ".....");
+        var pathfinder = new GridPathfinder(grid);
+        var path = new List<Point>();
+
+        Assert.True(pathfinder.FindPath(new Point(0, 0), new Point(4, 2), path));
+        var first = path.ToArray();
+        Assert.True(pathfinder.FindPath(new Point(0, 0), new Point(4, 2), path));
+
+        Assert.Equal(first, path); // generation-сброс не оставляет мусора между запросами
+    }
+
+    [Fact]
+    public void FindPath_AStarMatchesDijkstraCost()
+    {
+        var grid = new TestGrid(
+            "..3..",
+            ".#3#.",
+            "..3..",
+            ".###.",
+            ".....");
+        var start = new Point(0, 0);
+        var goal = new Point(4, 4);
+
+        var aStar = Path(grid, start, goal, PathAlgorithm.AStar);
+        var dijkstra = Path(grid, start, goal, PathAlgorithm.Dijkstra);
+
+        Assert.Equal(PathCost(grid, dijkstra), PathCost(grid, aStar), 3);
+    }
+
+    private static float PathCost(IPathGrid grid, List<Point> path)
+    {
+        var total = 0f;
+        for (var i = 1; i < path.Count; i++)
+        {
+            var diagonal = path[i].X != path[i - 1].X && path[i].Y != path[i - 1].Y;
+            total += (diagonal ? 1.4142135f : 1f) * grid.Cost(path[i].X, path[i].Y);
+        }
+
+        return total;
+    }
+}