How should I calculate the surface area of a 3D Mesh file

Question

How should I calculate the surface area of a 3D Mesh file. Is there any predefined function for surface area calculation. I am working on a project, where after selecting picture volume and area gets calculated automatically in there field.

Answer 1

There is no direct method to get the area but you can create your own custom logic. The logic is to create triangles out of your mesh and calculate there area and add them which will be equals to the area of your mesh.

The example is as follows:

function crossVectors( a, b ) {
   var ax = a.X, ay = a.Y, az = a.Z;
   var bx = b.X, by = b.Y, bz = b.Z;
    var P={X:ay * bz - az * by,
          Y:az * bx - ax * bz,
          Z:ax * by - ay * bx}

   return P;
}
 function SuperficialAreaOfMesh(points) {

   var _len =points.length,
      _area = 0.0;

   if (!_len) return 0.0;

   var i= 0,vols=0;
   var va,vb,vc;
   do  {
      va={X:points[i],Y:points[i+1],Z:points[i+2]};
      vb={X:points[i+3],Y:points[i+4],Z:points[i+5]};
      vc={X:points[i+6],Y:points[i+7],Z:points[i+8]};

      var ab = {X:vb.X-va.X,Y:vb.Y-va.Y,Z:vb.Z-va.Z};
         //vb.clone().sub(va);  var ac = {X:vc.X-va.X,Y:vc.Y-va.Y,Z:va.Z-vc.Z};
      //vc.clone().sub(va);   var cross = new THREE.Vector3();
      cross=crossVectors( ab, ac );
      _area += Math.sqrt(Math.pow(cross.X,2)+Math.pow(cross.Y,2)+Math.pow(cross.Z,2))/2;
      i+=9;
   }
   while (i<points.length);

   return customRound(Math.abs(_area)/100,2);

}
// Let's say you have mesh named mesh
SuperficialAreaOfMesh(mesh.vertices);

The example above follows the tutorial found here.

Here is another nice logic for your query.

Answer 2

 def crossVectors(a,b):
    P = {}
    ax = b[0]['X']
    ay = b[0]['Y']
    az = b[0]['Z']
    bx = b[1]['X']
    by = b[1]['Y']
    bz = b[1]['Z']
    P['X'] = ay * bz - az * by
    P['Y'] = az * bx - ax * bz
    P['Z'] = ax * by - ay * bx
    return P

 def find_mins_maxs(self, obj):
    minx = maxx = miny = maxy = minz = maxz = None
    # print"##############", obj #dir(obj)

    arr1 = obj.points
    length_1 =len(arr1)
    _area = 0.0;
    va ={}
    vb = {}
    vc = {} 
    ab= {}
    ac= {}
    val = []
    if length_1 ==0:
        return 0.0
    i= 0;
    while i<length_1-2:
        va['X'] = arr1[i][0]
        va['Y'] = arr1[i][1]
        va['Z'] = arr1[i][2]
        vb['X'] = arr1[i+1][0]
        vb['Y'] = arr1[i+1][1]
        vb['Z'] = arr1[i+1][2]
        vc['X'] = arr1[i+2][0]
        vc['Y'] = arr1[i+2][1]
        vc['Z'] = arr1[i+2][2]
        ab['X'] = vb['X']-va['X']
        ab['Y'] = vb['Y']-va['Y']
        ab['Z'] = vb['Z']-va['Z']
        ac['X'] = vc['X']-va['X']
        ac['Y'] = vc['Y']-va['Y']
        ac['Z'] = vc['Z']-va['Z']
        val.append(ab)
        val.append(ac)
        cross= self.crossVectors(val)
        _area +=np.sqrt(np.power(cross['X'],2)+np.power(cross['Y'],2)+np.power(cross['Z'],2))/2;
        i+=9;
        area = np.abs(_area)/100
        fractiondigits =2
        area =round(area*np.power(10,fractiondigits))/np.power(10,fractiondigits)
        print"@@@@@@@@@@@@@@@",area
    return area