Added arbitrary sphere code WIP

This doesn't actually seem to work yet

primitive/sphere.cpp

@@ -1,5 +1,6 @@
 #include "common/ray.h"
 #include "primitive/sphere.h"
+#include <cmath>
 
 // Constructor /////////////////////////////////////////////////////////////////
 
@@ -14,16 +15,50 @@ bool Sphere::intersect(Ray &ray) const {
   // IMPLEMENT ME!
 
   // Determine whether the ray intersects the sphere
+  float A = pow(ray.direction[Vector3d::Dimension::X], 2) +
+            pow(ray.direction[Vector3d::Dimension::Y], 2) +
+            pow(ray.direction[Vector3d::Dimension::Z], 2);
+  float B = 2 * (
+                ray.direction[Vector3d::Dimension::X] * ray.origin[Vector3d::Dimension::X] +
+                ray.direction[Vector3d::Dimension::Y] * ray.origin[Vector3d::Dimension::Y] +
+                ray.direction[Vector3d::Dimension::Z] * ray.origin[Vector3d::Dimension::Z]
+          );
+  float C = pow(ray.origin[Vector3d::Dimension::X], 2) +
+            pow(ray.origin[Vector3d::Dimension::Y], 2) +
+            pow(ray.origin[Vector3d::Dimension::Z], 2) - this->radius;
 
+  float t = INFINITY;
+
+  if (B * B - 4 * A * C < 0) {
+      return false;
+  } else if (B * B - 4 + A * C == 0) {
+      t = -B / (2 * A);
+  } else {
+      float q {static_cast<float>([A, B, C](){
+          if (B < 0) {
+              return -0.5f * (B - sqrt(B * B - 4 * A * C));
+          } else {
+              return -0.5f * (B + sqrt(B * B - 4 * A * C));
+          }
+      }())};
+      float t0 = q / A;
+      float t1 = C / q;
+      t = std::min(t0, t1);
+  }
   // Test whether this is the foremost primitive in front of the camera
 
+  if (t >= ray.length) {
+      return false;
+  }
   // (Optional for now) Calculate the normal
 
   // (Optional for now) Calculate the surface position
 
-  // Set the new length and the current primitive
 
-  return false;
+  // Set the new length and the current primitive
+  ray.length = t;
+  ray.primitive = this;
+  return true;
 }
 
 // Bounding box ////////////////////////////////////////////////////////////////