Python: find area of polygon from xyz coordinates

Question

I\'m trying to use the shapely.geometry.Polygon module to find the area of polygons but it performs all calculations on the xy plane. This is fine

Answer 1

Same as @Tom Smilack's answer, but in javascript

//determinant of matrix a
function det(a) {
  return a[0][0] * a[1][1] * a[2][2] + a[0][1] * a[1][2] * a[2][0] + a[0][2] * a[1][0] * a[2][1] - a[0][2] * a[1][1] * a[2][0] - a[0][1] * a[1][0] * a[2][2] - a[0][0] * a[1][2] * a[2][1];
}
//unit normal vector of plane defined by points a, b, and c
function unit_normal(a, b, c) {
  let x = math.det([
    [1, a[1], a[2]],
    [1, b[1], b[2]],
    [1, c[1], c[2]]
  ]);
  let y = math.det([
    [a[0], 1, a[2]],
    [b[0], 1, b[2]],
    [c[0], 1, c[2]]
  ]);
  let z = math.det([
    [a[0], a[1], 1],
    [b[0], b[1], 1],
    [c[0], c[1], 1]
  ]);
  let magnitude = Math.pow(Math.pow(x, 2) + Math.pow(y, 2) + Math.pow(z, 2), 0.5);
  return [x / magnitude, y / magnitude, z / magnitude];
}
// dot product of vectors a and b
function dot(a, b) {
  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2];
}
// cross product of vectors a and b
function cross(a, b) {
  let x = (a[1] * b[2]) - (a[2] * b[1]);
  let y = (a[2] * b[0]) - (a[0] * b[2]);
  let z = (a[0] * b[1]) - (a[1] * b[0]);
  return [x, y, z];
}

// area of polygon poly
function area(poly) {
  if (poly.length < 3) {
    console.log("not a plane - no area");
    return 0;
  } else {
    let total = [0, 0, 0]
    for (let i = 0; i < poly.length; i++) {
      var vi1 = poly[i];
      if (i === poly.length - 1) {
        var vi2 = poly[0];
      } else {
        var vi2 = poly[i + 1];
      }
      let prod = cross(vi1, vi2);
      total[0] = total[0] + prod[0];
      total[1] = total[1] + prod[1];
      total[2] = total[2] + prod[2];
    }
    let result = dot(total, unit_normal(poly[0], poly[1], poly[2]));

    return Math.abs(result/2);
  }

}