Mesh modification and UV problem

Hello Unity Community, today I come here seeking an answer to a problem I'm having with one of my projects.

Simply put, I'm trying to slice any convex object in half using a plane. The problem isn't with the slicing, its actually to do with generating new UV coordinates for the sliced mesh.

These are the steps I'm going through at the moment.

1) Grab a triangle from the original mesh, grab the UV coordinates that belong to the vertices.

2) Test against the plane, if no intersection, determine if its on the left or right side of plane, add the triangle as is to the new mesh with original UV coordinates.

3) if intersection is detected, grab the intersection points, which should be a maximum of 2 (only slicing with one plane)

4) triangulate the points using a convex hull algorithm, should yield either 1 or 2 triangles for 4 points.

5) using Barycentric coordinates of the original triangle, generate the new UV coordinates and add them to the mesh, perform same operation for the left/right hand side sliced meshes.

The primary problem I'm having is with step 5. There is severe inconsistency with the generated UV's, and I've spent more than a week testing my google-fu skills to try and fix the problem.

I'm going to share some code, mainly the calculation with the barycentric coordinates which i've used successfully in another project, so it should work as is.

 // compute the barycentric coordinates of triangle a-b-c in regards to point p and store result in references u-v-w respectively
 public static void barycentric(Vector3 a, Vector3 b, Vector3 c, Vector3 p, ref float u, ref float v, ref float w) {
     Vector3 m = Vector3.Cross(b - a, c - a);
     
     float nu;
     float nv;
     float ood;
     
     float x = Mathf.Abs(m.x);
     float y = Mathf.Abs(m.y);
     float z = Mathf.Abs(m.z);
     
     // compute areas of plane with largest projections
     if (x >= y && x >= z) {
         // area of PBC in yz plane
         nu = triArea2D(p.y, p.z, b.y, b.z, c.y, c.z);
         // area of PCA in yz plane
         nv = triArea2D(p.y, p.z, c.y, c.z, a.y, a.z);
         // 1/2*area of ABC in yz plane
         ood = 1.0f / m.x;
     }
     else if (y >= x && y >= z) {
         // project in xz plane
         nu = triArea2D(p.x, p.z, b.x, b.z, c.x, c.z);
         nv = triArea2D(p.x, p.z, c.x, c.z, a.x, a.z);
         ood = 1.0f / -m.y;
     }
     else {
         // project in xy plane
         nu = triArea2D(p.x, p.y, b.x, b.y, c.x, c.y);
         nv = triArea2D(p.x, p.y, c.x, c.y, a.x, a.y);
         ood = 1.0f / m.z;
     }
     
     u = nu * ood;
     v = nv * ood;
     w = 1.0f - u - v;
 }

and of course the triArea2D function

 public static float triArea2D(float x1, float y1, float x2, float y2, float x3, float y3) {
     return (x1 - x2) * (y2 - y3) - (x2 - x3) * (y1 - y2);    
 }

this is where newVertexUV = u oldUVA + v oldUVB + w * oldUVC

Below is some screenshot of the problem I'm having

And an even more severe defect, when I slice at a slightly different angle

And this is the end of my question, I am officially stuck and have exhausted my google-fu skills. Does anyone know how or why the UV's are not generated properly using the technique above? could the order of triangles actually play a role? Thank you in advance.

 w = 1.0f - u - v;

 public static void barycentricSign(Vector3 a, Vector3 b, Vector3 c, Vector3 p, ref float u, ref float v, ref float w) {
     Vector3 f1 = a - p;
     Vector3 f2 = b - p;
     Vector3 f3 = c - p;
     
     Vector3 va = Vector3.Cross(a - b, a - c);
     Vector3 va1 = Vector3.Cross(f2, f3);
     Vector3 va2 = Vector3.Cross(f3, f1);
     Vector3 va3 = Vector3.Cross(f1, f2);
     
     float area = va.magnitude;
     
     u = va1.magnitude / area * $$anonymous$$athf.Sign(Vector3.Dot(va, va1));
     v = va2.magnitude / area * $$anonymous$$athf.Sign(Vector3.Dot(va, va2));
     w = va3.magnitude / area * $$anonymous$$athf.Sign(Vector3.Dot(va, va3));
 }

 AB = B-A;
 AP = P-A;
 u = AP.magnitude / AB.magnitude
 v = 1-u;

 uv = UVA*v + UVB*u