From 9e16d5f112a3aea7e15017da246e7944a85ead40 Mon Sep 17 00:00:00 2001
From: Faerbit <faerbit@gmail.com>
Date: Wed, 3 Jun 2020 23:25:47 +0200
Subject: [PATCH] Implement sphere normals.

---
 wtracer.cpp | 19 ++++++++++++++-----
 1 file changed, 14 insertions(+), 5 deletions(-)

diff --git a/wtracer.cpp b/wtracer.cpp
index 5f7e7c5..3783243 100644
--- a/wtracer.cpp
+++ b/wtracer.cpp
@@ -1,23 +1,32 @@
 #include <iostream>
+#include <cmath>
 
 #include "color.h"
 #include "vec3.h"
 #include "ray.h"
 
-bool hit_sphere(const Point3& center, double radius, const Ray& r) {
+double 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;
+    if (disciminant < 0) {
+        return -1.0;
+    } else {
+        return (-b - std::sqrt(disciminant)) / (2.0 * a);
+    }
 }
 
 Color ray_color(const Ray& r) {
-    if (hit_sphere(Point3(0, 0, -1), 0.5, r))
-        return Color(1, 0, 0);
+    auto sphere_center = Point3(0, 0, -1);
+    auto t = hit_sphere(sphere_center, 0.5, r);
+    if (t > 0.0) {
+        Vec3 n = unit_vector(r.at(t) - sphere_center);
+        return 0.5 * Color(n.x()+1, n.y()+1, n.z()+1);
+    }
     Vec3 unit_direction = unit_vector(r.direction());
-    auto t = 0.5 * (unit_direction.y() + 1.0);
+    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);
 }