Merge pull request RayTracing#511 from RayTracing/aabb-offset

Add explanation for aarect padding

Author: hollasch

CHANGELOG.md

@@ -6,7 +6,8 @@ Change Log -- Ray Tracing in One Weekend
 
 ### Common
 - Fix: Scattered improvements to the text.
-- New: subchapters throughout all three books (#267)
+- New: Subchapters throughout all three books (#267)
+- New: Add explanation for padding `aarect` in the zero dimension (#488)
 - Change: Minor change to use new `point3` and `color` type aliases for `vec3` (#422)
 - Change: Renamed `constant_texture` to `solid_color`, add RGB constructor (#452)
 

books/RayTracingTheNextWeek.html

@@ -1999,6 +1999,11 @@
 
 It is a hit if $x_0 < x < x_1$ and $y_0 < y < y_1$.
 
+Because our rectangles are axis-aligned, their bounding boxes will have an infinitely-thin side.
+This can be a problem when dividing them up with our axis-aligned bounding volume hierarchy. To
+counter this, all hittable objects should get a bounding box that has finite width along every
+dimension. For our rectangles, we'll just pad the box a bit on the infnitely-thin side.
+
 <div class='together'>
 The actual `xy_rect` class is thus:
 
@@ -2013,7 +2018,9 @@
             virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
             virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
-                output_box =  aabb(point3(x0,y0, k-0.0001), point3(x1, y1, k+0.0001));
+                // The bounding box must have non-zero width in each dimension, so pad the Z
+                // dimension a small amount.
+                output_box = aabb(point3(x0,y0, k-0.0001), point3(x1, y1, k+0.0001));
                 return true;
             }
 
@@ -2117,7 +2124,9 @@
             virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
             virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
-                output_box =  aabb(point3(x0,k-0.0001,z0), point3(x1, k+0.0001, z1));
+                // The bounding box must have non-zero width in each dimension, so pad the Y
+                // dimension a small amount.
+                output_box = aabb(point3(x0,k-0.0001,z0), point3(x1, k+0.0001, z1));
                 return true;
             }
 
@@ -2136,7 +2145,9 @@
             virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
             virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
-                output_box =  aabb(point3(k-0.0001, y0, z0), point3(k+0.0001, y1, z1));
+                // The bounding box must have non-zero width in each dimension, so pad the X
+                // dimension a small amount.
+                output_box = aabb(point3(k-0.0001, y0, z0), point3(k+0.0001, y1, z1));
                 return true;
             }
 

books/RayTracingTheRestOfYourLife.html

@@ -1679,19 +1679,7 @@
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
     class xz_rect: public hittable {
         public:
-            xz_rect() {}
-
-            xz_rect(
-                double _x0, double _x1, double _z0, double _z1, double _k, shared_ptr<material> mat)
-                : x0(_x0), x1(_x1), z0(_z0), z1(_z1), k(_k), mp(mat) {};
-
-            virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
-
-            virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
-                output_box = aabb(point3(x0,k-0.0001,z0), point3(x1, k+0.0001, z1));
-                return true;
-            }
-
+            ...
 
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
             virtual double pdf_value(const point3& origin, const vec3& v) const {
@@ -1710,12 +1698,6 @@
                 auto random_point = point3(random_double(x0,x1), k, random_double(z0,z1));
                 return random_point - origin;
             }
-    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
-
-        public:
-            shared_ptr<material> mp;
-            double x0, x1, z0, z1, k;
-    };
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     [Listing [xz-rect-pdf]: <kbd>[aarect.h]</kbd> XZ rect with pdf]
 </div>

src/TheNextWeek/aarect.h

@@ -27,6 +27,8 @@ class xy_rect: public hittable {
         virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
+            // The bounding box must have non-zero width in each dimension, so pad the Z
+            // dimension a small amount.
             output_box = aabb(point3(x0,y0, k-0.0001), point3(x1, y1, k+0.0001));
             return true;
         }
@@ -47,6 +49,8 @@ class xz_rect: public hittable {
         virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
+            // The bounding box must have non-zero width in each dimension, so pad the Y
+            // dimension a small amount.
             output_box = aabb(point3(x0,k-0.0001,z0), point3(x1, k+0.0001, z1));
             return true;
         }
@@ -67,6 +71,8 @@ class yz_rect: public hittable {
         virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
+            // The bounding box must have non-zero width in each dimension, so pad the X
+            // dimension a small amount.
             output_box = aabb(point3(k-0.0001, y0, z0), point3(k+0.0001, y1, z1));
             return true;
         }

src/TheRestOfYourLife/aarect.h

@@ -27,6 +27,8 @@ class xy_rect: public hittable {
         virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
+            // The bounding box must have non-zero width in each dimension, so pad the Z
+            // dimension a small amount.
             output_box = aabb(point3(x0,y0, k-0.0001), point3(x1, y1, k+0.0001));
             return true;
         }
@@ -47,6 +49,8 @@ class xz_rect: public hittable {
         virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
+            // The bounding box must have non-zero width in each dimension, so pad the Y
+            // dimension a small amount.
             output_box = aabb(point3(x0,k-0.0001,z0), point3(x1, k+0.0001, z1));
             return true;
         }
@@ -84,6 +88,8 @@ class yz_rect: public hittable {
         virtual bool hit(const ray& r, double t0, double t1, hit_record& rec) const;
 
         virtual bool bounding_box(double t0, double t1, aabb& output_box) const {
+            // The bounding box must have non-zero width in each dimension, so pad the X
+            // dimension a small amount.
             output_box = aabb(point3(k-0.0001, y0, z0), point3(k+0.0001, y1, z1));
             return true;
         }