Merge pull request #916 from RayTracing/fix-textbf

Use mathbf{} instead of textbf{}

Author: hollasch

CHANGELOG.md

@@ -28,7 +28,7 @@ Change Log -- Ray Tracing in One Weekend
   - Fix: rect hit returning NaNs and infinities. Superseded with new `quad` primitive (#681)
   - Added: New 2D `quad` primitive of arbitrary orientation (#756)
   - Added: New `box()` utility function returns `hittable_list` of new `quad` primitives (#780)
-  - Fix: Add `\mathit` to italic math variables to fix slight kerning issues (#839)
+  - Fix: Add `\mathit` to italic math variables to fix slight kerning issues in equations (#839)
 
 ### In One Weekend
   - Added: More commentary about the choice between `double` and `float` (#752)

books/RayTracingTheRestOfYourLife.html

@@ -1345,18 +1345,18 @@
 PDF can also vary with _incident direction_: $\mathit{pScatter}(\omega_i, \omega_o)$. You can see
 this varying with incident direction when you look at reflections off a road -- they become
 mirror-like as your viewing angle (incident angle) approaches grazing. Lastly, the scattering PDF
-can also depend on the scattering position: $\mathit{pScatter}(\textbf{x}, \omega_i, \omega_o)$. The
-$\textbf{x}$ is just a vector representing the scattering position: $\textbf{x} = (x, y, z)$. The
-Albedo of an object can also depend on these quantities: $A(\textbf{x}, \omega_i, \omega_o)$.
+can also depend on the scattering position: $\mathit{pScatter}(\mathbf{x}, \omega_i, \omega_o)$. The
+$\mathbf{x}$ is just a vector representing the scattering position: $\mathbf{x} = (x, y, z)$. The
+Albedo of an object can also depend on these quantities: $A(\mathbf{x}, \omega_i, \omega_o)$.
 
 <div class='together'>
 The color of a surface is found by integrating these terms over the unit hemisphere by the incident
 direction:
 
-    $$ \text{Color}_o(\textbf{x}, \omega_o) = \int_{\omega_i}
-        A(\textbf{x}, \omega_i, \omega_o) \cdot
-        \mathit{pScatter}(\textbf{x}, \omega_i, \omega_o) \cdot
-        \text{Color}_i(\textbf{x}, \omega_i) $$
+    $$ \text{Color}_o(\mathbf{x}, \omega_o) = \int_{\omega_i}
+        A(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \mathit{pScatter}(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \text{Color}_i(\mathbf{x}, \omega_i) $$
 
 We've added a $\text{Color}_i$ term. The scattering PDF and the albedo at the surface of an object
 are acting as filters to the light that is shining on that point. So we need to solve for the light
@@ -1373,13 +1373,13 @@
 <div class='together'>
 If we apply the Monte Carlo basic formula we get the following statistical estimate:
 
-    $$ \text{Color}_o = \frac{A(\textbf{x}, \omega_i, \omega_o) \cdot
-        \mathit{pScatter}(\textbf{x}, \omega_i, \omega_o) \cdot
-        \text{Color}_i(\textbf{x}, \omega_i)}
-        {p(\textbf{x}, \omega_o)} $$
+    $$ \text{Color}_o = \frac{A(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \mathit{pScatter}(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \text{Color}_i(\mathbf{x}, \omega_i)}
+        {p(\mathbf{x}, \omega_o)} $$
 
-where $p(\textbf{x}, \omega_o)$ is the PDF of whatever outgoing direction we randomly generate.
-We'll simplify to just $p(\omega_o)$ because we won't be varying the PDF by $\textbf{x}$.
+where $p(\mathbf{x}, \omega_o)$ is the PDF of whatever outgoing direction we randomly generate.
+We'll simplify to just $p(\omega_o)$ because we won't be varying the PDF by $\mathbf{x}$.
 </div>
 
 For a Lambertian surface we already implicitly implemented this formula for the special case where
@@ -1414,8 +1414,8 @@
 
 The numerator and denominator cancel out, and we get:
 
-    $$ \text{Color}_o = A(\textbf{x}, \omega_i, \omega_o) \cdot
-        \text{Color}_i(\textbf{x}, \omega_i) $$
+    $$ \text{Color}_o = A(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \text{Color}_i(\mathbf{x}, \omega_i) $$
 
 This is exactly what we had in our original `ray_color()` function!
 
@@ -1427,8 +1427,8 @@
 volumes. If you read the literature, you’ll see reflection defined by the
 _Bidirectional Reflectance Distribution Function_ (BRDF). It relates pretty simply to our terms:
 
-    $$ BRDF(\omega_i, \omega_o) = \frac{A(\textbf{x}, \omega_i, \omega_o) \cdot
-        \mathit{pScatter}(\textbf{x}, \omega_i, \omega_o)}{\cos(\theta_o)} $$
+    $$ BRDF(\omega_i, \omega_o) = \frac{A(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \mathit{pScatter}(\mathbf{x}, \omega_i, \omega_o)}{\cos(\theta_o)} $$
 
 So for a Lambertian surface for example, $BRDF = A / \pi$. Translation between our terms and BRDF is
 easy. For participating media (volumes), our albedo is usually called the _scattering albedo_, and
@@ -1459,11 +1459,11 @@
 we can use any PDF: _all PDFs eventually converge to the correct answer_. So, the game is to figure
 out how to make the PDF larger where the product
 
-    $$ \mathit{pScatter}(\textbf{x}, \omega_i, \omega_o) \cdot
-        \text{Color}_i(\textbf{x}, \omega_i) $$
+    $$ \mathit{pScatter}(\mathbf{x}, \omega_i, \omega_o) \cdot
+        \text{Color}_i(\mathbf{x}, \omega_i) $$
 
 is largest. For diffuse surfaces, this is mainly a matter of guessing where
-$\text{Color}_i(\textbf{x}, \omega_i)$ is largest. Which is equivalent to guessing where the most
+$\text{Color}_i(\mathbf{x}, \omega_i)$ is largest. Which is equivalent to guessing where the most
 light is coming from.
 
 For a mirror, $\mathit{pScatter}()$ is huge only near one direction, so $\mathit{pScatter}()$