EUROGRAPHICS 2009 / P. Dutré and M. Stamminger(Guest Editors)

Volume 28 (2009), Number 2

Fast BVH Construction on GPUs
C. Lauterbach1 and M. Garland2 and S. Sengupta3 and D. Luebke2 and D. Manocha1
1 University of North Carolina at Chapel Hill

2 NVIDIA

3 University of California Davis

Abstract
We present two novel parallel algorithms for rapidly constructing bounding volume hierarchies on manycore
GPUs. The first uses a linear ordering derived from spatial Morton codes to build hierarchies extremely quickly
and with high parallel scalability. The second is a top-down approach that uses the surface area heuristic (SAH)to build hierarchies optimized for fast ray tracing. Both algorithms are combined into a hybrid algorithm thatremoves existing bottlenecks in the algorithm for GPU construction performance and scalability leading to significantly decreased build time. The resulting hierarchies are close in to optimized SAH hierarchies, but the construction process is substantially faster, leading to a significant net benefit when both construction and traversal
cost are accounted for. Our preliminary results show that current GPU architectures can compete with CPU implementations of hierarchy construction running on multicore systems. In practice, we can construct hierarchiesof models with up to several million triangles and use them for fast ray tracing or other applications.

1. Introduction
Bounding volume hierarchies (BVHs) are widely used to accelerate intersection computations for ray tracing, collision
detection, visibility culling, and similar applications. Thereis an extensive literature on fast computation of BVHs optimized for these applications. Our overarching goal is todesign real-time hierarchy construction methods for scenes
with non-rigid models undergoing deformations or topological changes, thus enabling interactive applications to process
such content.
As parallelism has become the main force driving increased
processor performance, hierarchy construction methods
must be parallel if they are to scale well on future architectures. However, nearly all prior work on BVH construction
has focused on purely serial construction algorithms. In thispaper, we develop efficient parallel algorithms for constructing BVHs on manycore processors supporting thousands ofconcurrent threads. Our approach is to design algorithms that
expose substantial amounts of fine-grained parallelism, thus
fully exploiting massively multi-threaded processors.
The first contribution of this paper is a novel algorithm using spatial Morton codes to reduce the BVH construction
problem to a simple sorting problem. This Linear Bounding
Volume Hierarchy (LBVH) algorithm is focused on minic 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.
Published by Blackwell Publishing, 9600 Garsington Road, Oxford OX4 2DQ, UK and
350 Main Street, Malden, MA 02148, USA.

mizing the cost of construction, while still producing BVHs
of good quality. Our second contribution is a breadth-firstqueue-based algorithm for constructing BVHs optimized forray tracing using the Surface Area Heuristic (SAH). This
incorporates a novel and very fast method for performing
the initial splits for the hierarchy in parallel, thus removing many of the existing bottlenecks in the construction algorithm. The SAH construction is best suited for the casewhere traversal cost is at a premium and construction costis relatively unimportant; our experiments demonstrate that
LBVH is over an order of magnitude faster than SAH construction, but can reduce ray tracing performance by up to
85% in some cases. Finally, our third contribution is a hybrid construction algorithm that builds the highest levels of
the tree with the LBVH algorithm and builds the rest with
the SAH algorithm. We demonstrate that this attains roughly
half the construction speed of LBVH while retaining essentially all the quality of the pure SAH-based construction.
To explore the performance of our algorithms, we have implemented our algorithms in CUDA [NBGS08] and benchmarked their performance on an NVIDIA GeForce 280 GTX
GPU. In practice, our techniques can compute BVHs composed of axis-aligned bounding boxes (AABBs) on models
with hundreds of thousands triangles in less than 100 milliseconds.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

construction algorithm should perform at most O(n log n)with a depth of at most O(log n), which are the bounds oncomparison-based parallel sort.

2.2. GPU traversal and construction

Figure 1: Flamenco benchmark: Screenshots from dynamic
scene with 49K triangles. Our algorithm can build the optimized BVH on a NVIDIA 280 GTX GPU in 25ms per frame,
allowing full real-time ray tracing at 11 fps at 10242 pixels.

2. Background
Bounding volume hierarchies (BVHs) have been extensively
used for ray tracing [RW80] and collision detection [Eri04].
In interactive ray tracing, object hierarchy based approaches
have recently regained interest with the adaptation of ray
packet techniques from kd-tree traversal on both the CPU[GM03, WBS07, LYTM06, WK06] and GPU [GPSS07].
While earlier approaches used simple update techniques tosupport dynamic data sets, fast construction techniques forrebuilding BVHs were introduced as well [WK06] and parallel CPU implementations have been developed [Wal07].
2.1. Parallel computing model
We focus on implementing our algorithms using the CUDA
programming model [NBGS08] and running them on modern NVIDIA GPUs [LNOM08]. A few basic attributes ofthis platform are relevant to our algorithmic discussions.
CUDA programs consist of a sequential host program that
can initiate parallel kernels on the GPU device. A given kernel executes a single program across many parallel threads.
These threads are decomposed into thread blocks; threads
within a given block may efficiently synchronize with eachand have shared access to per-block on-chip memory. Consequently, three design principles are crucial for achieving
scalable algorithms: (1) decomposing work into chunks suitable to be processed by each thread block, (2) exploiting
the on-chip memory given to each block, and (3) exposing enough fine-grained parallelism to exploit the massively
multi-threaded GPU hardware.
To analyze the complexity of parallel algorithms, we adopt
the standard approach of analyzing both the work and depth
complexity. Briefly, if a given computation is expressed asa dependence graph of parallel tasks, then its work complexity is the total amount of work performed by all tasks
and its depth complexity is the length of the critical pathin the graph. It is well-known that serial BVH construction
has the same O(n log n) complexity as comparison-basedsort. Therefore, an asymptotically efficient parallel BVH

The massive parallelism of programmable GPUs naturally
lends itself to inherently parallel problems such as ray
tracing. Early implementations [CHH02, PBMH02] wereconstrained by architectural limitations, but modern approaches use hierarchical acceleration structures such as
k-d trees [FS05, HSHH07] and BVHs [TS05, GPSS07].
While these approaches essentially implement techniques
similar to those used in CPU ray tracing, other specialized techniques for stack traversal have also been developed [HSHH07, PGSS07]. Some support for scenes with
deformable or dynamic geometry was introduced with geometry images [CHCH06] and a ray hierarchy based approach [RAH07]. Going beyond ray tracing, similar hierarchies have also been used for GPU-based collision detection [Eri04, GKJ∗ 05].
Most of these approaches have tended to rely on serial algorithms running on the CPU to construct the necessary hierarchical acceleration structures. While once a necessary restriction due to architectural limitations, modern GPUs provide all the facilities necessary to implement hierarchy construction directly. Doing so should provide a strong benefit,
as building structures directly on the GPU avoids the needfor the relatively expensive latency introduced by frequently
copying data structures between CPU and GPU memory
spaces.
There has been some initial work on constructing hierarchies on multi-core CPU processors, although gains appear
to decrease sharply even on CPUs with a low number ofcores [PGSS06], mainly due to memory bandwidth limitations [Wal07]. Very recently, initial work has been shownon constructing spatial hierarchies on GPUs [ZHWG08,
ZGHG08, AGCA08]. We present a more detailed comparison in section 6.

3. LBVH hierarchy construction
The simplest approach to parallelizing BVH construction isto reduce it to a sorting problem. This is the approach taken
by our LBVH construction which begins by ordering all n
input primitives along a space-filling curve, thus “linearizing” them into a single fixed sequence of length n. Given
this sequence, we construct the tree by recursively splittingintervals of this sequence and creating corresponding nodes.
The root corresponds to the interval [0, n), its children to apartition [0, m), [m, n) of the root interval, and so on. Thus
every node in the BVH will correspond to a range of indices[li , ri ) in the sequence of primitives.
c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

Note that this recursive partitioning is equivalent to thesteps of an most-significant-bit radix-2 sort using the Morton codes as the keys. By generalizing this radix-2 algorithm
to a radix-b algorithm—one which looks at log2 b bits at atime rather than 1—we can also trivially produce trees with
branching factor 2b rather than simply binary trees. We notethat for the radix-8 case, the recursive decomposition basedon Morton codes is equivalent to an octree decomposition of
the enclosing AABB.
3.2. Data-Parallel LBVH Construction

Figure 2: Example 2-D Morton code ordering of triangles
with the first two levels of the hierarchy. Blue and red bits
indicate x and y axes, respectively.

3.1. Tree Construction using Morton Codes
We use the well-known space-filling Morton curve—also
known as the Lebesgue and z-order curve—for ordering
primitives. This is because the Morton index code, which
determines a primitive’s order along the curve, can be computed directly from its geometric coordinates, whereas otherspace-filling curves require more expensive constructions todetermine the ordering of primitives.
We assume that each input primitive is represented by an
AABB and that the enclosing AABB of the entire input
geometry is known. We take the barycenter of each primitive AABB as its representative point. By constructing a
2k ×2k ×2k lattice within the enclosing AABB, we can quantize each of the 3 coordinates of the representative points
into k-bit integers. The 3k-bit Morton code for a point isconstructed by interleaving the successive bits of these quantized coordinates. Figure 2 shows a 2-D example of this construction. Sorting the representative points in increasing order of their Morton codes will lay out these points in order along a Morton curve. Thus, it will also order the corresponding primitives in a spatially coherent way. Because ofthis, sorting geometric primitives according to their Morton
code has been used for improving cache coherence in large
geometric databases [PF01].
Once we have assigned a Morton code to every primitive, we
can easily construct a BVH by bucketing primitives basedon the bits of their Morton codes. We construct the first level
split by examining the most significant bit of all codes, placing those with 0 and 1 bits in the first and second child, respectively, of the root. See Figure 2 for an example. We apply this bucketing procedure recursively in each child, looking at the second most significant bit. In each recursive step,
we look at the next bit in the Morton code until all bits are
consumed.
c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

One of the main virtues of the LBVH construction is that it
is inherently parallel. As noted above, the correct orderingof primitives can be computed simply by sorting them with
their Morton codes as the sort keys. Furthermore, the Morton
codes themselves encode all the necessary information about
where in the tree a particular primitive will go.
Given a list of primitives, each with its associated Morton code, we sort them using an efficient parallel radix
sort [SHG08]. Since the Morton codes may often have only
zeroes in the most significant bits, it is more efficient to
use radix-sort by least significant bit here. In the sorted sequence, consider two adjacent primitives at positions i and
i + 1. The bits of the Morton code uniquely encode the paththat a point will take from the root to the leaf that contains
only the primitive. Thus, we can determine their least common ancestor—the node farthest from the root whose subtree contains both—by determining the most significant bit
in which their Morton codes differ. The bits above this point,shared by both primitives, uniquely encode the least common ancestor node.
To construct the LBVH from the sorted primitive sequence,
we need to determine the interval dividing lines at which
nodes begin and end. In other words, for primitives i and
i + 1, we want to know at what levels (if any) they should be
split into separate nodes. We can construct these “split lists”
for each adjacent pair in parallel, using the Morton codes.
As we have just observed, the levels of the tree at whichthese two primitives are in separate sub-trees are those levels
corresponding to the bit after which their Morton codes are
no longer identical. If they first differ in bit position h, thenwe record the fact that a split must exist between them at
each level from h to 3k, since 3k is the maximum depth of thetree. We record this “split list” as a list of pairs [(i, h), (i, h +1), . . . , (i, 3k)] containing the index of the triangle and thelevels of the splits between the primitives. If we perform thiscomputation for each adjacent pair and concatenate all such
lists, we get a list of all splits in the tree sorted by the index
of the triangles in the linear Morton order. Once we havethis list, we resort it by level (i.e., the second item of eachpair). Now we have a list where, for each level, we have alist of all the splits that should occur on this level. This tells
us precisely what we want to know, namely the intervals in
the triangle list spanned by the various nodes at this level.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

One unwanted side effect of this parallel construction is thatit can create chains of singleton nodes in the tree. To deal
with this we must simply add an additional post-process thatstarts at the leaves of the tree and walks up to the root, rollingup singleton chains in the process.
As a final step, the representation of the BVH as splits bylevel needs to be converted in a form that is useable as a topdown hierarchy, mainly by computing the correct boundingboxes for each node, which is a similar process to a regular BVH refitting step and can be achieved in linear time.
In addition, we also compute the explicit child pointers for
top-down traversal which follow directly from the interval
information in the splits.
Finally, note that both sorts required by the parallel LBVH
construction can be implemented using a radix sort algorithm. The asymptotic work complexity of the LBVH construction is thus O(n). Its asymptotic depth complexity is thesame as parallel scan, which is O(log n). It is thus efficient,
as it performs asymptotically the same amount of work as thecorresponding sequential sort and has a logarithmic depth.

4. SAH hierarchy construction
The main disadvantage of the LBVH algorithm described in
the previous section is that it does not build hierarchies thatare optimized for performance in ray tracing since it uniformly subdivides space at the median. We now present analgorithm for GPU object hierarchy construction using thesurface area heuristic (SAH). Before presenting the actual
algorithm, we will first summarize how state-of-the-art implementations on the CPU build SAH-optimized hierarchies.

SAH approaches have moved towards only sampling several split positions per split and basing the decision on thissubset of split positions [PGSS06, HMS06, Wal07]. Results
have shown that this only has a negligible impact on rendering performance, but usually is an order of magnitude faster
during construction.
Other recent work has concentrated on parallel construction
on multi-core CPUs in order to achieve interactive per-frame
hierarchy rebuilds [PGSS06, SSK07, Wal07]. However, unlike ray tracing itself, hierarchy construction does not scale
well with the number of processors. In particular, the main
issues are that the first steps of the top-down algorithm
for construction are not easily parallelized, and more importantly that the implementation may become bandwidthlimited. Since memory bandwidth has traditionally not increased by Moore’s law like computing power, this remains
a serious issue.

4.2. GPU SAH construction
The main challenge for a GPU algorithm for hierarchy construction is that it has to be sufficiently parallel so as to exploit the computational power of the processors. In a topdown construction algorithm, there are two main ways tointroduce parallelism: a) process multiple splits in paralleland b) parallelize an actual split operation. In our approach,
we use multiple cores to run as many node splits in parallel
as possible and then use the data parallel computation units
in the processors to accelerate the SAH evaluation as well as
the actual split operation. In the further discussion we will
use some terms and common parallel programming primitives from the PRAM model that can be easily implemented
on vector architectures such as GPUs.

4.1. SAH hierarchy construction
The surface area heuristic [GS87, MB90, Hav00] method forbuilding hierarchies can be applied to many types of hierarchical acceleration structures – among them object and spatial hierarchies – since it has been shown to be a good indicator of expected ray intersections. The time complexity
for top-down construction of a hierarchy for n triangles isO(n log n) due to the equivalence to sorting, and research has
shown [WH06] that SAH optimized construction can also be
achieved in the same bound. Top-down builders proceed byrecursively splitting the set of geometric primitives — usually into two parts per step, resulting in a binary tree. The
manner in which the split is performed can have a large impact on the performance of a ray tracer or other application
using the BVH. The SAH provides a cost function that allows to evaluate all possible split positions at a node andthen pick the one with the lowest cost. Computing the costfunction for each possible split position can be costly andrequires a full sort, although a careful implementation needs
to perform this sort only once for each of the 3 axes and thenreuse the information [WH06]. Recently, new approximate

4.2.1. Breadth-first construction using work queues
We now present our algorithm for parallelizing the individual splits across all the cores. During top-down construction,
each split results in new nodes that still need to be processed,
i.e. split as well. Since each of the splits can be processed totally independently, processing all the open splits in parallelon multiple cores is an easy way to speed up construction.
The simplest approach to manage all this work is to introduce a queue that stores all the open splits such that eachprocessor can fetch work whenever it is finished working on
a node, as well as put new splits on the work queue when finishing up. However, even though current GPU architectures
support atomic operations that would make global synchronization possible, the problem is that the same architectures
do not provide a memory consistency model that would ensure writes to the queue are seen in the correct order by otherprocessors. Thus, implementing a global work queue is currently not practical yet. Instead, we opt for an iterative approach that processes all the currently open splits in parallel
and writes out new splits, but then performs a queue maintec 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

such that the order in the global list corresponds to the
new split
Note that unlike spatial partitioning approaches such as kdtrees each primitive can only be referenced on one side of
the split (commonly determined by the location of the centroid of the primitive), which means that the reordering canbe performed in-place and no additional memory is needed.
All of these steps can be performed by exploiting data parallelism and using common parallel operations such as reductions and prefix sums, and each split is executed on one
core.

Figure 3: Work queue construction: By using two work
queues, we can run all active splits in parallel. Since thesplit kernel may not output new splits, a compaction step after each split level removes empty space in the queue andallows it to be used in the next step.

nance step in between to provide a valid queue for the next
step (similar in spirit to [Hor05]).
In a binary tree, each split can result in either 0, 1 or 2 newopen splits as a result. Thus, if we have m open splits, weonly need a work queue of at most size 2m to hold all potential new splits. By using two work queues, one as an input
and one as an output, we can perform parallel splits without
any explicit coordination between them. In our algorithm,
each block i reads in its split item from the input queue andprocesses it (as described in the next section) and then either
writes out new splits or a null split to the output queue at
positions 2i and 2i + 1 (also see Fig. 3). After that step, theoutput work queue may have several null splits that need tobe eliminated. Therefore, we run a compaction kernel (suchas described in [SHG08]) on the queue and write the result
into the input queue. We again run the split algorithm on the
new input queue as long as there are still active splits left.
Note that this means that we generate and process all thenodes in the tree in breadth-first order, whereas recursive or
stack-based CPU approaches typically proceed in depth-firstorder (Fig. 3). Note that this form of work organization does
not add work overhead and the the overall work complexity
is still O(n log n).
4.2.2. Data-Parallel SAH split
In general, performing a SAH split for an object hierarchy
consists of two steps:
1. Determine the best split position by evaluating the SAH
2. Reorder the primitives (or the indices to the primitives)c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

We perform approximate SAH computation as describedabove and generate k uniformly sampled split candidates foreach of the three axes, and then use 3k threads so that wetest all the samples in parallel. Note that when k is larger or
equal to the number of primitives in the split, we can instead
use the positions of the primitives as the split candidates, inwhich case the algorithm produces exactly the same result as
the full SAH evaluation. The algorithm loads each primitivein the split in turn while each thread tests its position in reference to its split position and updates the SAH information(such as bounding boxes for the left and right node) accordingly. Once all primitives have been tested, each thread computes the SAH cost for its split candidate. Finally, a parallel
reduction using the minimum operator finds the split candidate sample with the lowest cost. We also test the SAH costfor not splitting the current node here and compare it to thecomputed minimal split cost. If it is lower, then we abort the
split operation and make the node a leaf in the hierarchy.
Given the split coordinate as determined by the previous
step, our algorithm then needs to sort the primitives into either the left or the right child node. To avoid copying thegeometry information, we only reorder the indices referencing the primitives instead. To parallelize this reordering step,
we go over all the indices in chunks of a size equal to thenumber of threads in the block. For each chunk, each thread
reads in the index and set a flag to 1 if the respective primitive is to the left or 0 if on the right. We then perform aparallel prefix sum over the flags. Based on that, each thread
can determine the new position to store its index. Finally, we
store the bounding box information computed during SAH
computation in both the child nodes and save back the new
split information to the output split list for the next step if
there is more than one primitive left in the respective node.
4.2.3. Small split optimizations
The algorithm as described above generates a hierarchy
practically identical in quality to CPU-based approximate
SAH techniques (see the results section). In practice, we canefficiently use more samples due to high data parallelism andthe SAH quality may be even better since the main change
has been to reorganize the split operation such that it uses
parallelism at every stage. Fig. 4 a) illustrates the performance characteristics of the algorithm by showing the timeC. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

Figure 4: Construction timings per level: In order to evaluate our SAH construction algorithm, we show the time taken to run
the split as well as compaction kernels for the 69K Bunny model per level of the tree, starting with the one split on level 1. We
also show how many splits are active at any level. Left: normal construction algorithm. Right: construction with small split
kernel as described in the text.

spent during construction by level of the split. There are twomain bottlenecks in the algorithm: similar to CPU implementations, the initial splits at the top levels of the hierarchy are slow due to lack of processor parallelism and large
numbers of very small splits at the end. All further splits
are much faster even though there is much more work done
per level because computational resources are more fully utilized and processors can hide memory latency by switching between active tasks. We present an improved scheme
to improve the parallelism at the top levels in section 4.3,
but we can also improve on the performance at the lower
levels of the hierarchy. The main sources of overhead here
are a) higher compaction costs since a high number of splits
are generated during each step and b) low vector utilization
due to only processing a few primitives per split. There isalso some constant administrative overhead during each operation for reading in information about the split etc. that
becomes more significant as the actual computational intensity decreases. We address these issues by using a different
split kernel for all splits with sizes below a specified threshold and modify the compaction kernel such that these splits
are automatically filtered from the main work queue into asmall split queue. Once all the normal splits are performed,
we can run the small split kernel on all the elements in thatqueue once.
The main idea about the new split kernel is to use each processor’s local memory to maintain a local work queue for all
the splits in the sub-tree defined by the input split, as wellas to keep all the geometric primitives in the sub-tree in local memory as well. Since local memory is very fast, we canthen run the complete sub-tree’s construction entirely without waiting for memory accesses. Essentially, we are using
this memory as an explicitly managed cache to reduce thememory bandwidth needed for construction. In addition, we
use as few threads as possible in the kernel to maximize
utilization of the vector operations. The threshold value ofprimitives for a split to be "small" depends on how muchgeometry data can be fit into local memory, i.e. the cachesize. In our case, we have set both the thread count as wellas the threshold to 32, which for our GPU architecture is
the effective SIMD width and will also fill up most of local
memory. Fig. 4 b) shows the impact of introducing this split
kernel. As the normal construction is run, all splits smaller
than the threshold are removed from the main work queue, so
the number of splits falls much quicker than previously. At
the very last split step, the small split kernel is invoked andcomplete processes all the remaining sub-trees in one run.
Overall, we have found that this leads to a 15-20% speedup
in our test cases due to practically full utilization of the computational resources and reduced overhead for queue compaction.
4.3. Hybrid GPU construction algorithm
It is also possible to combine both algorithms described inthis paper into a hybrid builder. As was mentioned, the main
bottleneck in the SAH construction algorithm is lack of parallelism in the initial splits when most processors are idle.
The LBVH algorithm with radix sort gives us the possibility of using only a subset of the bits in the Morton code. In
this case, our algorithm builds a very shallow hierarchy withlarge numbers of primitives at the leafs. We can then treat
all the leafs in that hierarchy as still active splits and process them in parallel with the SAH construction algorithm.
Essentially, this is similar to the bounding interval hierarchy [WK06] (BIH) and grid-assisted [Wal07] build methods,
but in a highly parallel approach. Overall, this combines the
speed and scalability of the LBVH algorithm with the ray
tracing performance optimizations in the SAH algorithm.
5. Results and Analysis
We now highlight results from the algorithms described in
the previous sections on several benchmark cases and scenarios. All algorithms are run on a Intel Xeon X5355 system
at 2.66GHz running Microsoft Windows XP with a NVIDIA
Geforce 280 GTX graphics card with 1 GB of memory andwere implemented using the NVIDIA CUDA programming
c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs
Model

Tris

CPU SAHGPU SAH

LBVH

HybridParallel SAH [Wal07]

Full SAH [Wal07]

Flamenco

49K

Sibenik

82K

Fairy

174K

Bunny/Dragon

252K

Conference

284K

Soda Hall

1.5M

144ms
30fps/99%
231ms
21.4fps/97%
661ms
11.5fps/98%
842ms
7.8fps/100%
819ms
24.4fps/91%
6176ms20.8fps/98%

85ms
30.3fps/100%
144ms
21.7fps/98%
488ms
21.7fps/100%
403ms
7.75fps/100%
477ms
24.5fps/91%
2390ms
21.4fps/101%

9.8ms
12.4fps/41%
10ms
3.5fps/16%
10.3ms
1.8fps/15%
17ms
7.3fps/94%
19ms
6.7fps/25%
66ms
3fps/14%17ms
29.9fps/99%
30ms
21.4fps/97%
124ms
11.6fps/99%
66ms
7.6fps/98%
105ms
22.9fps/85%
445ms
20.7fps/98%

n/a
n/a
n/a
n/a
21ms
93%
20ms
98%
26ms
86%
n/a
n/a

n/a
100%
n/a
100%
860ms
100%
1160ms100%1320ms
100%
n/a
100%

Table 1: Construction timings and hierarchy quality: First row for each scene: Timings (in ms) for complete hierarchy construction. Second row: relative and absolute ray tracing performance (in fps) on our GPU ray tracer compared to full SAH
solution at 10242 resolution and primary visbility only. CPU SAH is our non-optimized approximate SAH implementation using
just one core, GPU SAH is the algorithm as presented in section 4.2 and Hybrid the combined algorithm as presented in section
4.3. The parallel and full SAH are both from the grid-BVH build in [Wal07] and were generated on 8 and 1 core of an Intel
Xeon system at 2.6 GHz, respectively.

Figure 5: Benchmark models: Our benchmark scenes used to generate results. From left to right: Sibenik cathedral (80K tris),
Bunny/Dragon animation (252K tris), Conference room (284K tris), Soda Hall (2M tris).

language [NBGS08]. We use several benchmark scenes chosen to both allow comparison to other published approaches
as well as to cover several different model characteristics
such as architectural and CAD scenes as well as scannedmodels (see Fig. 5). Note that all benchmark timings cover
the full construction process starting with building the initial bounding boxes, but do not include any CPU-GPU copyof geometry. In our benchmark results for the hybrid algorithm, we used the LBVH algorithm for performing the first
6 levels of splits before switching to SAH construction. All
performance results and images in the paper were producedwith a BVH-based ray tracer running on the GPU. We implemented a relatively simple and unoptimized packet-based
BVH ray tracer similar to [GPSS07] in CUDA and tested
it on our benchmark scenes while rebuilding the hierarchy
for each frame. In combination with the hierarchy construction, this allows interactive ray tracing of arbitrary dynamic
scenes on the GPU.
To justify both the approximate SAH building algorithm aswell as the hybrid approach, we first compare relative rendering speed of all the algorithms presented in this paper
c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

to a hierarchy built on the CPU with a full SAH construction algorithm such as described in [WBS07]. Rendering
is performed using a standard CPU BVH ray tracer using
ray packets [LYTM06, WBS07]. The results listed in table1 demonstrate that for most scenes the approximate SAH
has close to no impact compared to a full SAH build andthat even the hybrid build is very close to the reference results. This backs results of similar splitting approaches in[WK06, Wal07]. Note that in some cases the approximate or
hybrid algorithm is in fact faster than the reference implementation. The SAH is only a local heuristic and thus it ispossible that a split that is non-optimal in the SAH sense may
still result in better performance in the actual ray tracer. The
efficiency of the LBVH construction is highly scene dependent. It can provide adequate quality for scenes with evenly
distributed geometry such as the Dragon/Bunny model, but
for architectural and CAD scenes the performance is clearly
inferior. Because it uses a fixed number of bits per axis, itsquality can degrade when very small details exist in a large
environment (the classic teapot in stadiumscenario). Thus,
the Fairy scene (benchmark 3 in Table 1) with a complex
model in the middle of a less complex environment is an

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

Analysis: Current GPU architectures have several featuresthat would make them suitable for hierarchy construction.
First, thanks to special graphics memory they have significantly higher memory bandwidth. At the same time, eventhough the individual processing units do not have a general cache, they have explicitly managed fast local memory.
Thus, if data for the current computation can be loaded frommain memory and held in local memory, memory access andbandwidth are very fast. GPUs also have very high available parallelism both in terms of independent processors aswell as data parallel units. However, exploiting this parallelism in the construction algorithm now becomes an harderchallenge. Unlike the thread parallelism in CPU implementations, using data parallelism is both more important as well
as difficult due to higher SIMD width.
The memory footprint of our construction algorithm is relatively low since object hierarchy construction does not require temporary memory and all elements can just be reordered in-place. We can size the main work queues conservatively since for n primitives there can be at most n/2 splits
active at a time. Otherwise, the algorithm stores an AABB
per primitive, the main index list as well as an array forholding the BVH nodes (which can be conservatively sized
at the theoretical maximum of 2n − 1 nodes.) Overall, ouralgorithm uses up to 113 bytes/triangle during construction
including the BVH, assuming the worst case of one triangle
per leaf. This allows construction of hierarchies for multimillion triangle models on current GPUs without problems.
We also analyzed the current bottlenecks in our construction algorithms. Figure 6 shows the impact of independently changing core (i.e. processing) and memory clock
for our construction methods. It is obvious that all three are
currently bound by computation, and both the hybrid and

900

Construction time (ms)

800

700
600
500
400

SAH

300

Hybrid

200

LBVH

100
0
250

350

450

550

650

Core clock frequency (MHz)450400
Construction time (ms)example of this problem. In the hybrid algorithm, it is always possible to limit the impact by limiting the numberof splits performed by LBVH. Furthermore, this problem is
mitigated if the scene has some pre-existing structure, sayfrom a scene graph that can assist the construction procedure. Having primitives with highly varying sizes can also
have an impact on performance here since the classificationaccording to Morton code does not take this into account.
However, this is usually also a problem for other construction algorithms and the common solution would be to subdivide large primitives [EG07] before construction. Table 1
also shows timings for the actual construction with our different approaches and also lists published numbers from afast parallel CPU BVH builder [Wal07] as well as our nonparallel CPU implementation of a sampling based SAH approach (similar to [HMS06, Wal07]) using 8 samples/split.
Note that since the GPU ray tracer uses a higher number ofsamples (in our case 64), it can provide slightly better hierarchy quality compared to the CPU solution. The full LBVH is
the fastest builder, but is dominated by kernel call and otheroverhead for small models.

350
300
250
200

SAH

150

Hybrid

100

LBVH

50
0
400

500

600

700

800

900

1000

1100

Memory clock frequency (MHz)Figure 6: Bottleneck analysis: Relative performance of thethree construction algorithms when modifying the core processor clock (top) and the memory clock (bottom).

SAH algorithms are not limited by memory bandwidth. The
LBVH algorithm shows the highest dependence on memory
speed: since GPU sort is known [GGKM06] to be bandwidth
limited and construction must have the same lower bounds
as sorting, we take this as a sign that the LBVH build is close
to the limit of achievable scalability. Overall, this means thatthe construction algorithms will very likely scale well withadded computational power in future architectures.
We also analyzed where time is spent in the construction.
Figure 7 shows a break-up of relative time for each of ourbenchmark scenes into several components (as described in
more detail in section 4): SAH split is the time for finding
the optimal subdivision, Reorder is the time spent reordering the triangles according to the split, Compaction consistsof the time for compacting and maintaining the work queues
between splits and LBVH is the initial split time in the hybrid construction (for 6 levels). The remaining time (Rest)
is spent reading in and writing back BVH node information,
setting up splits and otherwise joining the rest of the steps
together. Note that we did not include the time for computing the AABBs and Morton codes here as it makes up far
less than 1% of the total time in all benchmarks. Overall,
the results show that the full SAH build is clearly dominated by the cost of evaluating the SAH split information,
while the hybrid build is more balanced. Computing the initial splits using the LBVH algorithm only takes a relatively
small amount of time, but reduces both the overall construction time as well as some of the cost in work queue management.
c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs
SodahallSodahallConference

Conference
SAH split
SAH split

Bunny/Dragon

Bunny/Dragon

Reorder

Reorder

Fairy

Compaction

Compaction

Fairy

Rest
Rest

Sibenik

Sibenik

LBVH

Flamenco

Flamenco
0%

20%

40%

60%

80%

100%

0%

20%

40%

60%

80%

100%

Figure 7: Time spent: Split-up of the total time spent in construction into each part of the algorithm. Left: Full SAH build.
Right: Hybrid build. The "rest" times consist of all operations not explicitly in other parts, such as reading and writing BVH
nodes and setting up all the other components.

Comparison: There has been some concurrent work
on GPU hierarchy construction focused on building kdtrees [ZHWG08]. Our approach is similar in the organization of the splits by using a work queue, but the authors use
spatial median splits after sorting primitives into chunks inorder to speed up the top-level split computation. Despite thesimilarities in both approaches, we would like to point out
some differences in BVH and kd-tree construction. In particular, the memory overhead in object hierarchy construction
is very small, whereas dynamic allocation in kd-tree construction so far limits the GPU implementation — the current kd-tree algorithm would need about 1GB of memory toconstruct the kd-tree for a model with one million triangles,
whereas we could support about ten times that. On the other
hand, BVH splits are intrinsically more computationally intensive as the split kernel has to compute bounding boxes foreach split candidate whereas kd-tree splits are directly givenby the parent’s bounding box and the split plane. Thus, themain inner loop need to load 3 times the data (all 6 bounds
as opposed to 2) and a corresponding increase in computation. This difference may explain that our construction times
are slightly higher than the kd-tree numbers in [ZHWG08]
for the Fairy model (77ms compared to 124ms in our hybrid
approach.)
A similar approach to our linear BVH construction has also
been proposed, but for octrees of points [ZGHG08]. The authors use the Morton order in combination with a sort tobuild the hierarchy. However, the problem of building a spatial hierarchy on points is different than building an object
hierarchy on AABBs as in our case, so the rest of the algorithm differs. We also observe that even though our algorithm has to perform more work during construction, ourimplementation is faster, presumably due to more efficientsort.

implemented while exploiting both processor as well as data
parallelism with a reorganization of the construction process. We have also introduced a novel construction scheme
based on fast radix sort that can be used both as a standalone
builder as well as part of the SAH construction process andwe show how the combination leads to the fastest implementation. We believe that our approach will also be practical on
different highly parallel processors such as the CELL processor and on future upcoming architectures like Larrabeewith a high number of cores and increased data parallelism.
On current GPU architectures, there are still some limitations that could be removed in the future for better performance. For one, relatively static scheduling and lack of synchronization currently prevents the implementation of a truly
shared work queue in main memory which would remove
most of the overhead associated with maintaining the queueand repeatedly invoking the split kernel.
There are many opportunities for future work. It would beinteresting to integrate the construction algorithm into a full
rendering pipeline and combine a hybrid rasterization andray tracing algorithm. In that context, we would also liketo investigate using hierarchy construction directly on geometric primitives created on the GPU, e.g. using tessellation
techniques. In additon, it would be interesting to further extent our algorithm to work on systems with multiple GPUs.
Due to higher computational power GPUs should also be agood candidate for using other bounding volumes such as
OBBs or k-DOPs in the construction process, and our algorithm show easily extend to using these. Finally, we would
be interested to explore other applications of BVHs suchas continuous collision detection and response computation,
multi-agent navigation and more.

Acknowledgments
6. Conclusion and future work
In conclusion, we have presented algorithms for performing
fast construction of optimized object hierarchies on current
GPUs. We have shown that standard SAH techniques can be
c 2008 The Author(s)Journal compilation c 2008 The Eurographics Association and Blackwell Publishing Ltd.

This work was supported in part by ARO Contracts
DAAD19-02-1-0390 and W911NF-04-1-0088, NSF awards
0400134, 0429583 and 0404088, DARPA/RDECOM Contract N61339-04-C-0043, Disruptive Technology Office andIntel.

C. Lauterbach & M. Garland & S. Sengupta & D. Luebke & D. Manocha / Fast BVH Construction on GPUs

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