diffusion (#12)

Reviewed-on: #12

gdd.md

@@ -28,6 +28,27 @@ Add a tick counter as a UI element.
 Diffusing should use 'pull' operations; tiles should pull values from surrounding tiles.
 This is an attempt to think forwards to parallelising computation of diffusiong - ideally using the GPU.
 
+#### Diffusion Algorithm
+
+Diffusion is modelled as two-dimensional steady-state heat conduction.
+This means that the amount of a value does not change between the start and end of the computation of the diffusion step.
+The value at one 2D location is calculated based on the values of itself and its neighbours in the previous step.
+A diffusion coefficient controls the rate of diffusion.
+
+[Video explanation](https://www.youtube.com/watch?v=RGbV7T_iWT8)
+[Derivation](https://www.tec-science.com/thermodynamics/heat/heat-equation-diffusion-equation/)
+
+Implementation:
+
+```cs
+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);
+}
+```
+
 ### Tile Types
 
 Tiles start as wild tiles.

half-earth/materials/cursor.tres

@@ -4,6 +4,6 @@
 
 [resource]
 shader = ExtResource( 1 )
-shader_param/baseColor = Color( 0.992157, 1, 0, 1 )
+shader_param/lowColor = Color( 1, 0.960784, 0, 1 )
-shader_param/highlightColor = Color( 1, 0, 0.984314, 1 )
+shader_param/highColor = Color( 0.921569, 0, 1, 1 )
-shader_param/isHighlighted = 0
+shader_param/t = null

half-earth/materials/tile.tres

@@ -5,6 +5,6 @@
 [resource]
 resource_local_to_scene = true
 shader = ExtResource( 1 )
-shader_param/baseColor = Color( 0.0823529, 0, 1, 1 )
+shader_param/lowColor = Color( 0, 0, 0, 1 )
-shader_param/highlightColor = Color( 1, 0, 0, 1 )
+shader_param/highColor = Color( 1, 0.560784, 0, 1 )
-shader_param/isHighlighted = null
+shader_param/t = null

half-earth/nodes/clock.tscn

@@ -0,0 +1,7 @@
+[gd_scene load_steps=2 format=2]
+
+[ext_resource path="res://scripts/Clock.cs" type="Script" id=1]
+
+[node name="Clock" type="Node"]
+script = ExtResource( 1 )
+_tickRate = 10.0

half-earth/nodes/debug_ui.tscn

@@ -0,0 +1,36 @@
+[gd_scene load_steps=2 format=2]
+
+[ext_resource path="res://scripts/DebugUI.cs" type="Script" id=1]
+
+[node name="Debug UI" type="Control"]
+anchor_right = 1.0
+anchor_bottom = 1.0
+script = ExtResource( 1 )
+TicksLabelPath = NodePath("Ticks")
+PauseLabelPath = NodePath("Paused")
+
+[node name="Ticks" type="Label" parent="."]
+anchor_left = 1.0
+anchor_top = 1.0
+anchor_right = 1.0
+anchor_bottom = 1.0
+margin_right = -10.0
+margin_bottom = -30.0
+grow_horizontal = 0
+grow_vertical = 0
+text = "ticks: 0"
+align = 2
+valign = 2
+
+[node name="Paused" type="Label" parent="."]
+anchor_left = 1.0
+anchor_top = 1.0
+anchor_right = 1.0
+anchor_bottom = 1.0
+margin_right = -10.0
+margin_bottom = -10.0
+grow_horizontal = 0
+grow_vertical = 0
+text = "pause: false"
+align = 2
+valign = 2

half-earth/nodes/game.tscn

@@ -1,11 +1,23 @@
-[gd_scene load_steps=3 format=2]
+[gd_scene load_steps=5 format=2]
 
 [ext_resource path="res://nodes/grid.tscn" type="PackedScene" id=1]
 [ext_resource path="res://nodes/grid_cursor.tscn" type="PackedScene" id=2]
+[ext_resource path="res://nodes/debug_ui.tscn" type="PackedScene" id=3]
+[ext_resource path="res://nodes/clock.tscn" type="PackedScene" id=4]
 
-[node name="Root" type="Node2D"]
+[node name="Root" type="Node"]
 
 [node name="Grid" parent="." instance=ExtResource( 1 )]
+DiffusionCoefficient = 0.1
 
 [node name="Cursor" parent="." instance=ExtResource( 2 )]
 Grid = NodePath("../Grid")
+
+[node name="Debug UI" parent="." instance=ExtResource( 3 )]
+
+[node name="Clock" parent="." instance=ExtResource( 4 )]
+_autoTick = true
+
+[connection signal="OnPauseChanged" from="Clock" to="Debug UI" method="_on_Clock_OnPauseChanged"]
+[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/Clock.cs

@@ -0,0 +1,67 @@
+using Godot;
+using System;
+
+public class Clock : Node
+{
+    [Signal]
+    delegate void OnTick(int ticks);
+    [Signal]
+    delegate void OnPauseChanged(bool paused);
+
+    [Export(PropertyHint.None, "Number of ticks per second")]
+    private float _tickRate;
+    private float TickPeriod => 1.0f / _tickRate;
+
+    [Export]
+    private bool _autoTick;
+
+    private int _ticks = 0;
+    private bool _paused = false;
+
+    public override void _Input(InputEvent @event)
+    {
+        base._Input(@event);
+
+        if (@event is InputEventKey keyEvent && keyEvent.Pressed)
+        {
+            switch ((KeyList)keyEvent.Scancode)
+            {
+                case KeyList.Space:
+                    if (_autoTick)
+                    {
+                        _paused = !_paused;
+                        EmitSignal(nameof(OnPauseChanged), _paused);
+                        return;
+                    }
+                    Tick();
+                    break;
+            }
+        }
+    }
+
+    private float _secondsSinceLastTick;
+
+    public override void _Process(float delta)
+    {
+        base._Process(delta);
+
+        if (!_autoTick)
+            return;
+
+        if (_paused)
+            return;
+
+        _secondsSinceLastTick += delta;
+        if (_secondsSinceLastTick < TickPeriod)
+            return;
+
+        _secondsSinceLastTick -= TickPeriod;
+        Tick();
+    }
+
+    private void Tick()
+    {
+        _ticks++;
+        EmitSignal(nameof(OnTick), _ticks);
+    }
+}

half-earth/scripts/DebugUI.cs

@@ -0,0 +1,37 @@
+using Godot;
+using System;
+
+public class DebugUI : Control
+{
+    [Export]
+    public NodePath TicksLabelPath { private get; set; }
+    private Label _ticksLabel;
+
+    [Export]
+    public NodePath PauseLabelPath { private get; set; }
+    private Label _pauseLabel;
+
+    public override void _Ready()
+    {
+        _ticksLabel = GetNode<Label>(TicksLabelPath);
+        _pauseLabel = GetNode<Label>(PauseLabelPath);
+
+        SetTicksText(0);
+        SetPauseText(false);
+    }
+
+    #region Signals
+    public void _on_Clock_OnPauseChanged(bool paused) => SetPauseText(paused);
+    public void _on_Clock_OnTick(int ticks) => SetTicksText(ticks);
+    #endregion
+
+    private void SetTicksText(int ticks)
+    {
+        _ticksLabel.Text = $"ticks: {ticks}";
+    }
+
+    private void SetPauseText(bool paused)
+    {
+        _pauseLabel.Text = $"pause: {paused}";
+    }
+}

half-earth/scripts/GridCursor.cs

@@ -8,18 +8,18 @@ public class GridCursor : Sprite
     private WorldGrid _grid;
     private ShaderMaterial _material;
 
-    private const string IS_HIGHLIGHTED = "isHighlighted";
+    private const string T = "t";
 
     public override void _Ready()
     {
         _grid = GetNode<WorldGrid>(Grid);
         _material = (ShaderMaterial)Material;
     }
-    
+
     public override void _Input(InputEvent @event)
     {
         base._Input(@event);
-        
+
         if (@event is InputEventMouseMotion mouseMoveEvent)
         {
             var pos = mouseMoveEvent.Position;
@@ -37,12 +37,12 @@ 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(IS_HIGHLIGHTED, 1);
+                        _material.SetShaderParam(T, 1f);
                     }
                     else
                     {
-                        _material.SetShaderParam(IS_HIGHLIGHTED, 0);
+                        _material.SetShaderParam(T, 0f);
                     }
                     break;
             }

half-earth/scripts/Tile.cs

@@ -0,0 +1,8 @@
+using Godot;
+
+public struct Tile
+{
+    public bool isHighlighted;
+    public float value;
+    public ShaderMaterial material;
+}

half-earth/scripts/WorldGrid.cs

@@ -8,16 +8,15 @@ public class WorldGrid : Node2D
 
     [Export]
     public int Size { get; set; }
-    
+
     [Export]
     public int CellSize { get; set; }
-    
+
-    private struct Tile
+    [Export]
-    {
+    public float DiffusionCoefficient { get; set; } = 0.01f;
-        public bool isHighlighted;
+
-        public ShaderMaterial material;
-    }
     private Tile[,] _tiles;
+    private float[,] _nextValues = null;
 
     // Called when the node enters the scene tree for the first time.
     public override void _Ready()
@@ -28,18 +27,18 @@ public class WorldGrid : Node2D
     public override void _Process(float delta)
     {
         base._Process(delta);
-        
+
         for (int x = 0; x < Size; x++)
         {
             for (int y = 0; y < Size; y++)
             {
                 var tile = _tiles[x, y];
                 var material = tile.material;
-                material.SetShaderParam("isHighlighted", tile.isHighlighted ? 1 : 0);
+                material.SetShaderParam("t", tile.value);
             }
         }
     }
-    
+
     public bool IsInBounds(int x, int y)
     {
         return x >= 0 && x < Size && y >= 0 && y < Size;
@@ -53,6 +52,11 @@ public class WorldGrid : Node2D
         _tiles[x, y].isHighlighted ^= true;
     }
 
+    public void SetTileValue(int x, int y, float value)
+    {
+        _tiles[x, y].value = value;
+    }
+
     public void GetGridPos(Vector2 position, out int x, out int y)
     {
         x = Mathf.FloorToInt(position.x / CellSize);
@@ -75,8 +79,9 @@ public class WorldGrid : Node2D
     private void GenerateGrid(int size)
     {
         this.Clear();
-        
+
         _tiles = new Tile[size, size];
+        _nextValues = new float[size, size];
 
         for (int x = 0; x < size; x++)
         {
@@ -84,7 +89,8 @@ public class WorldGrid : Node2D
             {
                 var tile = new Tile();
                 tile.isHighlighted = false;
-                
+                tile.value = 0.0f;
+
                 var node = TileScene.Instance<Node2D>();
                 this.AddChild(node);
                 var position = new Vector2
@@ -95,9 +101,63 @@ public class WorldGrid : Node2D
                 node.Position = position;
                 var canvasItem = (CanvasItem)node;
                 tile.material = (ShaderMaterial)canvasItem.Material;
-                
+
                 _tiles[x, y] = tile;
             }
         }
     }
+
+    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];
+            }
+        }
+    }
 }

half-earth/shaders/tile_shader.gdshader

@@ -1,9 +1,9 @@
 shader_type canvas_item;
 
-uniform vec4 baseColor : hint_color;
+uniform vec4 lowColor : hint_color;
-uniform vec4 highlightColor : hint_color;
+uniform vec4 highColor : hint_color;
-uniform int isHighlighted;
+uniform float t;
 
 void fragment() {
-	COLOR = mix(baseColor, highlightColor, float(isHighlighted));
+	COLOR = mix(lowColor, highColor, t);
 }