二次元の三角形の内外判定

template<typename real_t>
inline bool isInTheTriangle(
  real_t px,  real_t py,
  real_t p0x, real_t p0y,
  real_t p1x, real_t p1y,
  real_t p2x, real_t p2y
) {
  real_t Area = 0.5 * (-p1y * p2x + p0y * (-p1x + p2x) + p0x * (p1y - p2y) + p1x * p2y);

  real_t s = 1.0 / (2.0 * Area) * (p0y * p2x - p0x * p2y + (p2y - p0y) * px + (p0x - p2x) * py);
  real_t t = 1.0 / (2.0 * Area) * (p0x * p1y - p0y * p1x + (p0y - p1y) * px + (p1x - p0x) * py);

  if (

    (0 < s) && (s < 1) &&
    (0 < t) && (t < 1) &&
    (0 < (1 - s - t)) &&
    ((1 - s - t) < 1)

    ) {
    return true;
  }
  else {
    return false;
  }
}