belogn.js

function belongsToTriangle(x1, y1, x2, y2, x3, y3, xp, yp, xq, yq) {
  // Calculate the length of the sides of the triangle
  const lab = Math.sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2);
  const lac = Math.sqrt((x3 - x1) ** 2 + (y3 - y1) ** 2);
  const lbc = Math.sqrt((x3 - x2) ** 2 + (y3 - y2) ** 2);

  // Check if the triangle is non-degenerate
  if (lab + lac <= lbc || lab + lbc <= lac || lac + lbc <= lab) {
    return "o";
  }

  // Calculate the area of the triangle using Heron's formula
  const s = (lab + lac + lbc) / 2;
  const area = Math.sqrt(s * (s - lab) * (s - lac) * (s - lbc));

  // Calculate the areas of the three sub-triangles formed by the point p
  const area1 = Math.abs((x1 * (y2 - yp) + x2 * (yp - y1) + xp * (y1 - y2)) / 2);
  const area2 = Math.abs((x2 * (y3 - yp) + x3 * (yp - y2) + xp * (y2 - y3)) / 2);
  const area3 = Math.abs((x3 * (y1 - yp) + x1 * (yp - y3) + xp * (y3 - y1)) / 2);

  // Check if point p is inside the triangle
  if (Math.abs(area - (area1 + area2 + area3)) <= Number.EPSILON) {
    // Point p belongs to the triangle
    if (xq >= Math.min(x1, x2, x3) && xq <= Math.max(x1, x2, x3) && yq >= Math.min(y1, y2, y3) && yq <= Math.max(y1, y2, y3)) {
      // Point q also belongs to the triangle
      return "a";
    } else {
      // Point q does not belong to the triangle
      return "1";
    }
  } else {
    // Point p does not belong to the triangle
    if (xq >= Math.min(x1, x2, x3) && xq <= Math.max(x1, x2, x3) && yq >= Math.min(y1, y2, y3) && yq <= Math.max(y1, y2, y3)) {
      // Point q belongs to the triangle
      return "2";
    } else {
      // Neither point p nor point q belongs to the triangle
      return "o";
    }
  }
}

// Example usage
console.log(belongsToTriangle(0, 0,