Procedural Mesh From Random List Of Veritces

Take a look at the unity triangulator and the delauny algorithm. Very interesting topic :)

@FairGamesProductions if you are still looking, The unity triangulator, as the server looks down~

 using System.Collections;
 using System.Collections.Generic;
 using UnityEngine;
 
 public class Triangulator
 {
     private List<Vector2> m_points = new List<Vector2>();
 
     public Triangulator(Vector2[] points)
     {
         m_points = new List<Vector2>(points);
     }
 
     public int[] Triangulate()
     {
         List<int> indices = new List<int>();
 
         int n = m_points.Count;
         if (n < 3)
             return indices.ToArray();
 
         int[] V = new int[n];
         if (Area() > 0)
         {
             for (int v = 0; v < n; v++)
                 V[v] = v;
         }
         else
         {
             for (int v = 0; v < n; v++)
                 V[v] = (n - 1) - v;
         }
 
         int nv = n;
         int count = 2 * nv;
         for (int m = 0, v = nv - 1; nv > 2;)
         {
             if ((count--) <= 0)
                 return indices.ToArray();
 
             int u = v;
             if (nv <= u)
                 u = 0;
             v = u + 1;
             if (nv <= v)
                 v = 0;
             int w = v + 1;
             if (nv <= w)
                 w = 0;
 
             if (Snip(u, v, w, nv, V))
             {
                 int a, b, c, s, t;
                 a = V[u];
                 b = V[v];
                 c = V[w];
                 indices.Add(a);
                 indices.Add(b);
                 indices.Add(c);
                 m++;
                 for (s = v, t = v + 1; t < nv; s++, t++)
                     V[s] = V[t];
                 nv--;
                 count = 2 * nv;
             }
         }
 
         indices.Reverse();
         return indices.ToArray();
     }
 
     private float Area()
     {
         int n = m_points.Count;
         float A = 0.0f;
         for (int p = n - 1, q = 0; q < n; p = q++)
         {
             Vector2 pval = m_points[p];
             Vector2 qval = m_points[q];
             A += pval.x * qval.y - qval.x * pval.y;
         }
         return (A * 0.5f);
     }
 
     private bool Snip(int u, int v, int w, int n, int[] V)
     {
         int p;
         Vector2 A = m_points[V[u]];
         Vector2 B = m_points[V[v]];
         Vector2 C = m_points[V[w]];
         if (Mathf.Epsilon > (((B.x - A.x) * (C.y - A.y)) - ((B.y - A.y) * (C.x - A.x))))
             return false;
         for (p = 0; p < n; p++)
         {
             if ((p == u) || (p == v) || (p == w))
                 continue;
             Vector2 P = m_points[V[p]];
             if (InsideTriangle(A, B, C, P))
                 return false;
         }
         return true;
     }
 
     private bool InsideTriangle(Vector2 A, Vector2 B, Vector2 C, Vector2 P)
     {
         float ax, ay, bx, by, cx, cy, apx, apy, bpx, bpy, cpx, cpy;
         float cCROSSap, bCROSScp, aCROSSbp;
 
         ax = C.x - B.x; ay = C.y - B.y;
         bx = A.x - C.x; by = A.y - C.y;
         cx = B.x - A.x; cy = B.y - A.y;
         apx = P.x - A.x; apy = P.y - A.y;
         bpx = P.x - B.x; bpy = P.y - B.y;
         cpx = P.x - C.x; cpy = P.y - C.y;
 
         aCROSSbp = ax * bpy - ay * bpx;
         cCROSSap = cx * apy - cy * apx;
         bCROSScp = bx * cpy - by * cpx;
 
         return ((aCROSSbp >= 0.0f) && (bCROSScp >= 0.0f) && (cCROSSap >= 0.0f));
     }
 }

And a short test class to show you how to use it, using UnityEngine;

 public class PolygonTester : MonoBehaviour
 {
     void Start()
     {
         // Create Vector2 vertices
         Vector2[] vertices2D = new Vector2[] {
             new Vector2(0,0),
             new Vector2(0,50),
             new Vector2(50,50),
             new Vector2(50,100),
             new Vector2(0,100),
             new Vector2(0,150),
             new Vector2(150,150),
             new Vector2(150,100),
             new Vector2(100,100),
             new Vector2(100,50),
             new Vector2(150,50),
             new Vector2(150,0),
         };
 
         // Use the triangulator to get indices for creating triangles
         Triangulator tr = new Triangulator(vertices2D);
         int[] indices = tr.Triangulate();
 
         // Create the Vector3 vertices
         Vector3[] vertices = new Vector3[vertices2D.Length];
         for (int i = 0; i < vertices.Length; i++)
         {
             vertices[i] = new Vector3(vertices2D[i].x, vertices2D[i].y, 0);
         }
 
         // Create the mesh
         Mesh msh = new Mesh();
         msh.vertices = vertices;
         msh.triangles = indices;
         msh.RecalculateNormals();
         msh.RecalculateBounds();
 
         // Set up game object with mesh;
         gameObject.AddComponent(typeof(MeshRenderer));
         MeshFilter filter = gameObject.AddComponent(typeof(MeshFilter)) as MeshFilter;
         filter.mesh = msh;
     }
 }