├── .gitignore
├── Assets
    ├── Delaunay2D.meta
    ├── Delaunay2D
    │   ├── Delaunay2D.cs
    │   ├── Delaunay2D.cs.meta
    │   ├── TestDelaunay2D.cs
    │   └── TestDelaunay2D.cs.meta
    ├── Resources.meta
    ├── Resources
    │   ├── Wireframe.mat
    │   ├── Wireframe.mat.meta
    │   ├── Wireframe.shader
    │   └── Wireframe.shader.meta
    ├── Scenes.meta
    └── Scenes
    │   ├── SampleScene.unity
    │   └── SampleScene.unity.meta
├── LICENSE
├── README.md
└── pic
    └── 2d.gif


/.gitignore:
--------------------------------------------------------------------------------
 1 | .vs/
 2 | Debug/
 3 | Library/
 4 | Packages/
 5 | ProjectSettings/
 6 | Temp/
 7 | UnityPackageManager/
 8 | *.csproj
 9 | *.opensdf
10 | *.sdf
11 | *.sln
12 | *.user
13 | *.userprefs
14 | 


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/Assets/Delaunay2D/Delaunay2D.cs:
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  1 | using System.Collections;
  2 | using System.Collections.Generic;
  3 | using UnityEngine;
  4 | 
  5 | public struct Triangle
  6 | {
  7 |     public Vector2 V0;
  8 |     public Vector2 V1;
  9 |     public Vector2 V2;
 10 |     public bool IsBad;
 11 |     public Edge E0;
 12 |     public Edge E1;
 13 |     public Edge E2;
 14 | 
 15 |     public Triangle(Vector2 v0, Vector2 v1, Vector2 v2 )
 16 |     {
 17 |         V0 = v0;
 18 |         V1 = v1;
 19 |         V2 = v2;
 20 |         E0 = new Edge(v0, v1);
 21 |         E1 = new Edge(v1, v2);
 22 |         E2 = new Edge(v2, v0);
 23 |         IsBad = false;
 24 |     }
 25 | 
 26 |     public bool circumCircleContains(Vector2 p)
 27 |     {
 28 |         float ab = V0.sqrMagnitude;
 29 |         float cd = V1.sqrMagnitude;
 30 |         float ef = V2.sqrMagnitude;
 31 |         float circumX = (ab*(V2.y - V1.y) + cd*(V0.y - V2.y) + ef*(V1.y - V0.y))/
 32 |                           (V0.x*(V2.y - V1.y) + V1.x*(V0.y - V2.y) + V2.x*(V1.y - V0.y));
 33 |         float circumY = (ab*(V2.x - V1.x) + cd*(V0.x - V2.x) + ef*(V1.x - V0.x))/
 34 |                           (V0.y*(V2.x - V1.x) + V1.y*(V0.x - V2.x) + V2.y*(V1.x - V0.x));
 35 |         Vector2 circum = new Vector2(circumX / 2, circumY / 2);
 36 |         float circumRadius = (V0 - circum).sqrMagnitude;
 37 |         float dist = (p - circum).sqrMagnitude;
 38 |         return dist <= circumRadius;
 39 |     }
 40 | 
 41 |     public bool ContainsVertex(Vector2 p)
 42 |     {
 43 |         return Mathf.Approximately(0, Vector2.Distance(p, V0)) ||
 44 |                Mathf.Approximately(0, Vector2.Distance(p, V1)) ||
 45 |                Mathf.Approximately(0, Vector2.Distance(p, V2));
 46 |     }
 47 | }
 48 | 
 49 | public struct Edge
 50 | {
 51 |     public Vector2 V0;
 52 |     public Vector2 V1;
 53 |     public bool IsBad;
 54 | 
 55 |     public Edge(Vector2 v0, Vector2 v1)
 56 |     {
 57 |         V0 = v0;
 58 |         V1 = v1;
 59 |         IsBad = false;
 60 |     }
 61 | 
 62 |     public bool AlmostEqual(Edge e)
 63 |     {
 64 |         return (Mathf.Approximately(0, Vector2.Distance(V0, e.V0)) && Mathf.Approximately(0, Vector2.Distance(V1, e.V1))) ||
 65 |                (Mathf.Approximately(0, Vector2.Distance(V0, e.V1)) && Mathf.Approximately(0, Vector2.Distance(V1, e.V0)));
 66 |     }
 67 | }
 68 | 
 69 | public class Delaunay2D {
 70 |     public List<Triangle> Triangulate(List<Vector2> vertices)
 71 |     {
 72 |         List<Triangle> triangles = new List<Triangle>();
 73 |         if (0 == vertices.Count)
 74 |         {
 75 |             return triangles;
 76 |         }
 77 |         float minX = vertices[0].x;
 78 |         float minY = vertices[0].y;
 79 |         float maxX = minX;
 80 |         float maxY = minY;
 81 |         for (int i = 0, imax = vertices.Count; i < imax; i++)
 82 |         {
 83 |             float x = vertices[i].x;
 84 |             float y = vertices[i].y;
 85 |             if (x < minX)
 86 |             {
 87 |                 minX = x;
 88 |             }
 89 |             else if (x > maxX)
 90 |             {
 91 |                 maxX = x;
 92 |             }
 93 |             if (y < minY)
 94 |             {
 95 |                 minY = y;
 96 |             }
 97 |             else if (y > maxY)
 98 |             {
 99 |                 maxY = y;
100 |             }
101 |         }
102 |         float dx = maxX - minX;
103 |         float dy = maxY - minY;
104 |         float deltaMax = Mathf.Max(dx, dy);
105 |         float midX = (minX + maxX)/2;
106 |         float midY = (minY + maxY)/2;
107 |         Vector2 p1 = new Vector2(midX - 20 * deltaMax, midY - deltaMax);
108 |         Vector2 p2 = new Vector2(midX, midY + 20 * deltaMax);
109 |         Vector2 p3 = new Vector2(midX + 20 * deltaMax, midY - deltaMax);
110 | 
111 |         triangles.Add(new Triangle(p1, p2, p3));
112 |         for (int i = 0, imax = vertices.Count; i < imax; i++)
113 |         {
114 |             Vector2 p = vertices[i];
115 |             List<Edge> polygon = new List<Edge>();
116 |             for (int j = 0, jmax = triangles.Count; j < jmax; j++)
117 |             {
118 |                 Triangle t = triangles[j];
119 |                 if (t.circumCircleContains(p))
120 |                 {
121 |                     t.IsBad = true;
122 |                     polygon.Add(t.E0);
123 |                     polygon.Add(t.E1);
124 |                     polygon.Add(t.E2);
125 |                     triangles[j] = t;
126 |                 }
127 |             }
128 |             triangles.RemoveAll((t) => t.IsBad);
129 |             for (int j = 0, jmax = polygon.Count; j < jmax; j++)
130 |             {
131 |                 Edge e = polygon[j];
132 |                 for (int k = j + 1; k < jmax; k++)
133 |                 {
134 |                     Edge e2 = polygon[k];
135 |                     if (e.AlmostEqual(e2))
136 |                     {
137 |                         e.IsBad = true;
138 |                         e2.IsBad = true;
139 |                         polygon[j] = e;
140 |                         polygon[k] = e2;
141 |                     }
142 |                 }
143 |             }
144 | 
145 |             polygon.RemoveAll((e) => e.IsBad);
146 |             foreach (Edge e in polygon)
147 |             {
148 |                 triangles.Add(new Triangle(e.V0, e.V1, p));
149 |             }
150 |         }
151 |         triangles.RemoveAll((t) => t.ContainsVertex(p1) || t.ContainsVertex(p2) || t.ContainsVertex(p3));
152 |         return triangles;
153 |     } 
154 | }
155 | 


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/Assets/Delaunay2D/TestDelaunay2D.cs:
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 1 | using System.Collections.Generic;
 2 | using UnityEngine;
 3 | 
 4 | public class TestDelaunay2D : MonoBehaviour {
 5 |     public Material mat;
 6 |     List<Vector2> points = new List<Vector2>();
 7 | 
 8 |     void Awake()
 9 |     {
10 |         points.Add(new Vector2(0, 0));
11 |         points.Add(new Vector2(1, 0));
12 |         points.Add(new Vector2(0.5f, 1));
13 |     }
14 | 
15 |     void Update()
16 |     {
17 |         if (Input.GetMouseButtonUp(0))
18 |         {
19 |             Vector2 mp = Input.mousePosition;
20 |             points.Add(new Vector2(mp.x / Screen.width, mp.y / Screen.height));
21 |         }
22 |     }
23 | 
24 |     void OnPostRender()
25 |     {
26 |         if (!mat)
27 |         {
28 |             Debug.LogError("Please Assign a material on the inspector");
29 |             return;
30 |         }
31 |         Delaunay2D d = new Delaunay2D();
32 |         List<Triangle> triangles = d.Triangulate(points);
33 |         GL.PushMatrix();
34 |         mat.SetPass(0);
35 |         GL.LoadOrtho();
36 |         GL.Begin(GL.TRIANGLES);
37 |         for (int i = 0, imax = triangles.Count; i < imax; i++)
38 |         {
39 |             GL.Vertex(triangles[i].V0);
40 |             GL.Vertex(triangles[i].V1);
41 |             GL.Vertex(triangles[i].V2);
42 |         }
43 |         GL.End();
44 |         GL.PopMatrix();
45 |     }
46 | }
47 | 


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/Assets/Resources/Wireframe.shader:
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 1 | Shader "Hidden/VertexColor"
 2 | {
 3 | 	Properties
 4 | 	{
 5 | 		_EdgeColor ("Edge Color", Color) = (1,1,1,1)
 6 | 	}
 7 | 	SubShader
 8 | 	{
 9 | 		Tags{ "RenderType" = "Opaque" "Queue" = "Geometry" }
10 | 		LOD 100
11 | 
12 | 		Pass
13 | 	{
14 | 		CGPROGRAM
15 | #pragma target 4.6
16 | #pragma vertex vert
17 | #pragma geometry geom
18 | #pragma fragment frag
19 | 
20 | #include "UnityCG.cginc"
21 | 
22 | 		struct v2g
23 | 	{
24 | 		float4 pos : SV_POSITION;
25 | 	};
26 | 	struct g2f
27 | 	{
28 | 		float4  pos : SV_POSITION;
29 | 		float3 dist : TEXCOORD1;
30 | 		float3 vd : TEXCOORD2;
31 | 	};
32 | 
33 | 
34 | 	float4 _EdgeColor;
35 | 	v2g vert(float4 vertex : POSITION, uint vid : SV_VertexID)
36 | 	{
37 | 		v2g o;
38 | 		o.pos = UnityObjectToClipPos(vertex);
39 | 		return o;
40 | 	}
41 | 
42 | 	[maxvertexcount(3)]
43 | 	void geom(triangle v2g IN[3], inout TriangleStream<g2f> triStream)
44 | 	{
45 | 
46 | 		float2 WIN_SCALE = float2(_ScreenParams.x / 2.0, _ScreenParams.y / 2.0);
47 | 
48 | 		//frag position
49 | 		float2 p0 = WIN_SCALE * IN[0].pos.xy / IN[0].pos.w;
50 | 		float2 p1 = WIN_SCALE * IN[1].pos.xy / IN[1].pos.w;
51 | 		float2 p2 = WIN_SCALE * IN[2].pos.xy / IN[2].pos.w;
52 | 
53 | 		//barycentric position
54 | 		float2 v0 = p2 - p1;
55 | 		float2 v1 = p2 - p0;
56 | 		float2 v2 = p1 - p0;
57 | 		//triangles area
58 | 		float area = abs(v1.x*v2.y - v1.y * v2.x);
59 | 
60 | 		g2f OUT;
61 | 		OUT.pos = IN[0].pos;
62 | 		OUT.dist = float3(area / length(v0),0,0);
63 | 		OUT.vd = float3(1,0,0);
64 | 		triStream.Append(OUT);
65 | 
66 | 		OUT.pos = IN[1].pos;
67 | 		OUT.dist = float3(0,area / length(v1),0);
68 | 		OUT.vd = float3(0,1,0);
69 | 		triStream.Append(OUT);
70 | 
71 | 		OUT.pos = IN[2].pos;
72 | 		OUT.dist = float3(0,0,area / length(v2));
73 | 		OUT.vd = float3(0,0,1);
74 | 		triStream.Append(OUT);
75 | 
76 | 	}
77 | 
78 | 	fixed4 frag(g2f IN) : SV_Target
79 | 	{
80 | 		//distance of frag from triangles center
81 | 		float d = min(IN.dist.x, min(IN.dist.y, IN.dist.z));
82 | 	//float vd = max(IN.vd.x, max(IN.vd.y, IN.vd.z));
83 | 	//fade based on dist from center
84 | 	float I = exp2(-4.0*d*d);
85 | 	//I += step(0.9, vd);
86 | 	return lerp(fixed4(0,0,0,0), _EdgeColor, I);
87 | 	}
88 | 		ENDCG
89 | 	}
90 | 	}
91 | }


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/LICENSE:
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 1 | MIT License
 2 | 
 3 | Copyright (c) 2019 Khaos
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


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/README.md:
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1 | # UnityDelaunay
2 | 
3 | # 2D
4 | 
5 | ![2D](pic/2d.gif)
6 | 
7 | # Reference
8 | 
9 | https://github.com/Bl4ckb0ne/delaunay-triangulation


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/pic/2d.gif:
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https://raw.githubusercontent.com/ecidevilin/UnityDelaunay/8af4cd71691b0e029714f8d1a4fa2702163e33f1/pic/2d.gif


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