csci5607/assignment-1/src/ray.rs

use crate::scene_data::Sphere;
use crate::vec3::Vec3;

/// A normalized parametric Ray of the form (origin + direction * time)
///
/// That means at any time t: f64, the point represented by origin + direction * time occurs on the
/// ray.
pub struct Ray {
  origin: Vec3,
  direction: Vec3,
}

impl Ray {
  /// Evaluate the ray at a certain point in time, yielding a point
  pub fn eval(&self, time: f64) -> Vec3 {
    self.origin + self.direction * time
  }
}

/// Given a ray and a sphere, returns the first time at which this ray intersects the sphere.
///
/// If there is no intersection point, returns None.
pub fn ray_intersection_time(ray: &Ray, sphere: &Sphere) -> Option<f64> {
  let a =
    ray.direction.x.powi(2) + ray.direction.y.powi(2) + ray.direction.z.powi(2);
  let b = 2.0
    * (ray.direction.x * (ray.origin.x - sphere.center.x)
      + ray.direction.y * (ray.origin.y - sphere.center.y)
      + ray.direction.z * (ray.origin.z - sphere.center.z));
  let c = (ray.origin.x - sphere.center.x).powi(2)
    + (ray.origin.y - sphere.center.y).powi(2)
    + (ray.origin.z - sphere.center.z).powi(2)
    - sphere.radius.powi(2);
  let discriminant = b * b - 4.0 * a * c;

  match discriminant {
    // Discriminant < 0, means the equation has no solutions.
    d if d < 0.0 => return None,

    // Discriminant == 0
    d if d == 0.0 => {
      return Some(-b / (2.0 * a));
    }

    d if d > 0.0 => {
      let solution_1 = (-b + discriminant.sqrt()) / (2.0 * a);
      let solution_2 = (-b - discriminant.sqrt()) / (2.0 * a);

      return Some(solution_1.min(solution_2));
    }

    // Probably hit some NaN or Infinity value due to faulty inputs...
    _ => unreachable!("Invalid determinant value: {discriminant}"),
  }
}

#[cfg(test)]
mod tests {
  use crate::scene_data::Sphere;
  use crate::vec3::Vec3;

  use super::{ray_intersection_time, Ray};

  #[test]
  fn practice_problem_slide_154() {
    let ray = Ray {
      origin: Vec3::new(0.0, 0.0, 0.0),
      direction: Vec3::new(0.0, 0.0, -1.0),
    };
    let sphere = Sphere {
      center: Vec3::new(0.0, 0.0, -10.0),
      radius: 4.0,
    };

    let point = ray_intersection_time(&ray, &sphere).map(|t| ray.eval(t));

    // the intersection point in this case is (0, 0, –6)
    assert_eq!(point, Some(Vec3::new(0.0, 0.0, -6.0)));
  }

  #[test]
  fn practice_problem_slide_158() {
    let ray = Ray {
      origin: Vec3::new(0.0, 0.0, 0.0),
      direction: Vec3::new(0.0, 0.5, -1.0),
    };
    let sphere = Sphere {
      center: Vec3::new(0.0, 0.0, -10.0),
      radius: 4.0,
    };

    // oops! In this case, the ray does not intersect the sphere.
    assert_eq!(ray_intersection_time(&ray, &sphere), None);
  }
}