initial commit

.gitignore

@@ -0,0 +1,56 @@
+/[Ll]ibrary/
+/[Tt]emp/
+/[Oo]bj/
+/[Bb]uild/
+/[Bb]uilds/
+/[Ll]ogs/
+/[Mm]emoryCaptures/
+
+# Never ignore Asset meta data
+!/[Aa]ssets/**/*.meta
+
+# Uncomment this line if you wish to ignore the asset store tools plugin
+# /[Aa]ssets/AssetStoreTools*
+
+# Autogenerated Jetbrains Rider plugin
+[Aa]ssets/Plugins/Editor/JetBrains*
+
+# Visual Studio cache directory
+.vs/
+
+# Gradle cache directory
+.gradle/
+
+# Autogenerated VS/MD/Consulo solution and project files
+ExportedObj/
+.consulo/
+*.csproj
+*.unityproj
+*.sln
+*.suo
+*.tmp
+*.user
+*.userprefs
+*.pidb
+*.booproj
+*.svd
+*.pdb
+*.mdb
+*.opendb
+*.VC.db
+
+# Unity3D generated meta files
+*.pidb.meta
+*.pdb.meta
+*.mdb.meta
+
+# Unity3D generated file on crash reports
+sysinfo.txt
+
+# Builds
+*.apk
+*.unitypackage
+
+# Crashlytics generated file
+crashlytics-build.properties
+

Assembly-CSharp.csproj.DotSettings

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+<wpf:ResourceDictionary xml:space="preserve" xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml" xmlns:s="clr-namespace:System;assembly=mscorlib" xmlns:ss="urn:shemas-jetbrains-com:settings-storage-xaml" xmlns:wpf="http://schemas.microsoft.com/winfx/2006/xaml/presentation">
+	<s:Boolean x:Key="/Default/CodeInspection/NamespaceProvider/NamespaceFoldersToSkip/=assets/@EntryIndexedValue">False</s:Boolean></wpf:ResourceDictionary>

Assets/Editor.meta

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+folderAsset: yes
+DefaultImporter:
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Assets/Editor/GraphGeneratorUI.cs

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+using System;
+using Assets;
+using UnityEditor;
+using UnityEngine;
+
+namespace Editor
+{
+    [CustomEditor(typeof (GraphGenerator))]
+    public class GraphGeneratorUI : UnityEditor.Editor
+    {
+        private string _threshold;
+        
+        public override void OnInspectorGUI()
+        {
+            GraphGenerator generator = (GraphGenerator)target;
+
+            DrawDefaultInspector();
+
+            if (GUILayout.Button("Reset")) {
+                generator.Reset();
+            }
+
+            if (GUILayout.Button("Generate")) {
+                generator.Generate();
+            }
+
+            if (GUILayout.Button("Step")) {
+                generator.Step();
+            }
+
+            GUILayout.BeginHorizontal();
+            {
+                _threshold = GUILayout.TextField(_threshold);
+
+                if (GUILayout.Button("Go")) {
+                    try
+                    {
+                        generator.Rewind(float.Parse(_threshold));
+                    }
+                    catch
+                    {
+                        GUILayout.Label("You should pass valid number.");
+                    }
+                }
+            }
+            GUILayout.EndHorizontal();
+        }
+
+        private void OnSceneGUI()
+        {
+            GraphGenerator generator = (GraphGenerator)target;
+
+            if (generator.generator != null)
+            {
+                var moved = Handles.PositionHandle(generator.transform.position + Vector3.up * (float)generator.generator.Line.Directrix, Quaternion.identity);
+                generator.generator.Line.Directrix = moved.y;
+            }
+        }
+    }
+}

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Assets/Generators.meta

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Assets/Generators/INoiseGenerator.cs

@@ -0,0 +1,9 @@
+using UnityEngine;
+
+namespace Generators
+{
+    public interface IGenerator
+    {
+        double GetValue(Vector2 position);
+    }
+}

Assets/Generators/INoiseGenerator.cs.meta

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Assets/Generators/IslandGenerator.cs

@@ -0,0 +1,29 @@
+using UnityEngine;
+
+namespace Generators
+{
+    public class IslandGenerator : IGenerator
+    {
+        private IGenerator noise;
+
+        public float Inner { get; set; } = 20;
+        public float Outer { get; set; } = 23;
+
+        public float Threshold { get; set; } = .5f;
+
+        public IslandGenerator(IGenerator noise)
+        {
+            this.noise = noise;
+        }
+
+        public double GetValue(Vector2 position)
+        {
+            var distance = position.magnitude / 10;
+            distance = (distance - Inner) / (Outer - Inner);
+
+            var result = noise.GetValue(position) + .75 * (Mathf.Clamp(0, distance, 1) - 1);
+
+            return result > Threshold ? 1 : 0;
+        }
+    }
+}

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Assets/Generators/PerlinNoiseGenerator.cs

@@ -0,0 +1,36 @@
+using UnityEngine;
+
+namespace Generators
+{
+    public class PerlinNoiseGenerator : IGenerator
+    {
+        public float Scale { get; set; } = 0.001f;
+        public Vector2 Offset { get; set; } = new Vector2(.0f, .0f);
+        public int Iterations { get; set; } = 8;
+        public float Decay { get; set; } = .7f;
+        public float Lacunarity { get; set; } = 1.71f;
+
+        public double GetValue(Vector2 position)
+        {
+            var amplitude = 1.0;
+            var scale     = Scale;
+            var result    = 0.0;
+
+            for (int i = 0; i < Iterations; i++) {
+                result += amplitude * Calculate(position, scale);
+
+                amplitude *= Decay;
+                scale     *= Lacunarity;
+            }
+
+            return result / ((1 - System.Math.Pow(Decay, Iterations)) / (1 - Decay));
+        }
+
+        private double Calculate(Vector2 position, float scale)
+        {
+            var final = (position + Offset) * scale;
+
+            return Mathf.PerlinNoise(final.x, final.y);
+        }
+    }
+}

Assets/Generators/PerlinNoiseGenerator.cs.meta

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Assets/Generators/PoissonDiskSampler.cs

@@ -0,0 +1,103 @@
+using System.Collections.Generic;
+using System.Linq;
+using UnityEngine;
+
+namespace Assets.Generators
+{
+    public class PoissonDiskSampler
+    {
+        public System.Random Generator { get; set; } = new System.Random();
+        
+        private int k;
+        private float r;
+
+        private float Random(float max, float min = 0)
+        {
+            return (float)Generator.NextDouble() * (max - min) + min;
+        }
+        
+        public PoissonDiskSampler(float r, int k = 30)
+        {
+            this.k = k;
+            this.r = r;
+        }
+
+        public IEnumerable<Vector3> Generate(float width, float height)
+        {
+            var size = r / Mathf.Sqrt(2);
+
+            var grid = new Dictionary<(int, int), Vector3>();
+            var active = new List<Vector3>();
+
+            var initial = new Vector3(Random(width), Random(height));
+
+            void AddToGrid(Vector3 point)
+            {
+                grid.Add(
+                    (Mathf.FloorToInt(point.x / size), Mathf.FloorToInt(point.y / size)),
+                    point
+                );
+
+                active.Add(point);
+            }
+
+            bool IsPointOk(Vector3 point)
+            {
+                if (point.x < 0 || point.y < 0 || point.x > width || point.y > height)
+                {
+                    return false;
+                }
+
+                var x = Mathf.FloorToInt(point.x / size);
+                var y = Mathf.FloorToInt(point.y / size);
+
+                var neighbours = (new List<(int, int)>() {
+                    (x - 1, y + 1), (x, y + 1), (x + 1, y + 1),
+                    (x - 1, y),     (x, y),     (x + 1, y),
+                    (x - 1, y - 1), (x, y - 1), (x + 1, y - 1)
+                });
+
+                return neighbours
+                    .Where(p => grid.ContainsKey(p))
+                    .All(p => Vector3.Distance(point, grid[p]) > r);
+            }
+
+            Vector3 RandomPoint(Vector3 origin)
+            {
+                var angle = Random(Mathf.PI * 2);
+                var length = Random(2 * r, r);
+
+                return origin + new Vector3(Mathf.Sin(angle), Mathf.Cos(angle)) * length;
+            }
+
+            AddToGrid(initial);
+            yield return initial;
+
+            int watchdog = 3000000;
+
+            while (active.Count > 0 && watchdog-- > 0)
+            {
+                var current = Mathf.FloorToInt(Random(active.Count));
+                var point = active[current];
+
+                var i = 0;
+                for (; i < k; i++)
+                {
+                    var candidate = RandomPoint(point);
+
+                    if (IsPointOk(candidate))
+                    {
+                        AddToGrid(candidate);
+                        yield return candidate;
+                        break;
+                    }
+                }
+
+                if (i >= k)
+                {
+                    active.RemoveAt(current);
+                }
+            }
+        }
+    }
+}

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Assets/Map/Graph.cs

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+using System.Collections.Generic;
+
+namespace Assets.Map
+{
+    public class Graph<T>
+    {
+        public IList<T> Vertices { get; internal set; } = new List<T>();
+        public ISet<(int, int)> Edges { get; internal set; } = new HashSet<(int, int)>();
+    }
+}

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Assets/Map/Map.cs

@@ -0,0 +1,10 @@
+using System;
+
+namespace Assets.Map
+{
+    [Serializable]
+    public class Map
+    {
+        public readonly Graph<Section> Sections = new Graph<Section>();  
+    }
+}

Assets/Map/Map.cs.meta

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Assets/Map/Section.cs

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+namespace Assets.Map
+{
+    public class Section
+    {
+        public double x;
+        public double y;
+    }
+}

Assets/Map/Section.cs.meta

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Assets/Scenes/SampleScene.unity.meta

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Assets/Scripts.meta

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Assets/Scripts/CircleGenerator.cs

@@ -0,0 +1,61 @@
+using System.Collections.Generic;
+using System.Linq;
+using UnityEngine;
+
+[RequireComponent(typeof(MeshFilter), typeof(MeshRenderer))]
+public class CircleGenerator : MonoBehaviour
+{
+    [Range(1, 200)]
+    public int NodeCount = 3;
+
+    public int Details = 150;
+
+    public float Radius = 20.0f;
+
+    [Range(0, 1)]
+    public float AngleVariation = 0.5f;
+
+    public float RadiusVariation = 2f;
+    private Random random = new Random();
+
+    private float RandomCoefficient(float multiplier) => 2 * (Random.value - 0.5f) * multiplier;
+
+    public void Generate()
+    {
+        Vector3 center = new Vector3(0, 0, 0);
+        Mesh mesh = new Mesh();
+
+        var maxAngleVariation = AngleVariation * Mathf.PI * 2 / Details;
+
+        var vertices = new List<Vector3>();
+        for (int i = 0; i < Details; i++)
+        {
+            var angle = i * Mathf.PI * 2 / Details + RandomCoefficient(maxAngleVariation);
+            var radius = Radius + RandomCoefficient(RadiusVariation);
+
+            Vector3 direction = new Vector3(Mathf.Sin(angle), 0, Mathf.Cos(angle));
+            vertices.Add(direction * radius);
+        }
+
+        var triangles = new List<int>();
+        for (int i = 0; i < Details - 2; i++)
+        {
+            triangles.Add(0);
+            triangles.Add(i);
+            triangles.Add(i + 1);
+        }
+
+        var normals = new List<Vector3>();
+        for (int i = 0; i < Details; i++)
+        {
+            normals.Add(-Vector3.forward);
+        }
+
+        mesh.vertices  = vertices.ToArray();
+        mesh.triangles = triangles.ToArray();
+        mesh.normals   = normals.ToArray();
+
+        var mf = GetComponent<MeshFilter>();
+        mf.mesh = mesh;
+    }
+}

Assets/Scripts/CircleGenerator.cs.meta

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Assets/Scripts/GraphGenerator.cs

@@ -0,0 +1,190 @@
+using System;
+using System.Collections.Generic;
+using System.Linq;
+using Assets.Generators;
+using Assets.Voronoi;
+using UnityEditor;
+using UnityEngine;
+using Random = System.Random;
+
+namespace Assets
+{
+    [Serializable]
+    public class GraphGeneratorDebug
+    {
+        public bool enabled = true;
+        public bool displayPoints = true;
+        public bool displayBeachLine = true;
+        public bool displayParabolas = false;
+        public bool displayVertices = true;
+        public bool displayNeighbours = false;
+        public bool displayLabels= false;
+    }
+
+    [RequireComponent(typeof(MeshRenderer), typeof(MeshFilter)), ExecuteInEditMode]
+    public class GraphGenerator : MonoBehaviour
+    {
+        MeshFilter _filter;
+        private PoissonDiskSampler _sampler;
+        IList<Vector3> _points = new List<Vector3>();
+    
+        public VoronoiGenerator generator;
+        public int seed = Environment.TickCount;
+        public Vector2 size = new Vector2();
+        public GraphGeneratorDebug debug;
+        [Range(2.0f, 64.0f)]
+        public float radius = 8;
+    
+        private double _directrix = 0.0f;
+
+        private Random _random;
+        private Dictionary<Vector3, Color> _colors;
+
+        void Start()
+        {
+            _filter = GetComponent<MeshFilter>();
+
+            Reset();
+        }
+
+        public Vector3 RandomPoint()
+        {
+            return _points[_random.Next(_points.Count)];
+        }
+
+        public void Reset()
+        {
+            _colors = new Dictionary<Vector3, Color>();
+            _random = new System.Random(seed);
+            
+            _sampler = new PoissonDiskSampler(radius);
+            _sampler.Generator = _random;
+        
+            _points = new List<Vector3>(_sampler.Generate(size.x, size.y));
+
+            for (int i = 0; i < 10; i++)
+            {
+                _colors[RandomPoint()] = Color.yellow;
+            }
+
+//        points = new List<Vector3>()
+//        {
+//            new Vector3(15.7f, 5.9f),
+//            new Vector3(37.9f, 10.3f),
+//            new Vector3(24.6f, 18.1f),
+//            new Vector3(53.5f, 8.0f),
+//        };
+        
+            generator = new VoronoiGenerator(_points.Select(x => new Point(x.x, x.y)).ToList());
+        }
+
+        public void Generate()
+        {
+            generator.Generate();
+        }
+    
+        public void Step()
+        {
+            generator.Step();
+            _directrix = generator.Line.Directrix;
+        }
+
+        void OnDrawGizmos()
+        {
+            
+            if (!debug.enabled) return;
+
+            if (debug.displayPoints)
+            {
+
+                foreach (var point in _points)
+                {
+                    Gizmos.color = _colors.ContainsKey(point) ? _colors[point] : Color.white;
+                    Gizmos.DrawSphere(point, 1);
+                    
+                    if (debug.displayLabels) Handles.Label(point, $"({point.x:F1}, {point.y:F1})");
+                }
+            }
+            
+            if (generator is null) return;
+
+            if (debug.displayNeighbours)
+            {
+                Gizmos.color = Color.yellow;
+
+                foreach (var site in generator.Sites)
+                {
+                    var vecStart = new Vector3((float)site.Point.x, (float)site.Point.y);
+                    foreach (var neighbour in site.Neighbours)
+                    {
+                        var vecEnd = new Vector3((float)neighbour.Point.x, (float)neighbour.Point.y);
+                        Gizmos.DrawLine(vecStart, vecEnd);
+                    }
+                }
+            }
+
+            
+            Gizmos.color = Color.green;
+            foreach (var edge in generator.Edges)
+            {
+                var vecStart = new Vector3((float)edge.start.x, (float)edge.start.y);
+                var vecEnd = new Vector3((float)edge.end.x, (float)edge.end.y);
+                
+                Gizmos.DrawLine(vecStart, vecEnd);
+            }
+
+            Gizmos.color = Color.red;
+            Gizmos.DrawLine(new Vector3(0, (float)generator.Line.Directrix), new Vector3(size.x, (float)generator.Line.Directrix));
+            Gizmos.color = Color.blue;
+
+            Vector3 start;
+            
+            if (debug.displayParabolas)
+            {
+                foreach (var parabola in generator.Line.Parabolas)
+                {
+                    start = new Vector3(-size.x, (float)generator.Line.EvalParabola(parabola.Site.Point, -size.x));
+                    for (var x = -size.x + 0.1f; x < size.x * 2; x += 0.1f)
+                    {
+                        var point = new Vector3(x, (float)generator.Line.EvalParabola(parabola.Site.Point, x));
+                        Gizmos.DrawLine(start, point);
+
+                        start = point;
+                    }
+                }
+            }
+
+            if (debug.displayVertices)
+            {
+                foreach (var vertex in generator.Vertices)
+                {
+                    var point = new Vector3((float)vertex.x, (float)vertex.y);
+                
+                    Gizmos.DrawSphere(point, 1);
+                    if (debug.displayLabels) Handles.Label(point, $"({point.x:F1}, {point.y:F1})");
+                }
+            }
+        
+            if (debug.displayBeachLine)
+            {
+                Gizmos.color = Color.white;
+                start = new Vector3(-size.x, (float)generator.Line.Eval(-size.x));
+                for (var x = -size.x + 0.1f; x < size.x * 2; x += 0.1f)
+                {
+                    var point = new Vector3(x, (float)generator.Line.Eval(x));
+                    Gizmos.DrawLine(start, point);
+
+                    start = point;
+                }
+            }
+        }
+
+        public void Rewind(float y)
+        {
+            while (generator.Line.Directrix < y && !generator.Done)
+            {
+                generator.Step();
+            }
+        }
+    }
+}

Assets/Scripts/GraphGenerator.cs.meta

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Assets/Scripts/MapRenderer.cs

@@ -0,0 +1,57 @@
+using System;
+using Generators;
+using UnityEngine;
+
+public class MapRenderer : MonoBehaviour
+{
+    public Renderer mapRenderer;
+    public IGenerator generator;
+
+    public Vector2 Offset;
+    public float Scale;
+
+    [Range(0, 1)]
+
+    public float Decay;
+    [Range(0, 4)]
+    public float Lacunarity;
+
+    [Range(0, 1)]
+    public float Threshold;
+
+    public void DrawMap(int width, int height)
+    {
+        var texture = new Texture2D(width, height);
+        var colors  = new Color[width * height];
+
+        var position = new Vector2(0.0f, 0.0f);
+
+        generator = new PerlinNoiseGenerator { 
+            Scale = Scale, 
+            Offset = Offset,
+            Decay = Decay,
+            Lacunarity = Lacunarity
+        };
+
+        generator = new IslandGenerator(generator) { 
+            Threshold = Threshold
+        };
+
+        for (int x = 0; x < width; x++)
+        {
+            for (int y = 0; y < height; y++)
+            {
+                position.x = x - width / 2;
+                position.y = y - height / 2;
+
+                colors[y * width + x] = Color.Lerp(Color.black, Color.white, (float)generator.GetValue(position));
+            }
+        }
+
+        texture.SetPixels(colors);
+        texture.Apply();
+
+        mapRenderer.sharedMaterial.mainTexture = texture;
+        mapRenderer.transform.localScale = new Vector3(width / 100.0f, 1, height / 100.0f);
+    } 
+}

Assets/Scripts/MapRenderer.cs.meta

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Assets/Voronoi.meta

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Assets/Voronoi/BeachLine.cs

@@ -0,0 +1,205 @@
+using System;
+using System.Collections.Generic;
+using System.Runtime.CompilerServices;
+using static System.Math;
+
+namespace Assets.Voronoi
+{
+
+    public class Edge
+    {
+        public Point start = null;
+        public Point end = null;
+    }
+    
+    public class Parabola
+    {
+        public Parabola(Site site)
+        {
+            Site = site;
+        }
+
+        public Site Site { get; internal set; }
+        public EdgeEvent Event { get; internal set; }
+        
+        public Edge LeftEdge { get; set; }
+        public Edge RightEdge { get; set; }
+
+        public override string ToString()
+        {
+            return $"({Site.Point.x}, {Site.Point.y})";
+        }
+    }
+    
+    public class BeachLine
+    {
+        private IDictionary<RedBlackNode<Point>, EdgeEvent> _events = new Dictionary<RedBlackNode<Point>, EdgeEvent>();
+        private RedBlackTree<Parabola> _tree = new RedBlackTree<Parabola>();
+        public double Directrix { get; set; } = 0.0f;
+
+        public IEnumerable<Parabola> Parabolas
+        {
+            get
+            {
+                if (!_tree.IsEmpty)
+                {
+                    var current = _tree.Root;
+
+                    while (current.Left != null)
+                        current = current.Left;
+
+                    while (current != null)
+                    {
+                        yield return current.Value;
+                        current = current.Next;
+                    }
+                }
+            }
+        }
+
+        public RedBlackNode<Parabola> AddParabola(Site site, RedBlackNode<Parabola> node = null)
+        {
+            if (node == null)
+            {
+                node = new RedBlackNode<Parabola>(new Parabola(site));
+                
+                _tree.Root = node;
+            }
+            else
+            {
+                if (node.Value.Event != null) node.Value.Event.IsValid = false;
+
+                _tree.InsertBefore(node, new Parabola(node.Value.Site));
+                _tree.InsertAfter(node, new Parabola(node.Value.Site));
+
+                node.Value = new Parabola(site);
+            }
+
+            return node;
+        }
+
+        public void RemoveParabola(RedBlackNode<Parabola> parabola)
+        {
+            _tree.Remove(parabola);
+        }
+
+        public RedBlackNode<Parabola> FindParabola(double x)
+        {
+            if (_tree.IsEmpty) 
+                return null;
+            
+            var current = _tree.Root;
+
+            while (current != null)
+            {
+                if (x < Left(current))
+                {
+                    current = current.Left;
+                }
+                else if (x > Right(current))
+                {
+                    current = current.Right;
+                }
+                else
+                {
+                    return current;
+                }
+            }
+
+            throw new Exception("WTF?");
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public double Left(RedBlackNode<Parabola> node)
+        {
+            return node.Previous == null 
+                ? double.NegativeInfinity 
+                : IntersectParabola(node.Previous.Value.Site.Point, node.Value.Site.Point);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        public double Right(RedBlackNode<Parabola> node)
+        {
+            return node.Next == null 
+                ? double.PositiveInfinity 
+                : IntersectParabola(node.Value.Site.Point, node.Next.Value.Site.Point);
+        }
+
+        public double EvalParabola(Point f, double x)
+        {
+            var nominator = Pow(x - f.x, 2) + f.y * f.y - Directrix * Directrix;
+            return nominator / (2 * (f.y - Directrix));
+        }
+
+        public double Eval(double x)
+        {
+            var parabola = FindParabola(x);
+
+            if (parabola is null) return Directrix;
+
+            return EvalParabola(parabola.Value.Site.Point, x);
+        }
+
+        private Point Circle(RedBlackNode<Parabola> node)
+        {
+            if (node.Previous == null || node.Next == null)
+                return null;
+
+            var a = node.Previous.Value.Site.Point;
+            var b = node.Value.Site.Point;
+            var c = node.Next.Value.Site.Point;
+
+            if ((a.x - b.x) * (c.y - b.y) - (c.x - b.x) * (a.y - b.y) > 0.000001)
+                return null;
+            
+            var A = a.x * (b.y - c.y) - a.y * (b.x - c.x) + b.x * c.y - c.x * b.y;
+            var B = (a.x * a.x + a.y * a.y) * (c.y - b.y)
+                    + (b.x * b.x + b.y * b.y) * (a.y - c.y)
+                    + (c.x * c.x + c.y * c.y) * (b.y - a.y);
+            var C = (a.x * a.x + a.y * a.y) * (b.x - c.x)
+                    + (b.x * b.x + b.y * b.y) * (c.x - a.x)
+                    + (c.x * c.x + c.y * c.y) * (a.x - b.x);
+
+            if (Math.Abs(A) < 0.1)
+                return null;
+
+            var x = -B / (2 * A);
+            var y = -C / (2 * A);
+
+            return new Point(x, y);
+        }
+
+        public EdgeEvent CheckCircleEvent(RedBlackNode<Parabola> node)
+        {
+            if (node == null)
+                return null;
+            
+            var circle = Circle(node);
+
+            if (circle == null) 
+                return null;
+            
+            return node.Value.Event = new EdgeEvent() { vertex = circle, node = node };
+        }
+
+        private double IntersectParabola(Point q, Point p)
+        {
+            if (Abs(p.y - Directrix) < 0.0001) return p.x;
+            if (Abs(q.y - Directrix) < 0.0001) return q.x;
+
+            if (Abs(p.y - q.y) < 0.0001) return (q.x + p.x) / 2;
+            
+            var alpha = 1 / (2 * (q.y - Directrix));
+            var beta = 1 / (2 * (p.y - Directrix));
+
+            double a = alpha - beta;
+            double b = -2 * alpha * q.x + 2 * beta * p.x;
+            double c = alpha * (Pow(q.x, 2) + Pow(q.y, 2) - Pow(Directrix, 2))
+                    - beta * (Pow(p.x, 2) + Pow(p.y, 2) - Pow(Directrix, 2));
+
+            double d = Sqrt(b * b - 4.0 * a * c);
+            
+            return (-b - d) / (2 * a);
+        }
+    }
+}

Assets/Voronoi/BeachLine.cs.meta

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Assets/Voronoi/Tree.cs

@@ -0,0 +1,349 @@
+using System;
+using System.Runtime.CompilerServices;
+
+namespace Assets.Voronoi
+{
+    public enum RedBlackNodeType
+    {
+        Black,
+        Red
+    }
+    
+    public class RedBlackNode<T>
+    {
+        public T Value { get; internal set; }
+
+        internal RedBlackNodeType Color { get; set; } = RedBlackNodeType.Red;
+
+        internal RedBlackNode<T> _left;
+        internal RedBlackNode<T> _right;
+
+
+        public RedBlackNode<T> Next => GetSuccessor();
+        public RedBlackNode<T> Previous => GetPredecessor();
+
+        internal RedBlackNode<T> GrandParent => Parent?.Parent;
+
+        internal RedBlackNode<T> Uncle => Parent?.Parent?.Left == Parent
+            ? Parent?.Parent?.Right
+            : Parent?.Parent?.Left;
+
+        public RedBlackNode<T> Parent { get; internal set; }
+
+        public RedBlackNode<T> Right
+        {
+            get => _right;
+            internal set
+            {
+                _right = value;
+                if (value != null) value.Parent = this;
+            }
+        }
+
+        public RedBlackNode<T> Left
+        {
+            get => _left;
+            internal set
+            {
+                _left = value;
+                if (value != null) value.Parent = this;
+            }
+        }
+
+        public RedBlackNode(T value = default)
+        {
+            Value = value;
+        }
+
+        private RedBlackNode<T> GetSuccessor()
+        {
+            RedBlackNode<T> successor, node = this;
+
+            if (node.Right != null)
+            {
+                successor = node.Right;
+
+                while (successor.Left != null)
+                    successor = successor.Left;
+
+                return successor;
+            }
+
+            successor = node.Parent;
+            while (successor != null && successor.Right == node)
+            {
+                node = successor;
+                successor = successor.Parent;
+            }
+
+            return successor;
+        }
+
+        private RedBlackNode<T> GetPredecessor()
+        {
+            RedBlackNode<T> predecessor, node = this;
+
+            if (node.Left != null)
+            {
+                predecessor = node.Left;
+
+                while (predecessor.Right != null)
+                    predecessor = predecessor.Right;
+
+                return predecessor;
+            }
+
+            predecessor = node.Parent;
+            while (predecessor != null && predecessor.Left == node)
+            {
+                node = predecessor;
+                predecessor = predecessor.Parent;
+            }
+
+            return predecessor;
+        }
+    }
+
+    public class RedBlackTree<T>
+    {
+        private RedBlackNode<T> _root;
+
+        public RedBlackNode<T> Root
+        {
+            get => _root;
+            internal set
+            {
+                _root = value;
+                _root.Color = RedBlackNodeType.Black;
+            }
+        }
+
+        public bool IsEmpty => _root == null;
+
+        public RedBlackNode<T> First
+        {
+            get
+            {
+                var current = _root;
+
+                while (current?.Left != null) current = current.Left;
+
+                return current;
+            }
+        }
+
+        public RedBlackNode<T> Last
+        {
+            get
+            {
+                var current = _root;
+
+                while (current?.Right != null) current = current.Right;
+
+                return current;
+            }
+        }
+
+        public void Rebalance(RedBlackNode<T> node)
+        {
+            while (node != Root && node.Parent.Color == RedBlackNodeType.Red)
+            {
+                if (node.Uncle != null && node.Uncle.Color == RedBlackNodeType.Red)
+                {
+                    node.Parent.Color = RedBlackNodeType.Black;
+                    node.Uncle.Color = RedBlackNodeType.Black;
+
+                    node = node.GrandParent;
+                }
+                else
+                {
+                    (node.Parent.Color, node.GrandParent.Color) = (node.GrandParent.Color, node.Parent.Color);
+
+                    if (node == node.Parent.Left)
+                    {
+                        if (node.Parent == node.GrandParent.Right)
+                        {
+                            RotateLeft(node.Parent);
+                        }
+
+                        RotateRight(node.GrandParent);
+                    }
+                    else
+                    {
+                        if (node.Parent == node.GrandParent.Left)
+                        {
+                            RotateRight(node.Parent);
+                        }
+
+                        RotateRight(node.GrandParent);
+                    }
+                }
+            }
+        }
+
+        public void InsertAfter(RedBlackNode<T> node, T value)
+        {
+            var current = node.Right;
+            var inserted = new RedBlackNode<T>(value);
+
+            if (current is null)
+            {
+                node.Right = inserted;
+            }
+            else
+            {
+                while (current.Left != null)
+                    current = current.Left;
+
+                current.Left = inserted;
+            }
+
+//            Rebalance(inserted);
+        }
+
+        public void InsertBefore(RedBlackNode<T> node, T value)
+        {
+            var current = node.Left;
+            var inserted = new RedBlackNode<T>(value);
+
+            if (current is null)
+            {
+                node.Left = inserted;
+            }
+            else
+            {
+                while (current.Right != null)
+                    current = current.Right;
+
+                current.Right = inserted;
+            }
+
+//            Rebalance(inserted);
+        }
+
+        private void RotateLeft(RedBlackNode<T> current)
+        {
+            var right = current.Right;
+
+            current.Right = right.Left;
+            right.Left = current;
+            right.Parent = current.Parent;
+            current.Parent = right;
+
+            FixRoot(current, right);
+        }
+
+        private void RotateRight(RedBlackNode<T> current)
+        {
+            var left = current.Left;
+
+            current.Left = left.Right;
+            left.Right = current;
+            left.Parent = current.Parent;
+            current.Parent = left;
+
+            FixRoot(current, left);
+        }
+
+        [MethodImpl(MethodImplOptions.AggressiveInlining)]
+        private void FixRoot(RedBlackNode<T> old, RedBlackNode<T> current)
+        {
+            if (Root == old)
+            {
+                Root = current;
+                Root.Color = RedBlackNodeType.Black;
+                Root.Parent = null;
+            }
+        }
+
+        public void Remove(RedBlackNode<T> node)
+        {
+            if (node.Left == null && node.Right == null)
+                RemoveLeaf(node);
+            else if (node.Left == null || node.Right == null)
+                RemoveOneChild(node);
+            else
+                Substitute(node, node.Next);
+        }
+
+        private void RemoveOneChild(RedBlackNode<T> node)
+        {
+            var replacement = node.Left ?? node.Right;
+            
+            if (Root == node)
+                Root = replacement;
+            else if (node.Parent.Left == node)
+                node.Parent.Left = replacement;
+            else if (node.Parent.Right == node)
+                node.Parent.Right = replacement;
+            else
+                throw new Exception("WTF?");
+        }
+
+        private void Swap(RedBlackNode<T> a, RedBlackNode<T> b)
+        {
+            if (b.Parent == a)
+                (a, b) = (b, a);
+
+            if (a.Parent == b)
+            {
+                if (b.Parent?.Left == b) b.Parent.Left = a;
+                if (b.Parent?.Right == b) b.Parent.Right = a;
+                if (b.Parent == null) a.Parent = null;
+
+                if (b.Left == a)
+                {
+                    (b.Right, a.Right) = (a.Right, b.Right);
+                    
+                    b.Left = a.Left;
+                    a.Left = b;
+                }
+                else
+                {
+                    (b.Left, a.Left) = (a.Left, b.Left);
+                    
+                    b.Right = a.Right;
+                    a.Right = b;
+                }
+            }
+            else
+            {
+                (a.Right, b.Right) = (b.Right, a.Right);
+                (a.Left, b.Left) = (b.Left, a.Left);
+
+                var bparent = b.Parent;
+                
+                if (a.Parent != null && a.Parent.Left == a) a.Parent.Left = b;
+                else if (a.Parent != null && a.Parent.Right == a) a.Parent.Right = b;
+                else b.Parent = null;
+
+                if (bparent != null && bparent.Left == b) bparent.Left = a;
+                else if (bparent != null && bparent.Right == b) bparent.Right = a;
+                else a.Parent = null;
+            }
+
+            if (b.Parent == null) Root = b;
+            if (a.Parent == null) Root = a;
+        }
+        
+        private void Substitute(RedBlackNode<T> node, RedBlackNode<T> replacement)
+        {
+//            (node.Value, replacement.Value) = (replacement.Value, node.Value);
+            Swap(node, replacement);            
+
+            Remove(node);
+        }
+
+        private void RemoveLeaf(RedBlackNode<T> leaf)
+        {
+            if (leaf.Parent == null)
+            {
+                Root = null;
+                return;
+            }
+
+            if (leaf.Parent.Left == leaf) leaf.Parent.Left = null;
+            else leaf.Parent.Right = null;
+        }
+    }
+}

Assets/Voronoi/Tree.cs.meta

@@ -0,0 +1,3 @@
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+guid: dc397bc0f0ca489297be4d21bf0e53a1
+timeCreated: 1563555455

Assets/Voronoi/VoronoiGenerator.cs

@@ -0,0 +1,196 @@
+using System.Collections.Generic;
+using System.Linq;
+using Priority_Queue;
+
+namespace Assets.Voronoi
+{
+    public interface IEvent 
+    {
+        double Priority { get; }
+        bool IsValid { get; }
+    }
+
+    public class SiteEvent : IEvent 
+    {
+        public Site Site { get; internal set; }
+        
+        public double Priority => Site.Point.y;
+        public bool IsValid => true;
+    }
+
+    public class EdgeEvent : IEvent
+    {
+        public RedBlackNode<Parabola> node;
+        public Point vertex;
+        public bool IsValid { get; set; } = true;
+
+        public double Priority => vertex.y + Point.Dist(vertex, node.Value.Site.Point);
+    }
+
+    public class Site
+    {
+        public ISet<Site> Neighbours { get; internal set; } = new HashSet<Site>();
+        public Point Point { get; internal set; }
+        
+        public Site(Point point)
+        {
+            Point = point;
+        }
+    }
+    
+    public class VoronoiGenerator
+    {
+        public IList<Site> Sites { get; }
+
+        public IPriorityQueue<IEvent, double> Queue { get; internal set; }
+        public IList<Point> Vertices { get; internal set; }
+        public IList<Edge> Edges { get; internal set; }
+        
+        public BeachLine Line { get; private set; }
+        
+        public bool Done => Queue.Count == 0;
+        
+        public VoronoiGenerator(IList<Point> sites)
+        {
+            Sites = sites.Select(x => new Site(x)).ToList();
+            
+            Reset();
+        }
+        
+        private void Reset()
+        {
+            Queue = new SimplePriorityQueue<IEvent, double>();
+            Line = new BeachLine();
+            
+            Vertices = new List<Point>();
+            Edges    = new List<Edge>();
+
+            foreach (var site in Sites)
+            {
+                var @event = new SiteEvent { Site = site };
+                Queue.Enqueue(@event, @event.Priority);
+            }
+        }
+
+        public void Step()
+        {
+            while (Queue.Count > 0)
+            {
+                var ev = Queue.Dequeue();
+                if (!ev.IsValid) continue;
+
+                Line.Directrix = ev.Priority;
+                
+                switch (ev)
+                {
+                    case SiteEvent site: 
+                        HandleSiteEvent(site);
+                        return;
+                    
+                    case EdgeEvent edge: 
+                        HandleEdgeEvent(edge);
+                        return;
+                }
+            }
+        }
+
+        public void Generate()
+        {
+            Reset();
+            
+            while (Queue.Count > 0)
+                Step();
+        }
+
+        private void Enqueue(EdgeEvent @event)
+        {
+            if (@event.Priority > Line.Directrix)
+                Queue.Enqueue(@event, @event.Priority);
+        }
+
+        private void HandleEdgeEvent(EdgeEvent @event)
+        {
+            var queue = new Queue<RedBlackNode<Parabola>>();
+            
+            var node = @event.node;
+            var parabola = node.Value;
+            
+            var previous = node.Previous;
+            var next     = node.Next;
+            
+            if (previous?.Value.Event != null) previous.Value.Event.IsValid = false;
+            if (next?.Value.Event != null) next.Value.Event.IsValid = false;
+
+            Vertices.Add(@event.vertex);
+
+            node.Value.LeftEdge.end = @event.vertex;
+            node.Value.RightEdge.end = @event.vertex;
+            
+            Edges.Add(node.Value.LeftEdge);
+            Edges.Add(node.Value.RightEdge);
+            
+            var newEdge = new Edge() { start = @event.vertex };
+            
+            node.Previous.Value.RightEdge = newEdge;
+            node.Next.Value.LeftEdge = newEdge;
+
+            Line.RemoveParabola(node);
+            
+            if (Line.CheckCircleEvent(previous) is EdgeEvent p) 
+                Enqueue(p);
+            
+            if (Line.CheckCircleEvent(next) is EdgeEvent n) 
+                Enqueue(n);
+
+            if (previous != null && next != null)
+            {
+                previous.Value.Site.Neighbours.Add(next.Value.Site);
+                next.Value.Site.Neighbours.Add(previous.Value.Site);
+            }
+        }
+
+        private void HandleSiteEvent(SiteEvent @event)
+        {
+            var site = @event.Site;
+            var start = new Point(site.Point.x, Line.Eval(site.Point.x));
+
+            var above = Line.FindParabola(site.Point.x);
+
+            if (above != null)
+            {
+                var left  = above.Value.LeftEdge;
+                var right = above.Value.RightEdge;
+                
+                var node = Line.AddParabola(@event.Site, above);
+                
+                var newLeft  = new Edge() { start = start };
+                var newRight = new Edge() { start = start };
+
+                node.Previous.Value.LeftEdge = left;
+                node.Previous.Value.RightEdge = newLeft;
+
+                node.Value.LeftEdge = newLeft;
+                node.Value.RightEdge = newRight;
+
+                node.Next.Value.LeftEdge = newRight;
+                node.Next.Value.RightEdge = right;
+
+                if (Line.CheckCircleEvent(node.Previous) is EdgeEvent p) 
+                    Enqueue(p);
+                
+                if (Line.CheckCircleEvent(node.Next) is EdgeEvent n) 
+                    Enqueue(n);
+
+                if (node.Previous != null)
+                {
+                    @event.Site.Neighbours.Add(node.Previous.Value.Site);
+                    node.Previous.Value.Site.Neighbours.Add(@event.Site);
+                }
+            }
+            else
+            {
+                Line.AddParabola(@event.Site);
+            }
+        }
+    }
+}

Assets/Voronoi/VoronoiGenerator.cs.meta

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+MonoImporter:
+  externalObjects: {}
+  serializedVersion: 2
+  defaultReferences: []
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+  userData: 
+  assetBundleName: 
+  assetBundleVariant: 

Assets/Voronoi/VoronoiGraph.cs

@@ -0,0 +1,27 @@
+using System;
+using UnityEngine;
+
+namespace Assets.Voronoi
+{
+    public class Point
+    {
+        public double x;
+        public double y;
+
+        public Point(double x, double y)
+        {
+            this.x = x;
+            this.y = y;
+        }
+
+        public static double Dist(Point a, Point b)
+        {
+            return Math.Sqrt(Math.Pow(a.x - b.x, 2) + Math.Pow(a.y - b.y, 2));
+        }
+    }
+    
+    public class VoronoiGraph
+    {
+        
+    }
+}

Assets/Voronoi/VoronoiGraph.cs.meta

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+timeCreated: 1563289564

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+    "com.unity.modules.terrainphysics": "1.0.0",
+    "com.unity.modules.tilemap": "1.0.0",
+    "com.unity.modules.ui": "1.0.0",
+    "com.unity.modules.uielements": "1.0.0",
+    "com.unity.modules.umbra": "1.0.0",
+    "com.unity.modules.unityanalytics": "1.0.0",
+    "com.unity.modules.unitywebrequest": "1.0.0",
+    "com.unity.modules.unitywebrequestassetbundle": "1.0.0",
+    "com.unity.modules.unitywebrequestaudio": "1.0.0",
+    "com.unity.modules.unitywebrequesttexture": "1.0.0",
+    "com.unity.modules.unitywebrequestwww": "1.0.0",
+    "com.unity.modules.vehicles": "1.0.0",
+    "com.unity.modules.video": "1.0.0",
+    "com.unity.modules.vr": "1.0.0",
+    "com.unity.modules.wind": "1.0.0",
+    "com.unity.modules.xr": "1.0.0"
+  }
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