Mesh based on noise

I have been trying to generate a mesh based on some noise, and I want to say if the noise is 0 don't generate a vertices. But the problem is that the mesh will end up look really weird because of the way I generate my triangles.

Code:

     private void CreateMesh()
     {
         var m = new RidgeNoise(Random.seed);
         m.OctaveCount = 2;
         m.Frequency = 0.01f;

         int hw = Terrain.activeTerrain.terrainData.heightmapWidth;
         float[,] heightmap = Terrain.activeTerrain.terrainData.GetHeights(0, 0, hw, hw);
 
         int ChunkWidth = hw / 8;
         int ChunkCount = hw / ChunkWidth;
 
         float scale = Terrain.activeTerrain.terrainData.size.x / hw;
 
         Vector2 uvScale = new Vector2(1.0f / hw, 1.0f / hw);
 
         for (int cx = 0; cx < ChunkCount; cx++)
         {
             for (int cy = 0; cy < ChunkCount; cy++)
             {
                 int CW = hw / ChunkCount;
                 GameObject water = new GameObject();
                 Vector3 p = new Vector3(cx * ChunkWidth, 0f, cy * ChunkWidth);
 
                 water.transform.localScale = new Vector3(scale, 0.95f, scale);
                 water.transform.position = new Vector3(cx * (ChunkWidth * scale), 0f, cy * (ChunkWidth * scale));
                 water.name = "Water";
                 water.transform.parent = Terrain.activeTerrain.transform;
 
                 water.AddComponent<MeshRenderer>();
                 Mesh w = new Mesh();
                 MeshFilter mf = water.AddComponent<MeshFilter>();
 
                 Vector3[] tVertices = new Vector3[(CW + 1) * (CW + 1)];
                 Vector2[] tUV = new Vector2[tVertices.Length];
                 int[] triangles = new int[tVertices.Length * 6];
 
                 for (int y = 0; y < CW; y++)
                 {
                     for (int x = 0; x < CW; x++)
                     {
                         Vector2 curPos = new Vector2((p.x + x), (p.z + y));
                         float height = heightmap[(int)curPos.y, (int)curPos.x] * Terrain.activeTerrain.terrainData.size.y;
                         if (height < WaterLevel)
                         {
                             height = WaterLevel;
                         }
 
                         float v = Mathf.Max(0f, m.GetValue(curPos.x, curPos.y, 0f) - 0.875f) / 25.0f;
 
                         map.SetPixel((int)curPos.x, (int)curPos.y, Color.white * (v * 25));
                         if (v != 0)
                         {
                             tVertices[y * CW + x] = new Vector3(x, height, y);
                             tUV[y * CW + x] = Vector2.Scale(new Vector2(x, y), uvScale);
                             heightmap[(int)curPos.y, (int)curPos.x] -= v;
 
                         }
                     }
                 }
 
                 int index = 0;
                 for (int y = 0; y < CW - 1; y++)
                 {
                     for (int x = 0; x < CW - 1; x++)
                     {
                         triangles[index] = (y * CW) + x;
                         triangles[index + 1] = ((y + 1) * CW) + x;
                         triangles[index + 2] = ((y + 1) * CW) + x + 1;
 
                         triangles[index + 3] = (y * CW) + x;
                         triangles[index + 4] = ((y + 1) * CW) + x + 1;
                         triangles[index + 5] = (y * CW) + x + 1;
                         index += 6;
                     }
                 }
 
                 w.vertices = tVertices;
                 w.uv = tUV;
                 w.triangles = triangles;
 
                 w.RecalculateNormals();
                 w.Optimize();
 
                 mf.mesh = w;
             }
         }
     }

Noise: Result: