Changes made per requests

Author: trevordblack

books/RayTracingInOneWeekend.html

@@ -292,7 +292,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [vec3-class]: <kbd>[vec3.h]</kbd> `vec3` class]
+    [Listing [vec3-class]: <kbd>[vec3.h]</kbd> vec3 class]
 </div>
 
 We use `double` here, but some ray tracers use `float`. Either one is fine -- follow your own
@@ -350,7 +350,7 @@
         return v / v.length();
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [vec3-utility]: <kbd>[vec3.h]</kbd> `vec3` utility functions]
+    [Listing [vec3-utility]: <kbd>[vec3.h]</kbd> vec3 utility functions]
 
 <div class='together'>
 Now we can change our main to use this:
@@ -391,23 +391,20 @@
 --------------
 <div class='together'>
 The one thing that all ray tracers have is a ray class, and a computation of what color is seen
-along a ray. Let’s think of a ray as a function:
-
-  $$ \mathbf{p}(t) = \mathbf{a} + t \vec{\mathbf{b}} $$
-
-Where $\mathbf{p}$ is a 3D position along a line in 3D, $\mathbf{a}$ is the ray origin, and
+along a ray. Let’s think of a ray as a function $\mathbf{p}(t) = \mathbf{a} + t \vec{\mathbf{b}}$.
+Here $\mathbf{p}$ is a 3D position along a line in 3D. $\mathbf{a}$ is the ray origin and
 $\vec{\mathbf{b}}$ is the ray direction. The ray parameter $t$ is a real number (`double` in the
-code). Plug in a different $t$ and $\mathbf{p}(t)$ moves the point along the ray. Add in negative
-$t$ and you can go anywhere on the 3D line. For positive $t$, you get only the parts in front of
-$\mathbf{a}$, and this is what is often called a half-line or ray. This is where the _ray_ in
+code). Plug in a different $t$ and $p(t)$ moves the point along the ray. Add in negative $t$ and you
+can go anywhere on the 3D line. For positive $t$, you get only the parts in front of $\mathbf{a}$,
+and this is what is often called a half-line or ray. This is where the _ray_ in
 _ray tracing_ comes from.
 
   ![Figure [lerp]: Linear interpolation](../images/fig.lerp.jpg)
 
 </div>
 
 <div class='together'>
-The function $\mathbf{p}(t)$ in more verbose code form I call `ray::at(t)`:
+The function $p(t)$ in more verbose code form I call `ray::at(t)`:
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     #ifndef RAY_H
@@ -436,7 +433,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [ray-initial]: <kbd>[ray.h]</kbd> The `ray` class]
+    [Listing [ray-initial]: <kbd>[ray.h]</kbd> The ray class]
 </div>
 
 
@@ -569,11 +566,11 @@
 
 <div class='together'>
 We can read this as “any point $\mathbf{p}$ that satisfies this equation is on the sphere”. We want
-to know if our ray $\mathbf{p}(t) = \mathbf{a} + t\vec{\mathbf{b}}$ ever hits the sphere anywhere.
-If it does hit the sphere, there is some $t$ for which $\mathbf{p}(t)$ satisfies the sphere
-equation. So we are looking for any $t$ where this is true:
+to know if our ray $p(t) = \mathbf{a} + t\vec{\mathbf{b}}$ ever hits the sphere anywhere. If it does
+hit the sphere, there is some $t$ for which $p(t)$ satisfies the sphere equation. So we are looking
+for any $t$ where this is true:
 
-  $$ (\mathbf{p}(t) - \mathbf{c})\cdot(\mathbf{p}(t) - \mathbf{c}) = R^2 $$
+  $$ (p(t) - \mathbf{c})\cdot(p(t) - \mathbf{c}) = R^2 $$
 
 or expanding the full form of the ray $p(t)$:
 
@@ -810,7 +807,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [hittable-initial]: <kbd>[hittable.h]</kbd> The `hittable` class]
+    [Listing [hittable-initial]: <kbd>[hittable.h]</kbd> The hittable class]
 </div>
 
 <div class='together'>
@@ -865,7 +862,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [sphere-initial]: <kbd>[sphere.h]</kbd> The `sphere` class]
+    [Listing [sphere-initial]: <kbd>[sphere.h]</kbd> The sphere class]
 
 </div>
 
@@ -963,7 +960,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [hittable-time-side]: <kbd>[hittable.h]</kbd> The `hittable` class with time and side]
+    [Listing [hittable-time-side]: <kbd>[hittable.h]</kbd> The hittable class with time and side]
 
 <div class='together'>
 And then we add the surface side determination to the class:
@@ -1002,7 +999,7 @@
         return false;
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [sphere-final]: <kbd>[sphere.h]</kbd> The `sphere` class with normal determination]
+    [Listing [sphere-final]: <kbd>[sphere.h]</kbd> The sphere class with normal determination]
 
 </div>
 
@@ -1057,7 +1054,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [hittable-list-initial]: <kbd>[hittable_list.h]</kbd> The `hittable_list` class]
+    [Listing [hittable-list-initial]: <kbd>[hittable_list.h]</kbd> The hittable_list class]
 </div>
 
 
@@ -1092,7 +1089,7 @@
     auto vec3_ptr   = make_shared<vec3>(1.414214, 2.718281, 1.618034);
     auto sphere_ptr = make_shared<sphere>(point3(0,0,0), 1.0);
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [shared-ptr-auto]: An example allocation using `shared_ptr` with `auto` type]
+    [Listing [shared-ptr-auto]: An example allocation using shared_ptr with auto type]
 
 </div>
 
@@ -1159,7 +1156,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [rtweekend-initial]: <kbd>[rtweekend.h]</kbd> The `rtweekend.h` common header]
+    [Listing [rtweekend-initial]: <kbd>[rtweekend.h]</kbd> The rtweekend.h common header]
 </div>
 
 <div class='together'>
@@ -1226,7 +1223,7 @@
         std::cerr << "\nDone.\n";
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [main-with-rtweekend-h]: <kbd>[main.cc]</kbd> The new main with `hittables`]
+    [Listing [main-with-rtweekend-h]: <kbd>[main.cc]</kbd> The new main with hittables]
 </div>
 
 <div class='together'>
@@ -1279,7 +1276,7 @@
         return min + (max-min)*random_double();
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [random-double]: <kbd>[rtweekend.h]</kbd> `random_double()` functions]
+    [Listing [random-double]: <kbd>[rtweekend.h]</kbd> random_double() functions]
 </div>
 
 <div class='together'>
@@ -1299,7 +1296,7 @@
         return rand_generator();
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [random-double-alt]: <kbd>[rtweekend.h]</kbd> `random_double()`, alternate implemenation]
+    [Listing [random-double-alt]: <kbd>[rtweekend.h]</kbd> random_double(), alternate implemenation]
 </div>
 
 
@@ -1344,7 +1341,7 @@
     };
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [camera-initial]: <kbd>[camera.h]</kbd> The `camera` class]
+    [Listing [camera-initial]: <kbd>[camera.h]</kbd> The camera class]
 </div>
 
 To handle the multi-sampled color computation, we update the `vec3::write_color()` function. Rather
@@ -1360,7 +1357,7 @@
         return x;
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [clamp]: <kbd>[rtweekend.h]</kbd> The `clamp()` utility function]
+    [Listing [clamp]: <kbd>[rtweekend.h]</kbd> The clamp() utility function]
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     void write_color(std::ostream &out, int samples_per_pixel) {
@@ -1376,7 +1373,7 @@
             << static_cast<int>(256 * clamp(b, 0.0, 0.999)) << '\n';
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [write-color-clamped]: <kbd>[vec3.h]</kbd> The `write_color()` function]
+    [Listing [write-color-clamped]: <kbd>[vec3.h]</kbd> The write_color() function]
 
 <div class='together'>
 Main is also changed:
@@ -1496,7 +1493,7 @@
             return vec3(random_double(min,max), random_double(min,max), random_double(min,max));
         }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [vec-rand-util]: <kbd>[vec3.h]</kbd> `vec3` random utility functions]
+    [Listing [vec-rand-util]: <kbd>[vec3.h]</kbd> vec3 random utility functions]
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     vec3 random_in_unit_sphere() {
@@ -1507,7 +1504,7 @@
         }
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [random-in-unit-sphere]: <kbd>[vec3.h]</kbd> The `random_in_unit_sphere()` function]
+    [Listing [random-in-unit-sphere]: <kbd>[vec3.h]</kbd> The random_in_unit_sphere() function]
 </div>
 
 <div class='together'>
@@ -1529,7 +1526,7 @@
         return (1.0-t)*color(1.0, 1.0, 1.0) + t*color(0.5, 0.7, 1.0);
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [ray-color-random-unit]: <kbd>[main.cc]</kbd> `ray_color()` using a random ray direction]
+    [Listing [ray-color-random-unit]: <kbd>[main.cc]</kbd> ray_color() using a random ray direction]
 </div>
 
 
@@ -1595,7 +1592,7 @@
         std::cerr << "\nDone.\n";
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [ray-color-depth]: <kbd>[main.cc]</kbd> `ray_color()` with depth limiting]
+    [Listing [ray-color-depth]: <kbd>[main.cc]</kbd> ray_color() with depth limiting]
 </div>
 
 <div class='together'>
@@ -1639,7 +1636,7 @@
             << static_cast<int>(256 * clamp(b, 0.0, 0.999)) << '\n';
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [write-color-gamma]: <kbd>[vec3.h]</kbd> `write_color()`, with gamma correction]
+    [Listing [write-color-gamma]: <kbd>[vec3.h]</kbd> write_color(), with gamma correction]
 
 </div>
 
@@ -1694,7 +1691,7 @@
         return vec3(r*cos(a), r*sin(a), z);
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [random-unit-vector]: <kbd>[vec3.h]</kbd> The `random_unit_vector()` function]
+    [Listing [random-unit-vector]: <kbd>[vec3.h]</kbd> The random_unit_vector() function]
 
   ![Figure [rand-unit-vector]: Generating a random unit vector](../images/fig.rand-unitvector.png)
 
@@ -1724,7 +1721,7 @@
         return (1.0-t)*color(1.0, 1.0, 1.0) + t*color(0.5, 0.7, 1.0);
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [ray-color-unit-sphere]: <kbd>[main.cc]</kbd> `ray_color()` with replacement diffuse]
+    [Listing [ray-color-unit-sphere]: <kbd>[main.cc]</kbd> ray_color() with replacement diffuse]
 </div>
 
 <div class='together'>
@@ -1782,7 +1779,7 @@
             return -in_unit_sphere;
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [random-in-hemisphere]: <kbd>[vec3.h]</kbd> The `random_in_hemisphere(normal)` function]
+    [Listing [random-in-hemisphere]: <kbd>[vec3.h]</kbd> The random_in_hemisphere(normal) function]
 
 </div>
 
@@ -1809,7 +1806,7 @@
         return (1.0-t)*color(1.0, 1.0, 1.0) + t*color(0.5, 0.7, 1.0);
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [ray-color-hemisphere]: <kbd>[main.cc]</kbd> `ray_color()` with hemispherical scattering]
+    [Listing [ray-color-hemisphere]: <kbd>[main.cc]</kbd> ray_color() with hemispherical scattering]
 
 Gives us the following image:
 
@@ -1860,7 +1857,7 @@
 
     #endif
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [material-initial]: <kbd>[material.h]</kbd> The `material` class]
+    [Listing [material-initial]: <kbd>[material.h]</kbd> The material class]
 </div>
 
 
@@ -2003,7 +2000,7 @@
             color albedo;
     };
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [lambertian-initial]: <kbd>[material.h]</kbd> The `lambertian` material class]
+    [Listing [lambertian-initial]: <kbd>[material.h]</kbd> The lambertian material class]
 </div>
 
 Note we could just as well only scatter with some probability $p$ and have attenuation be
@@ -2031,7 +2028,7 @@
         return v - 2*dot(v,n)*n;
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-    [Listing [vec3-reflect]: <kbd>[vec3.h]</kbd> `vec3` reflection function]
+    [Listing [vec3-reflect]: <kbd>[vec3.h]</kbd> vec3 reflection function]
 </div>
 
 <div class='together'>
@@ -2351,7 +2348,7 @@
 
 The value of $\sin\theta'$ cannot be greater than 1. So, if,
 
-  $$ \frac{1.5}{1.0} \cdot \sin\theta > 1.0 $$
+  $$ \frac{1.5}{1.0} \cdot \sin\theta > 1.0 $$,
 
 <div class="together">
 the equality between the two sides of the equation is broken and a solution cannot exist. If a
@@ -2655,9 +2652,9 @@
   ![Figure [cam-up]: Camera view up direction](../images/fig.cam-up.jpg)
 
 Remember that `vup`, `v`, and `w` are all in the same plane. Note that, like before when our fixed
-camera faced `-Z`, our arbitrary view camera faces `-w`. And keep in mind that we can -- but we
-don’t have to -- use world up `(0,1,0)` to specify vup. This is convenient and will naturally keep
-your camera horizontally level until you decide to experiment with crazy camera angles.
+camera faced -Z, our arbitrary view camera faces -w. And keep in mind that we can -- but we don’t
+have to -- use world up $(0,1,0)$ to specify vup. This is convenient and will naturally keep your
+camera horizontally level until you decide to experiment with crazy camera angles.
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     class camera {