Find edge/surface/ledge of mesh

So I have been trying to do something with this all day long. And I managed to get the quad that the player hits, get the top edge of it and check if it is climable. I think it only works with perfect quads, and its not very good at all, but it works. So its far from perfect but its a good base for you to start building on!

 using UnityEngine;
 using System.Collections;
 //using System.Collections.Generic;
 //using System.Threading;
 
 //TODO Clean up stuff. Fix bug and tweak stuff. Optimize stuff. Animation support. Add climbing support. Make usable for non-perfect quads. Find all edges within reach instead of just the closest.
 //Made in a day by Imre Angelo aka Lahzar @ the unity forums - Enjoy!
 public class RunFree3o : MonoBehaviour {
         public float reach = 3;    //TODO Check from players arms, legs etc
 private Vector3[] quad;
 private Vector3[] top;

 void Start()    {
     quad = new Vector3[4];
 }

 void Update()    {
     if(top[0] != new Vector3())
         Debug.DrawLine(top[0], top[1], Color.green, 1);
 }

 void OnControllerColliderHit(ControllerColliderHit col)    {
     RaycastHit hit;
     Debug.DrawRay(col.point, col.moveDirection, Color.blue, 1);
     if(Physics.Raycast(transform.position, col.moveDirection, out hit, 0.5f))    {
         if(hit.normal.y == transform.position.y-(GetComponent<CharacterController>().height/2))
             return;

         MeshCollider meshCollider = hit.collider as MeshCollider;
         if (meshCollider == null || meshCollider.sharedMesh == null)
             return;
         
         Mesh mesh = meshCollider.sharedMesh;
         Vector3[] vertices = mesh.vertices;
         int[] triangles = mesh.triangles;
         Transform hitTransform = hit.collider.transform;

         StartCoroutine(CoroutineThing(mesh, hitTransform, vertices, triangles, hit.triangleIndex));
     }
 }

 IEnumerator CoroutineThing(Mesh mesh, Transform hitTransform, Vector3[] vertices, int[] triangles, int triangleIndex)    {
     #region Get hit triangle
     Vector3 p0 = vertices[triangles[triangleIndex * 3 + 0]];
     Vector3 p1 = vertices[triangles[triangleIndex * 3 + 1]];
     Vector3 p2 = vertices[triangles[triangleIndex * 3 + 2]];
     p0 = hitTransform.TransformPoint(p0);
     p1 = hitTransform.TransformPoint(p1);
     p2 = hitTransform.TransformPoint(p2);
     #endregion

     Debug.DrawLine(p0, p1, Color.blue, 4);
     Debug.DrawLine(p1, p2, Color.blue, 4);
     Debug.DrawLine(p2, p0, Color.blue, 4);

     #region Get last triangle
     Vector3 p3 = new Vector3();
     for(int i = 10; i > -10; i--)    {
         Vector3 p4 = new Vector3();
         if(vertices[triangles[triangleIndex * 3 + i]] == null)
             continue;

         try {
             p4 = hitTransform.TransformPoint(vertices[triangles[triangleIndex * 3 + i]]);
         } catch (System.Exception ex)    {
             ex.Source = "ignore";
             continue;
         }

         if(p4 != p0 && p4 != p1 && p4 != p2)    {

             int ex = 0, wai = 0, zed = 0;
             if(Mathf.FloorToInt(p4.x) == Mathf.FloorToInt(p0.x))    {    ex++;    }
             if(Mathf.FloorToInt(p4.y) == Mathf.FloorToInt(p0.y))    {    wai++;    }
             if(Mathf.FloorToInt(p4.z) == Mathf.FloorToInt(p0.z))    {    zed++;    }
             if(Mathf.FloorToInt(p4.x) == Mathf.FloorToInt(p1.x))    {    ex++;    }
             if(Mathf.FloorToInt(p4.y) == Mathf.FloorToInt(p1.y))    {    wai++;    }
             if(Mathf.FloorToInt(p4.z) == Mathf.FloorToInt(p1.z))    {    zed++;    }
             if(Mathf.FloorToInt(p4.x) == Mathf.FloorToInt(p2.x))    {    ex++;    }
             if(Mathf.FloorToInt(p4.y) == Mathf.FloorToInt(p2.y))    {    wai++;    }
             if(Mathf.FloorToInt(p4.z) == Mathf.FloorToInt(p2.z))    {    zed++;    }
             
             if(ex+wai+zed == 5)    {
                 if(wai == 1)    {
                     p3 = p4;
                     break;
                 }
             }
         }
     }
     #endregion
     
     Debug.DrawLine(p0, p3, Color.red, 4);
     Debug.DrawLine(p1, p3, Color.red, 4);
     Debug.DrawLine(p2, p3, Color.red, 4);

     if(p3 != new Vector3())    {
         quad = new Vector3[4];
         quad[3] = p3;
     }

     quad[0] = p0;
     quad[1] = p1;
     quad[2] = p2;

     StartCoroutine(CheckMoves());
     yield return null;
 }



 IEnumerator CheckMoves()    {
     top = new Vector3[2];
     foreach(Vector3 v in quad)    {
         if(v == new Vector3())
             continue;

         if(Mathf.FloorToInt(v.y) == Mathf.FloorToInt(top[0].y) && v.y > top[1].y)    {
             top[1] = top[0];
             top[0] = v;
         } else if(v.y > top[0].y)    {
             top[1] = top[0];
             top[0] = v;
         }
     }

     if(Vector3.Distance(transform.position, (top[0]+top[1])/2) <= reach)    {  //This code block doesn't always work!
         if(!Physics.CheckCapsule((top[0]+top[1])/2, (top[0]+top[1])/2+Vector3.up*2, 0.5f) && !Physics.Raycast((top[0]+top[1])/2+Vector3.up*2, Vector3.down, 1.95f))    {
             if(Physics.Raycast((top[0]+top[1])/2+Vector3.up*2+transform.forward/2, Vector3.down, 2.1f))    {
                 transform.position = (top[0]+top[1])/2+Vector3.up*2;
             }
         }
     }

     yield return null;
 }
 }

First it gets the triangle that the players controllercollider hits. Then it Tries to figure out which vertex is the needed vertex to find the adjacent triangle and thus the whole quad. Now that its sure there is a level top edge, it finds the highest edge. Then it checks if the standard unity FPS controller can fit ontop of said edge! That last part is buggy but it works okay. Try it for yourself!