58 lines
1.7 KiB
C++
58 lines
1.7 KiB
C++
#include "Triangle.h"
|
|
#include "Ray.h"
|
|
#include <Eigen/Geometry> // hint
|
|
|
|
bool Triangle::intersect(
|
|
const Ray &ray, const double min_t, double &t, Eigen::Vector3d &n) const {
|
|
/* 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;
|
|
const 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;
|
|
}
|