Merge pull request #659 from RayTracing/refracted_ray_notation

Refracted Ray Components Swap

Author: hollasch

CHANGELOG.md

@@ -29,6 +29,7 @@ Change Log -- Ray Tracing in One Weekend
   - Change: Listing 52: Refactored assignment of `etai_over_etat`
   - Change: Listing 56: Refactored material declarations
   - Change: Listing 61: Refactored material and geometry declarations
+  - Fix: Rewrote refracted ray perpendicular and parallel components for correctness
   - Fix: Corrected various missed change highlights in code listings
   - Fix: Listing 7: Added missing `color.h`, `vec3.h` includes
   - Fix: Listing 18: Add missing `double t` member of struct `hit_record` (#428)

books/RayTracingInOneWeekend.html

@@ -2346,14 +2346,14 @@
 
 On the refracted side of the surface there is a refracted ray $\mathbf{R'}$ and a normal
 $\mathbf{n'}$, and there exists an angle, $\theta'$, between them. We can split $\mathbf{R'}$ into
-the parts of the ray that are parallel to $\mathbf{n'}$ and perpendicular to $\mathbf{n'}$:
+the parts of the ray that are perpendicular to $\mathbf{n'}$ and parallel to $\mathbf{n'}$:
 
-  $$ \mathbf{R'} = \mathbf{R'}_{\parallel} + \mathbf{R'}_{\bot} $$
+  $$ \mathbf{R'} = \mathbf{R'}_{\bot} + \mathbf{R'}_{\parallel} $$
 
-If we solve for $\mathbf{R'}_{\parallel}$ and $\mathbf{R'}_{\bot}$ we get:
+If we solve for $\mathbf{R'}_{\bot}$ and $\mathbf{R'}_{\parallel}$ we get:
 
-  $$ \mathbf{R'}_{\parallel} = \frac{\eta}{\eta'} (\mathbf{R} + \cos\theta \mathbf{n}) $$
-  $$ \mathbf{R'}_{\bot} = -\sqrt{1 - |\mathbf{R'}_{\parallel}|^2} \mathbf{n} $$
+  $$ \mathbf{R'}_{\bot} = \frac{\eta}{\eta'} (\mathbf{R} + \cos\theta \mathbf{n}) $$
+  $$ \mathbf{R'}_{\parallel} = -\sqrt{1 - |\mathbf{R'}_{\bot}|^2} \mathbf{n} $$
 
 You can go ahead and prove this for yourself if you want, but we will treat it as fact and move on.
 The rest of the book will not require you to understand the proof.
@@ -2367,19 +2367,19 @@
 
   $$ \mathbf{a} \cdot \mathbf{b} = \cos\theta $$
 
-We can now rewrite $\mathbf{R'}_{\parallel}$ in terms of known quantities:
+We can now rewrite $\mathbf{R'}_{\bot}$ in terms of known quantities:
 
-  $$ \mathbf{R'}_{\parallel} =
+  $$ \mathbf{R'}_{\bot} =
      \frac{\eta}{\eta'} (\mathbf{R} + (\mathbf{-R} \cdot \mathbf{n}) \mathbf{n}) $$
 
 When we combine them back together, we can write a function to calculate $\mathbf{R'}$:
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat) {
         auto cos_theta = dot(-uv, n);
-        vec3 r_out_parallel =  etai_over_etat * (uv + cos_theta*n);
-        vec3 r_out_perp = -sqrt(fabs(1.0 - r_out_parallel.length_squared())) * n;
-        return r_out_parallel + r_out_perp;
+        vec3 r_out_perp =  etai_over_etat * (uv + cos_theta*n);
+        vec3 r_out_parallel = -sqrt(fabs(1.0 - r_out_perp.length_squared())) * n;
+        return r_out_perp + r_out_parallel;
     }
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     [Listing [refract]: <kbd>[vec3.h]</kbd> Refraction function]

src/common/vec3.h

@@ -156,9 +156,9 @@ vec3 reflect(const vec3& v, const vec3& n) {
 
 vec3 refract(const vec3& uv, const vec3& n, double etai_over_etat) {
     auto cos_theta = fmin(dot(-uv, n), 1.0);
-    vec3 r_out_parallel =  etai_over_etat * (uv + cos_theta*n);
-    vec3 r_out_perp = -sqrt(1.0 - r_out_parallel.length_squared()) * n;
-    return r_out_parallel + r_out_perp;
+    vec3 r_out_perp =  etai_over_etat * (uv + cos_theta*n);
+    vec3 r_out_parallel = -sqrt(fabs(1.0 - r_out_perp.length_squared())) * n;
+    return r_out_perp + r_out_parallel;
 }