Add simple sphere.

vec3.h

@@ -89,7 +89,7 @@ inline Vec3 operator/(const Vec3& v, double t) {
 inline double dot(const Vec3 &u, const Vec3& v) {
     return u.e[0] * v.e[0]
          + u.e[1] * v.e[1]
-         + u.e[2] * v.e[1];
+         + u.e[2] * v.e[2];
 }
 
 inline Vec3 cross(const Vec3 &u, const Vec3& v) {

wtracer.cpp

@@ -4,7 +4,18 @@
 #include "vec3.h"
 #include "ray.h"
 
+bool hit_sphere(const Point3& center, double radius, const Ray& r) {
+    Vec3 oc = r.origin() - center;
+    auto a = dot(r.direction(), r.direction());
+    auto b = 2.0 * dot(oc, r.direction());
+    auto c = dot(oc, oc) - radius * radius;
+    auto disciminant = b*b - 4*a*c;
+    return disciminant > 0;
+}
+
 Color ray_color(const Ray& r) {
+    if (hit_sphere(Point3(0, 0, -1), 0.5, r))
+        return Color(1, 0, 0);
     Vec3 unit_direction = unit_vector(r.direction());
     auto t = 0.5 * (unit_direction.y() + 1.0);
     return (1.0 - t) * Color(1.0, 1.0, 1.0) + t * Color(0.5, 0.7, 1.0);