Get the mesh Project Plane on Click and calculate its area

Question

Here is the excerpt of my script which is calculating the surface area and face area of a mesh on OnMouseDown Event.

    private void OnMouseDown()
    {
         Mesh selectedMesh = this.gameObject.GetComponent<MeshFilter>().mesh;

        float surfaceArea   = CalculateSurfaceArea(selectedMesh);
        float areaFromXFace = CalculateFacingArea(selectedMesh, new Vector3(1, 0, 0));
        float areaFromYFace = CalculateFacingArea(selectedMesh, new Vector3(0, 1, 0));
        float areaFromZFace = CalculateFacingArea(selectedMesh, new Vector3(0, 0, 1));
        float areaFromClickedFace = ProjectionPlaneClickedArea(selectedMesh);    

       string areas =  "\n Surface Area            : " + surfaceArea;
        areas += "\n Area From X-axis Face   : " + areaFromXFace;
        areas += "\n Area From Y-axis Face   : " + areaFromYFace;
        areas += "\n Area From Z-axis Face   : " + areaFromZFace;
        areas += "\n Area From Selected Face : " + areaFromClickedFace;
        Debug.Log("Areas :"+ areas);

     }

     float ProjectionPlaneClickedArea(Mesh selcectedMesh)
     {

        Camera c = Camera.main;
        Ray ray = c.ScreenPointToRay(Input.mousePosition);
        RaycastHit hit;
        if (Physics.Raycast(ray, out hit, 100f))
        {
             Debug.DrawRay(ray.origin, ray.direction * 100, Color.yellow);
             Debug.Log("normal :" + hit.normal);
             Debug.Log("Area from normal/direction : " + CalculateFacingArea(selcectedMesh, hit.normal));
                    return CalculateFacingArea(selcectedMesh, hit.normal);
                }
                return 0f;
       }

       float CalculateSurfaceArea(Mesh mesh)
       {
         //Limitation: Note that if your mesh has any double-sided faces or internal faces, they can bias this result.
         var triangles = mesh.triangles;
         var vertices = mesh.vertices;

         double sum = 0.0;

         for (int i = 0; i < triangles.Length; i += 3)               //iterate over the triangles of the mesh
         {
           Vector3 corner = vertices[triangles[i]];            //for each triangle, we'll compute vectors representing the two edges
          Vector3 a = vertices[triangles[i + 1]] - corner;
          Vector3 b = vertices[triangles[i + 2]] - corner;

          sum += Vector3.Cross(a, b).magnitude; //half the magnitude of the cross product of these edges gives us the area of the triangle
         }

        return (float)(sum / 2.0);
     }

     /// <summary>
     /// compute just the area of the mesh facing in a particular direction, you can try this version instead. 
    /// Pass the direction you want to view the mesh from and it should compute the projected surface area of
    /// the faces facing at least partially in that direction.
   /// </summary>
    /// <param name="mesh"></param>
     /// <param name="direction"></param>
     /// <returns></returns>
      float CalculateFacingArea(Mesh mesh, Vector3 direction)
      {
          direction = direction.normalized;
          var triangles = mesh.triangles;
          var vertices = mesh.vertices;

          double sum = 0.0;

         for (int i = 0; i < triangles.Length; i += 3)    //iterate over the triangles of the mesh
         {
             //"Subtracting each 2nd & 3rd vertex" just gives the two edges of the triangle radiating from the initial corner. 
             Vector3 corner  = vertices[triangles[i]];
             Vector3 a       = vertices[triangles[i + 1]] - corner; 
             Vector3 b       = vertices[triangles[i + 2]] - corner;

            //The cross product divided by two gives the area of the triangle.
            //The dot product is what handles projecting this area onto the plane of interest. 
            float projection = Vector3.Dot(Vector3.Cross(b, a), direction);

            if (projection > 0f)//only sum projected triangles
                 sum += projection;
                }
                return (float)(sum / 2.0);
      }

I am able calculate face area by CalculateFacingArea method it needs a mesh and direction which is working fine, as if i want to calculate the area of x direction i can use it

float areaFromXFace = CalculateFacingArea(selectedMesh, new Vector3(1, 0, 0));

BUT I have to provide the face/direction information dynamically which is i am doing in this function ProjectionPlaneClickedArea using a raycast. It is getting a hit point normals which i am using as a direction and passing it to the function. It is working well with some of the meshes but not with all meshes, for example below image:

As you can see if I click this object from the front then it should calculate Y Face area but it is calculating with X direction. The click point normal value is (1.0, 0.0, 0.1).

While it is working fine if my clicked object axis are something like this:

In this case x is the facing are and it is working fine. I have this value of normal (1.0, 0.0, 0.0).

I am neither geometry/math expert nor a modeler so I cannot identify that its Object's normal problem or it is calculation problem.

Remember I don't want to model all the objects in the same direction/axis, where i can get the direction hard-coded. I want to calculate the direction dynamically but correctly.

Answer 1

You'll need to transform the normal into local coordinates before using it with the mesh.

float ProjectionPlaneClickedArea(Mesh selcectedMesh)
{
        Camera c = Camera.main;
        Ray ray = c.ScreenPointToRay(Input.mousePosition);
        RaycastHit hit;
        if (Physics.Raycast(ray, out hit, 100f))
        {
             Vector3 localNormal = hit.transform.InverseTransformDirection(hit.normal);
             return CalculateFacingArea(selcectedMesh, localNormal);
        }
        return 0f;
}