feat(raytracer): add minimal implementation

src/raytracer/sphere.rs

@@ -0,0 +1,49 @@
+use super::types::{Intersect, Material, Point3, Ray, Scalar, Vector3};
+
+extern crate nalgebra as na;
+
+pub struct Sphere {
+    center: Point3,
+    radius: Scalar,
+    material: Material,
+}
+
+/// Numerical error tolerance
+const EPSILON: Scalar = 1e-5;
+
+impl Intersect for Sphere {
+    fn intersect<'a>(&'a self, ray: &Ray) -> Option<(Point3, Vector3, Scalar, &'a Material)> {
+        let co = ray.origin - self.center;
+
+        let a = ray.direction.dot(&ray.direction);
+        let b = 2.0 * ray.direction.dot(&co);
+        let c = co.dot(&co) - (self.radius * self.radius);
+        let d = b * b - 4.0 * a * c;
+
+        if d >= 0.0 {
+            let e = d.sqrt();
+            let t1 = (-b - e) / (2.0 * a);
+            let t2 = (-b + e) / (2.0 * a);
+            let mut t = Scalar::MAX;
+
+            if t1 > EPSILON && t1 < t {
+                t = t1;
+            }
+            if t2 > EPSILON && t2 < t {
+                t = t2;
+            }
+
+            if t < Scalar::MAX {
+                let isect_pt: Point3 = ray.origin + ray.direction * t;
+                return Some((
+                    isect_pt,
+                    (isect_pt - self.center) / self.radius,
+                    t,
+                    &self.material,
+                ));
+            }
+        }
+
+        None
+    }
+}