Add 3 new type of object: Sphere, Object and Intersect.

Add Intersect object as a way to report where a ray intersect another object and which one it is.
Add an Object base class for all object that can be rendered.
Add the Sphere object.

source/objects/object.cpp

@@ -0,0 +1,17 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Object implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+
+#include <ray.h>
+#include <object.h>
+#include <intersect.h>
+
+Intersect Object::intersect(Ray r)
+{
+    return Intersect();
+};

source/objects/sphere.cpp

@@ -0,0 +1,35 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Sphere implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <math.h>
+
+#include <sphere.h>
+#include <ray.h>
+#include <tuple.h>
+#include <intersect.h>
+
+Intersect Sphere::intersect(Ray r)
+{
+    Intersect ret;
+    double a, b, c, discriminant;
+    Tuple sphere_to_ray = r.origin - Point(0, 0, 0);
+
+    a = r.direction.dot(r.direction);
+    b = 2 * r.direction.dot(sphere_to_ray);
+    c = sphere_to_ray.dot(sphere_to_ray) - 1;
+
+    discriminant = b * b - 4 * a * c;
+
+    if (discriminant >= 0)
+    {
+        ret.add(newIntersection((-b - sqrt(discriminant)) / (2 * a), this));
+        ret.add(newIntersection((-b + sqrt(discriminant)) / (2 * a), this));
+    }
+
+    return ret;
+}