feat: Intersect with Triangle

src/Triangle.cpp

@@ -5,10 +5,55 @@
 bool Triangle::intersect(
     const Ray & ray, const double min_t, double & t, Eigen::Vector3d & n) const
 {
-  ////////////////////////////////////////////////////////////////////////////
-  // Replace with your code here:
-  return false;
-  ////////////////////////////////////////////////////////////////////////////
+    /* Based on
+     * Fundamentals in Computer Graphics - Fourth Edition, Chapter 4.4.2. Ray-Triangle Intersection.
+     * Steve Marschner & Peter Shirley
+     */
+
+    Eigen::Vector3d a = std::get<0>(corners);
+    Eigen::Vector3d b = std::get<1>(corners);
+    Eigen::Vector3d c = std::get<2>(corners);
+    Eigen::Vector3d e = ray.origin;
+    Eigen::Vector3d d = ray.direction;
+
+    /* Using Cramer's rule. */
+
+    /* Calculate the determinant of A. */
+    Eigen::Matrix3d A;
+    A.col(0) = a - b;
+    A.col(1) = a - c;
+    A.col(2) = d;
+    double determinant_A = A.determinant();
+
+    Eigen::Matrix3d t_matrix;
+    t_matrix.col(0) = a - b;
+    t_matrix.col(1) = a - c;
+    t_matrix.col(2) = a - e;
+    t = t_matrix.determinant() / determinant_A;
+
+    if (t < min_t) return false;
+
+    Eigen::Matrix3d gamma_matrix;
+    gamma_matrix.col(0) = a - b;
+    gamma_matrix.col(1) = a - e;
+    gamma_matrix.col(2) = d;
+    double gamma = gamma_matrix.determinant() / determinant_A;
+
+    if (gamma < 0 || gamma > 1) return false;
+
+    Eigen::Matrix3d beta_matrix;
+    beta_matrix.col(0) = a - e;
+    beta_matrix.col(1) = a - c;
+    beta_matrix.col(2) = d;
+    double beta = beta_matrix.determinant() / determinant_A;
+
+    if (beta < 0 || beta + gamma > 1) return false;
+
+    /* Calculate the surface normal vector using the cross product of two edges.
+     * See https://en.wikipedia.org/wiki/Cross_product#Computational_geometry */
+    Eigen::Vector3d edge1 = a - b;
+    Eigen::Vector3d edge2 = a - c;
+    n = edge1.cross(edge2).normalized(); /* Don't forget to normalize the vector. */
+
+    return true;
 }
-
-