Get Mesh Data From Texture Positions

I am working on generating a texture that updates in real time based on a few different parameters. To accomplish this I am looking to find information about the mesh the texture is applied to and use that information to do my calculations. The issue I've run into is that there doesn't appear to be a means to accomplish this.

I am looking to find the Normal and Position of the point on a model from texture coordinates but all I have been able to accomplish is to pull the raw data from the mesh (using the uv, normal and other properties of the Mesh object). This doesn't accomplish what I am looking for as my algorithm needs complete coverage to work, that is, I can't skip over a point on the texture.

Is there some way to efficiently get these values or am I going to need another solution?

Edit: Currently I am using a precalculation to figure this out. This calculation takes approximately a minute to run on my computer for a 16x16 texture. That is hardly optimal. While I could thread this I think that'd would just serve to hide a less than optimal solution. My code is as follows (WrappingGrid is a custom class for calculating nearby points based on a grid which wraps (like UV cords do)):

 void Start () {
     grid = new WrappingGrid(1, 1);
     nodes = new MeshTextureNode[heatmap.width, heatmap.height];
     for (int x = 0; x < heatmap.width; ++x)
     {
         for (int y = 0; y < heatmap.height; ++y)
         {
             float u = (float)x / (float)heatmap.width;
             float v = (float)y / (float)heatmap.height;
             int closest = 0;

             for (int i = 0; i < mesh.uv.Length; ++i)
             {
                 closest = CalculateClosest(u, v, closest, i);
             }

             nodes[x, y] = new MeshTextureNode()
             {
                 normal = mesh.normals[closest],
                 localPosition = mesh.vertices[closest]
             };
         }
     }
 }

 private int CalculateClosest(float u, float v, int closest, int i)
 {
     Vector2 thisDiff = mesh.uv[i];
     Vector2 closestDiff = mesh.uv[closest];
     if (grid.NearerThanPoint(new Vector2(u, v), thisDiff, closestDiff)) closest = i;
     return closest;
 }