BVH optimization: split on the longest bbox axis

books/RayTracingTheNextWeek.html

@@ -372,8 +372,10 @@
 <div class='together'>
 This gives the following result:
 
+  <div id="image-bouncing-spheres">
   ![<span class='num'>Image 1:</span> Bouncing spheres
   ](../images/img-2.01-bouncing-spheres.png class='pixel')
+  </div>
 
 </div>
 
@@ -923,13 +925,14 @@
       public:
         ...
         bvh_node(const std::vector<shared_ptr<hittable>>& src_objects, size_t start, size_t end) {
-            auto objects = src_objects; // Create a modifiable array of the source scene objects
-
             int axis = random_int(0,2);
+
             auto comparator = (axis == 0) ? box_x_compare
                             : (axis == 1) ? box_y_compare
                                           : box_z_compare;
 
+            auto objects = src_objects; // A modifiable array of the source scene objects
+
             size_t object_span = end - start;
 
             if (object_span == 1) {
@@ -1035,6 +1038,111 @@
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     [Listing [random-spheres-bvh]: <kbd>[main.cc]</kbd> Random spheres, using BVH]
 
+The rendered image should be identical to the non-BVH version shown in
+[image 1](#image-bouncing-spheres). However, if you time the two versions, the BVH version should be
+faster. I see a speedup of almost _six and a half times_ the prior version.
+
+
+Another BVH Optimization
+-------------------------
+We can speed up the BVH optimization a bit more. Instead of choosing a random splitting axis, let's
+split the longest axis of the enclosing bounding box to get the most subdivision. The change is
+straight-forward, but we'll add a few things to the `aabb` class in the process.
+
+The first task is to construct an axis-aligned bounding box of the span of objects in the BVH
+constructor. Basically, we'll construct the `bvh_node`s bounding box from this span by initializing
+the bounding box to empty, and then augmenting it with each bounding box in the span of objects.
+
+We don't have a way yet to express an empty bounding box, so we'll imagine one for now and
+implementing it shortly.
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+    class bvh_node : public hittable {
+      public:
+        ...
+        bvh_node(const std::vector<shared_ptr<hittable>>& src_objects, size_t start, size_t end) {
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
+            // Build the bounding box of the span of source objects.
+            bbox = aabb::empty;
+            for (int object_index=start; object_index < end; ++object_index)
+                bbox = aabb(bbox, src_objects[object_index]->bounding_box());
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+
+            ...
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+    [Listing [object-span-bbox]: <kbd>[bvh.h]</kbd> Building the bbox for the span of BVH objects]
+
+Now that we have the bounding box, set the splitting axis to the one with the longest side. Again,
+we'll imagine a function that does that for us: `aabb::longest_axis()`. Finally, since we're
+computing the bounding box of the object span up front, we can delete the original line that
+computed it as the union of the left and right sides.
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+    class bvh_node : public hittable {
+      public:
+        ...
+        bvh_node(const std::vector<shared_ptr<hittable>>& src_objects, size_t start, size_t end) {
+            // Build the bounding box of the span of source objects.
+            bbox = aabb::empty;
+            for (int object_index=start; object_index < end; ++object_index)
+                bbox = aabb(bbox, src_objects[object_index]->bounding_box());
+
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
+            int axis = bbox.longest_axis();
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+
+            auto comparator = (axis == 0) ? box_x_compare
+                            : (axis == 1) ? box_y_compare
+                                          : box_z_compare;
+
+            ...
+
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ delete
+            bbox = aabb(left->bounding_box(), right->bounding_box());
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+        }
+
+        ...
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+    [Listing [object-span-bbox]: <kbd>[bvh.h]</kbd> Building the bbox for the span of BVH objects]
+
+Now to implement the empty `aabb` code and the new `aabb::longest_axis()` function:
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+    class aabb {
+      public:
+        ...
+
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++ highlight
+        int longest_axis() const {
+            // Returns the index of the longest axis of the bounding box.
+
+            if (x.size() > y.size())
+                return x.size() > z.size() ? 0 : 2;
+            else
+                return y.size() > z.size() ? 1 : 2;
+        }
+
+        static const aabb empty, universe;
+    };
+
+    const aabb aabb::empty    = aabb(interval::empty,    interval::empty,    interval::empty);
+    const aabb aabb::universe = aabb(interval::universe, interval::universe, interval::universe);
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C++
+
+    ...
+
+    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+    [Listing [aabb-empty-and-axis]: <kbd>[aabb.h]</kbd>
+    New aabb constants and longest_axis() function]
+
+As before, you should see identical results to [image 1](#image-bouncing-spheres), but rendering a
+little bit faster. On my system, this yields something like an additional 18% render speedup. Not
+bad for a little extra work.
+
 
 
 Texture Mapping

src/TheNextWeek/aabb.h

@@ -72,8 +72,22 @@ class aabb {
         }
         return true;
     }
+
+    int longest_axis() const {
+        // Returns the index of the longest axis of the bounding box.
+
+        if (x.size() > y.size())
+            return x.size() > z.size() ? 0 : 2;
+        else
+            return y.size() > z.size() ? 1 : 2;
+    }
+
+    static const aabb empty, universe;
 };
 
+const aabb aabb::empty    = aabb(interval::empty,    interval::empty,    interval::empty);
+const aabb aabb::universe = aabb(interval::universe, interval::universe, interval::universe);
+
 aabb operator+(const aabb& bbox, const vec3& offset) {
     return aabb(bbox.x + offset.x(), bbox.y + offset.y(), bbox.z + offset.z());
 }

src/TheNextWeek/bvh.h

@@ -13,6 +13,7 @@
 
 #include "rtweekend.h"
 
+#include "aabb.h"
 #include "hittable.h"
 #include "hittable_list.h"
 
@@ -24,13 +25,19 @@ class bvh_node : public hittable {
     bvh_node(const hittable_list& list) : bvh_node(list.objects, 0, list.objects.size()) {}
 
     bvh_node(const std::vector<shared_ptr<hittable>>& src_objects, size_t start, size_t end) {
-        auto objects = src_objects; // Create a modifiable array of the source scene objects
+        // Build the bounding box of the span of source objects.
+        bbox = aabb::empty;
+        for (int object_index=start; object_index < end; ++object_index)
+            bbox = aabb(bbox, src_objects[object_index]->bounding_box());
+
+        int axis = bbox.longest_axis();
 
-        int axis = random_int(0,2);
         auto comparator = (axis == 0) ? box_x_compare
                         : (axis == 1) ? box_y_compare
                                       : box_z_compare;
 
+        auto objects = src_objects; // A modifiable array of the source scene objects
+
         size_t object_span = end - start;
 
         if (object_span == 1) {
@@ -50,8 +57,6 @@ class bvh_node : public hittable {
             left = make_shared<bvh_node>(objects, start, mid);
             right = make_shared<bvh_node>(objects, mid, end);
         }
-
-        bbox = aabb(left->bounding_box(), right->bounding_box());
     }
 
     bool hit(const ray& r, interval ray_t, hit_record& rec) const override {

src/TheRestOfYourLife/aabb.h

@@ -72,8 +72,22 @@ class aabb {
         }
         return true;
     }
+
+    int longest_axis() const {
+        // Returns the index of the longest axis of the bounding box.
+
+        if (x.size() > y.size())
+            return x.size() > z.size() ? 0 : 2;
+        else
+            return y.size() > z.size() ? 1 : 2;
+    }
+
+    static const aabb empty, universe;
 };
 
+const aabb aabb::empty    = aabb(interval::empty,    interval::empty,    interval::empty);
+const aabb aabb::universe = aabb(interval::universe, interval::universe, interval::universe);
+
 aabb operator+(const aabb& bbox, const vec3& offset) {
     return aabb(bbox.x + offset.x(), bbox.y + offset.y(), bbox.z + offset.z());
 }

src/TheRestOfYourLife/bvh.h

@@ -13,6 +13,7 @@
 
 #include "rtweekend.h"
 
+#include "aabb.h"
 #include "hittable.h"
 #include "hittable_list.h"
 
@@ -24,13 +25,19 @@ class bvh_node : public hittable {
     bvh_node(const hittable_list& list) : bvh_node(list.objects, 0, list.objects.size()) {}
 
     bvh_node(const std::vector<shared_ptr<hittable>>& src_objects, size_t start, size_t end) {
-        auto objects = src_objects; // Create a modifiable array of the source scene objects
+        // Build the bounding box of the span of source objects.
+        bbox = aabb::empty;
+        for (int object_index=start; object_index < end; ++object_index)
+            bbox = aabb(bbox, src_objects[object_index]->bounding_box());
+
+        int axis = bbox.longest_axis();
 
-        int axis = random_int(0,2);
         auto comparator = (axis == 0) ? box_x_compare
                         : (axis == 1) ? box_y_compare
                                       : box_z_compare;
 
+        auto objects = src_objects; // A modifiable array of the source scene objects
+
         size_t object_span = end - start;
 
         if (object_span == 1) {
@@ -50,8 +57,6 @@ class bvh_node : public hittable {
             left = make_shared<bvh_node>(objects, start, mid);
             right = make_shared<bvh_node>(objects, mid, end);
         }
-
-        bbox = aabb(left->bounding_box(), right->bounding_box());
     }
 
     bool hit(const ray& r, interval ray_t, hit_record& rec) const override {