add basic heat transfer #4

half-earth/materials/tile.tres

@@ -5,6 +5,6 @@
 [resource]
 resource_local_to_scene = true
 shader = ExtResource( 1 )
-shader_param/lowColor = Color( 0.0313726, 0, 1, 1 )
-shader_param/highColor = Color( 1, 0, 0, 1 )
+shader_param/lowColor = Color( 0, 0, 0, 1 )
+shader_param/highColor = Color( 1, 0.560784, 0, 1 )
 shader_param/t = null

half-earth/nodes/game.tscn

@@ -16,4 +16,5 @@ Grid = NodePath("../Grid")
 
 [node name="Clock" parent="." instance=ExtResource( 4 )]
 
+[connection signal="OnTick" from="Clock" to="Grid" method="_on_Clock_OnTick"]
 [connection signal="OnTick" from="Clock" to="Debug UI" method="_on_Clock_OnTick"]

half-earth/scripts/GridCursor.cs

@@ -37,7 +37,7 @@ public class GridCursor : Sprite
                     {
                         var pos = mouseButtonEvent.Position;
                         _grid.GetGridPos(pos, out var x, out var y);
-                        _grid.ToggleTileHighlight(x, y);
+                        _grid.SetTileValue(x, y, 1.0f);
                         _material.SetShaderParam(T, 1f);
                     }
                     else

half-earth/scripts/WorldGrid.cs

@@ -12,7 +12,11 @@ public class WorldGrid : Node2D
     [Export]
     public int CellSize { get; set; }
 
+    [Export]
+    public float DiffusionCoefficient { get; set; } = 0.01f;
+
     private Tile[,] _tiles;
+    private float[,] _nextValues = null;
 
     // Called when the node enters the scene tree for the first time.
     public override void _Ready()
@@ -30,7 +34,7 @@ public class WorldGrid : Node2D
             {
                 var tile = _tiles[x, y];
                 var material = tile.material;
-                material.SetShaderParam("t", tile.isHighlighted ? 1f : 0f);
+                material.SetShaderParam("t", tile.value);
             }
         }
     }
@@ -77,6 +81,7 @@ public class WorldGrid : Node2D
         this.Clear();
 
         _tiles = new Tile[size, size];
+        _nextValues = new float[size, size];
 
         for (int x = 0; x < size; x++)
         {
@@ -101,4 +106,58 @@ public class WorldGrid : Node2D
             }
         }
     }
+
+    public void _on_Clock_OnTick(int ticks)
+    {
+        Diffuse();
+    }
+
+    private float TransferHeat(float t0, float alpha, float nx, float ny, float px, float py)
+    {
+        float d2tdx2 = nx - 2 * t0 + px;
+        float d2tdy2 = ny - 2 * t0 + py;
+        return t0 + alpha * (d2tdx2 + d2tdy2);
+    }
+
+    private void GetNeighbourTemperatures(int x, int y, out float nx, out float ny, out float px, out float py)
+    {
+        // default value
+        var t = _tiles[x, y].value;
+
+        nx = x > 0 ? _tiles[x - 1, y].value : t;
+        px = x < Size - 1 ? _tiles[x + 1, y].value : t;
+
+        ny = y > 0 ? _tiles[x, y - 1].value : t;
+        py = y < Size - 1 ? _tiles[x, y + 1].value : t;
+    }
+
+    private void Diffuse()
+    {
+        for (int x = 0; x < Size; x++)
+        {
+            for (int y = 0; y < Size; y++)
+            {
+                float t = _tiles[x, y].value;
+                var D = DiffusionCoefficient;
+
+                GetNeighbourTemperatures(
+                    x, y,
+                    out var nx,
+                    out var ny,
+                    out var px,
+                    out var py);
+
+                // current value
+                _nextValues[x, y] = TransferHeat(t, D, nx, ny, px, py);
+            }
+        }
+
+        for (int x = 0; x < Size; x++)
+        {
+            for (int y = 0; y < Size; y++)
+            {
+                _tiles[x, y].value = _nextValues[x, y];
+            }
+        }
+    }
 }