6952 - raytracing: much better

The image is now visually indistinguishable from the baseline, though the
file isn't quite bit-for-bit correct.

I found 3 bugs:
a) I forgot to normalize the ray. After creating a helper to "automatically"
do it for me, it turns out said helper requires manually using.
b) I forgot to multiply by t at one place.
c) vec3-length was half-written.

For the umpteenth time, the bugs were all in the last place I looked. I
was worried about spending a lot of time transcribing `main` without any
feedback, but that turned out to be perfect.

1 files changed, 102 insertions, 0 deletions

diff --git a/apps/raytracing/vec3.h b/apps/raytracing/vec3.h
new file mode 100644
index 00000000..d8341d36
--- /dev/null
+++ b/apps/raytracing/vec3.h
@@ -0,0 +1,102 @@
+#ifndef VEC3_H
+#define VEC3_H
+
+#include <cmath>
+#include <iostream>
+
+using std::sqrt;
+
+class vec3 {
+    public:
+        vec3() : e{0,0,0} {}
+        vec3(float e0, float e1, float e2) : e{e0, e1, e2} {}
+
+        float x() const { return e[0]; }
+        float y() const { return e[1]; }
+        float z() const { return e[2]; }
+
+        vec3 operator-() const { return vec3(-e[0], -e[1], -e[2]); }
+        float operator[](int i) const { return e[i]; }
+        float& operator[](int i) { return e[i]; }
+
+        vec3& operator+=(const vec3 &v) {
+            e[0] += v.e[0];
+            e[1] += v.e[1];
+            e[2] += v.e[2];
+            return *this;
+        }
+
+        vec3& operator*=(const float t) {
+            e[0] *= t;
+            e[1] *= t;
+            e[2] *= t;
+            return *this;
+        }
+
+        vec3& operator/=(const float t) {
+            return *this *= 1/t;
+        }
+
+        float length() const {
+            return sqrt(length_squared());
+        }
+
+        float length_squared() const {
+            return e[0]*e[0] + e[1]*e[1] + e[2]*e[2];
+        }
+
+    public:
+        float e[3];
+};
+
+// Type aliases for vec3
+using point3 = vec3;   // 3D point
+using color = vec3;    // RGB color
+
+// vec3 Utility Functions
+
+inline std::ostream& operator<<(std::ostream &out, const vec3 &v) {
+    return out << v.e[0] << ' ' << v.e[1] << ' ' << v.e[2];
+}
+
+inline vec3 operator+(const vec3 &u, const vec3 &v) {
+    return vec3(u.e[0] + v.e[0], u.e[1] + v.e[1], u.e[2] + v.e[2]);
+}
+
+inline vec3 operator-(const vec3 &u, const vec3 &v) {
+    return vec3(u.e[0] - v.e[0], u.e[1] - v.e[1], u.e[2] - v.e[2]);
+}
+
+inline vec3 operator*(const vec3 &u, const vec3 &v) {
+    return vec3(u.e[0] * v.e[0], u.e[1] * v.e[1], u.e[2] * v.e[2]);
+}
+
+inline vec3 operator*(float t, const vec3 &v) {
+    return vec3(t*v.e[0], t*v.e[1], t*v.e[2]);
+}
+
+inline vec3 operator*(const vec3 &v, float t) {
+    return t * v;
+}
+
+inline vec3 operator/(vec3 v, float t) {
+    return (1/t) * v;
+}
+
+inline float 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[2];
+}
+
+inline vec3 cross(const vec3 &u, const vec3 &v) {
+    return vec3(u.e[1] * v.e[2] - u.e[2] * v.e[1],
+                u.e[2] * v.e[0] - u.e[0] * v.e[2],
+                u.e[0] * v.e[1] - u.e[1] * v.e[0]);
+}
+
+inline vec3 unit_vector(vec3 v) {
+    return v / v.length();
+}
+
+#endif