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FireRays, AMD's OpenCL based high performance ray tracing renderer

Pretty big news for GPU rendering: about 6 years after Nvidia released the source code of their high performance GPU ray tracing kernels and 4 years after Intel released Embree (high performance CPU ray tracing kernels), last week at Siggraph AMD finally released their own GPU rendering framework in the form of FireRays, an OpenCL based ray tracing SDK, first shown in prototype form at Siggraph 2014 by Takahiro Harada (who also conducted research into foveated ray tracing for VR):

The FireRays, SDK can be downloaded from the AMD Developer site: http://developer.amd.com/tools-and-sdks/graphics-development/firepro-sdk/

More details  can be found at http://developer.amd.com/tools-and-sdks/graphics-development/firepro-sdk/firerays-sdk/. The acceleration structure is a BVH with spatial splits and the option to build the BVH with or without the surface area heuristic (SAH). For instances and motion blur, a two level BVH is used, which enables very efficient object transformations (translation, rotation, scaling) at virtually no cost. 

AMD's own graphs show that their OpenCL renderer is roughly 10x faster running on 2 D700 FirePro GPUs than Embree running on the CPU:

There are already a few OpenCL based path tracers available today such as Blender's Cycles engine and LuxRays (even V-Ray RT GPU was OpenCL based at some point), but none of them have been able to challenge their CUDA based GPU rendering brethren. AMD's OpenCL dev tools have historically been lagging behind Nvidia's CUDA SDK tools which made compiling large and complex OpenCL kernels a nightmare (splitting the megakernel in smaller parts was the only option). Hopefully the OpenCL developer tools have gotten a makeover as well with the release of this SDK, but at least I'm happy to see AMD taking GPU ray tracing serious. This move could truly bring superfast GPU rendering to the masses and with the two big GPU vendors in the ray tracing race, there will hopefully be more ray tracing specific hardware improvements in future GPU architectures.

(thanks heaps to CPFUUU for pointing me to this)

UPDATE: Alex Evans from Media Molecule had a great talk at Siggraph 2015 about his research into raymarching signed distance fields for Dreams. Alex Evans is currently probably the biggest innovator in real-time game rendering since John Carmack (especially since Carmack spends all his time on VR now, which is a real shame). Alex's presentation can be downloaded from http://www.mediamolecule.com/blog/article/siggraph_2015 and is well worth reading. It sums up a bunch of approaches to rendering voxels, signed distance fields and global illumination in real-time that ultimately were not as successful as hoped, but they came very close to real-time on the PS4 (and research is still ongoing).

For people interested in the real-world physics of light bouncing, there was also this very impressive video from Karoly Zsolnai about ultra high speed femto-photography cameras able to shoot images at the speed of light, demonstrating how light propagates and is transprorted as an electromagnetic wave through a scene, illuminating objects a fraction of a nanosecond before their mirror image becomes visible:

GPU path tracing tutorial 1: Drawing First Blood

In early 2011 I developed a simple real-time path traced Pong game together with Kerrash on top of an open source GPU path tracer called tokaspt (developed by Thierry Berger-Perrin) which could only render spheres, but was bloody fast at it. The physics were bodged, but the game proved that path tracing of very simple scenes at 30 fps was feasible, although a bit noisy. You can still download it from https://code.google.com/p/tokap-the-once-known-as-pong/. Since that time I've always wanted to write a short and simple tutorial about GPU path tracing to show how to make your GPU draw an image with high quality ray traced colour bleeding with a minimum of code and now is a good time to do exactly that.

This tutorial is not meant as an introduction to ray tracing or path tracing as there are plenty of excellent ray tracing tutorials for beginners online such as Scratch-a-Pixel (also check out the old version which contains more articles) and Minilight (more links at the bottom of this article). The goal of this tutorial is simply to show how incredibly easy it is to turn a simple CPU path tracer into a CUDA accelerated version. Being a fan of the KISS principle from design and engineering (Keep It Simple Stupid) and aiming to avoid unnecessary complexity, I've chosen to cudafy Kevin Beason's smallpt, the most basic but still fully functional CPU path tracer around. It's a very short piece of code that doesn't require the user to install any tedious libraries to compile the code (apart from Nvidia's CUDA Toolkit).

The full CPU version of smallpt can be found at http://www.kevinbeason.com/smallpt/ Due to its compactness the code is not very easy to read, but fortunately David Cline made a great Powerpoint presentation explaining what each line in smallpt is doing with references to Peter Shirley's "Realistic Ray Tracing" book. 

To keep things simple and free of needless clutter, I've stripped out the code for the tent filter, supersampling, Russian Roulette and the material BRDFs for reflective and refractive materials, leaving only the diffuse BRDF. The 3D vector class from smallpt is replaced by CUDA's own built-in float3 type (built-in CUDA types are more efficient due to automatic memory alignment) which has the same linear algebra math functions as a vector such as addition, subtraction, multiplication, normalize, length, dot product and cross product. For reasons of code clarity, there is no error checking when initialising CUDA. To compile the code, save the code in a file with ".cu" file extension and follow these CUDA installation guides to install Nvidia's GPU Computing Toolkit and configure the programming tools to work with CUDA.

After reading the slides from David Cline, the commented code below should speak for itself, but feel free to drop me a comment below if some things are still not clear.

So without further ado, here's the full CUDA code:

// smallptCUDA by Sam Lapere, 2015
// based on smallpt, a path tracer by Kevin Beason, 2008

#include <iostream>
#include <cuda_runtime.h>
#include <vector_types.h>
#include "device_launch_parameters.h"
#include <cutil_math.h> // from http://www.icmc.usp.br/~castelo/CUDA/common/inc/cutil_math.h

#define M_PI 3.14159265359f // pi
#define width 512 // screenwidth
#define height 384 // screenheight
#define samps 1024 // samples

// __device__ : executed on the device (GPU) and callable only from the device

struct Ray {
float3 orig; // ray origin
float3 dir; // ray direction
__device__ Ray(float3 o_, float3 d_) : orig(o_), dir(d_) {}

enum Refl_t { DIFF, SPEC, REFR }; // material types, used in radiance(), only DIFF used here

struct Sphere {

float rad; // radius
float3 pos, emi, col; // position, emission, colour
Refl_t refl; // reflection type (e.g. diffuse)

__device__ float intersect_sphere(const Ray &r) const {

// ray/sphere intersection
// returns distance t to intersection point, 0 if no hit
// ray equation: p(x,y,z) = ray.orig + t*ray.dir
// general sphere equation: x^2 + y^2 + z^2 = rad^2
// classic quadratic equation of form ax^2 + bx + c = 0
// solution x = (-b +- sqrt(b*b - 4ac)) / 2a
// solve t^2*ray.dir*ray.dir + 2*t*(orig-p)*ray.dir + (orig-p)*(orig-p) - rad*rad = 0
// more details in "Realistic Ray Tracing" book by P. Shirley or Scratchapixel.com

float3 op = pos - r.orig; // distance from ray.orig to center sphere
float t, epsilon = 0.0001f; // epsilon required to prevent floating point precision artefacts
float b = dot(op, r.dir); // b in quadratic equation
float disc = b*b - dot(op, op) + rad*rad; // discriminant quadratic equation
if (disc<0) return 0; // if disc < 0, no real solution (we're not interested in complex roots)
else disc = sqrtf(disc); // if disc >= 0, check for solutions using negative and positive discriminant
return (t = b - disc)>epsilon ? t : ((t = b + disc)>epsilon ? t : 0); // pick closest point in front of ray origin

// 9 spheres forming a Cornell box
// small enough to be in constant GPU memory
// { float radius, { float3 position }, { float3 emission }, { float3 colour }, refl_type }
__constant__ Sphere spheres[] = {
{ 1e5f, { 1e5f + 1.0f, 40.8f, 81.6f }, { 0.0f, 0.0f, 0.0f }, { 0.75f, 0.25f, 0.25f }, DIFF }, //Left
{ 1e5f, { -1e5f + 99.0f, 40.8f, 81.6f }, { 0.0f, 0.0f, 0.0f }, { .25f, .25f, .75f }, DIFF }, //Rght
{ 1e5f, { 50.0f, 40.8f, 1e5f }, { 0.0f, 0.0f, 0.0f }, { .75f, .75f, .75f }, DIFF }, //Back
{ 1e5f, { 50.0f, 40.8f, -1e5f + 600.0f }, { 0.0f, 0.0f, 0.0f }, { 1.00f, 1.00f, 1.00f }, DIFF }, //Frnt
{ 1e5f, { 50.0f, 1e5f, 81.6f }, { 0.0f, 0.0f, 0.0f }, { .75f, .75f, .75f }, DIFF }, //Botm
{ 1e5f, { 50.0f, -1e5f + 81.6f, 81.6f }, { 0.0f, 0.0f, 0.0f }, { .75f, .75f, .75f }, DIFF }, //Top
{ 16.5f, { 27.0f, 16.5f, 47.0f }, { 0.0f, 0.0f, 0.0f }, { 1.0f, 1.0f, 1.0f }, DIFF }, // small sphere 1
{ 16.5f, { 73.0f, 16.5f, 78.0f }, { 0.0f, 0.0f, 0.0f }, { 1.0f, 1.0f, 1.0f }, DIFF }, // small sphere 2
{ 600.0f, { 50.0f, 681.6f - .77f, 81.6f }, { 2.0f, 1.8f, 1.6f }, { 0.0f, 0.0f, 0.0f }, DIFF } // Light

__device__ inline bool intersect_scene(const Ray &r, float &t, int &id){

float n = sizeof(spheres) / sizeof(Sphere), d, inf = t = 1e20; // t is distance to closest intersection, initialise t to a huge number outside scene
for (int i = int(n); i--;) // test all scene objects for intersection
if ((d = spheres[i].intersect_sphere(r)) && d<t){ // if newly computed intersection distance d is smaller than current closest intersection distance
t = d; // keep track of distance along ray to closest intersection point
id = i; // and closest intersected object
return t<inf; // returns true if an intersection with the scene occurred, false when no hit

// random number generator from https://github.com/gz/rust-raytracer

__device__ static float getrandom(unsigned int *seed0, unsigned int *seed1) {
*seed0 = 36969 * ((*seed0) & 65535) + ((*seed0) >> 16); // hash the seeds using bitwise AND and bitshifts
*seed1 = 18000 * ((*seed1) & 65535) + ((*seed1) >> 16);

unsigned int ires = ((*seed0) << 16) + (*seed1);

// Convert to float
union {
float f;
unsigned int ui;
} res;

res.ui = (ires & 0x007fffff) | 0x40000000; // bitwise AND, bitwise OR

return (res.f - 2.f) / 2.f;

// radiance function, the meat of path tracing
// solves the rendering equation:
// outgoing radiance (at a point) = emitted radiance + reflected radiance
// reflected radiance is sum (integral) of incoming radiance from all directions in hemisphere above point,
// multiplied by reflectance function of material (BRDF) and cosine incident angle
__device__ float3 radiance(Ray &r, unsigned int *s1, unsigned int *s2){ // returns ray color

float3 accucolor = make_float3(0.0f, 0.0f, 0.0f); // accumulates ray colour with each iteration through bounce loop
float3 mask = make_float3(1.0f, 1.0f, 1.0f);

// ray bounce loop (no Russian Roulette used)
for (int bounces = 0; bounces < 4; bounces++){ // iteration up to 4 bounces (replaces recursion in CPU code)

float t; // distance to closest intersection
int id = 0; // index of closest intersected sphere

// test ray for intersection with scene
if (!intersect_scene(r, t, id))
return make_float3(0.0f, 0.0f, 0.0f); // if miss, return black

// else, we've got a hit!
// compute hitpoint and normal
const Sphere &obj = spheres[id]; // hitobject
float3 x = r.orig + r.dir*t; // hitpoint
float3 n = normalize(x - obj.pos); // normal
float3 nl = dot(n, r.dir) < 0 ? n : n * -1; // front facing normal

// add emission of current sphere to accumulated colour
// (first term in rendering equation sum)
accucolor += mask * obj.emi;

// all spheres in the scene are diffuse
// diffuse material reflects light uniformly in all directions
// generate new diffuse ray:
// origin = hitpoint of previous ray in path
// random direction in hemisphere above hitpoint (see "Realistic Ray Tracing", P. Shirley)

// create 2 random numbers
float r1 = 2 * M_PI * getrandom(s1, s2); // pick random number on unit circle (radius = 1, circumference = 2*Pi) for azimuth
float r2 = getrandom(s1, s2); // pick random number for elevation
float r2s = sqrtf(r2);

// compute local orthonormal basis uvw at hitpoint to use for calculation random ray direction
// first vector = normal at hitpoint, second vector is orthogonal to first, third vector is orthogonal to first two vectors
float3 w = nl;
float3 u = normalize(cross((fabs(w.x) > .1 ? make_float3(0, 1, 0) : make_float3(1, 0, 0)), w));
float3 v = cross(w,u);

// compute random ray direction on hemisphere using polar coordinates
// cosine weighted importance sampling (favours ray directions closer to normal direction)
float3 d = normalize(u*cos(r1)*r2s + v*sin(r1)*r2s + w*sqrtf(1 - r2));

// new ray origin is intersection point of previous ray with scene
r.orig = x + nl*0.05f; // offset ray origin slightly to prevent self intersection
r.dir = d;

mask *= obj.col; // multiply with colour of object
mask *= dot(d,nl); // weigh light contribution using cosine of angle between incident light and normal
mask *= 2; // fudge factor

return accucolor;

// __global__ : executed on the device (GPU) and callable only from host (CPU)
// this kernel runs in parallel on all the CUDA threads

__global__ void render_kernel(float3 *output){

// assign a CUDA thread to every pixel (x,y)
// blockIdx, blockDim and threadIdx are CUDA specific keywords
// replaces nested outer loops in CPU code looping over image rows and image columns
unsigned int x = blockIdx.x*blockDim.x + threadIdx.x;
unsigned int y = blockIdx.y*blockDim.y + threadIdx.y;

unsigned int i = (height - y - 1)*width + x; // index of current pixel (calculated using thread index)

unsigned int s1 = x; // seeds for random number generator
unsigned int s2 = y;

// generate ray directed at lower left corner of the screen
// compute directions for all other rays by adding cx and cy increments in x and y direction
Ray cam(make_float3(50, 52, 295.6), normalize(make_float3(0, -0.042612, -1))); // first hardcoded camera ray(origin, direction)
float3 cx = make_float3(width * .5135 / height, 0.0f, 0.0f); // ray direction offset in x direction
float3 cy = normalize(cross(cx, cam.dir)) * .5135; // ray direction offset in y direction (.5135 is field of view angle)
float3 r; // r is final pixel color

r = make_float3(0.0f); // reset r to zero for every pixel

for (int s = 0; s < samps; s++){ // samples per pixel

// compute primary ray direction
float3 d = cam.dir + cx*((.25 + x) / width - .5) + cy*((.25 + y) / height - .5);

// create primary ray, add incoming radiance to pixelcolor
r = r + radiance(Ray(cam.orig + d * 40, normalize(d)), &s1, &s2)*(1. / samps);
} // Camera rays are pushed ^^^^^ forward to start in interior

// write rgb value of pixel to image buffer on the GPU, clamp value to [0.0f, 1.0f] range
output[i] = make_float3(clamp(r.x, 0.0f, 1.0f), clamp(r.y, 0.0f, 1.0f), clamp(r.z, 0.0f, 1.0f));

inline float clamp(float x){ return x < 0.0f ? 0.0f : x > 1.0f ? 1.0f : x; }

inline int toInt(float x){ return int(pow(clamp(x), 1 / 2.2) * 255 + .5); } // convert RGB float in range [0,1] to int in range [0, 255] and perform gamma correction

int main(){

float3* output_h = new float3[width*height]; // pointer to memory for image on the host (system RAM)
float3* output_d; // pointer to memory for image on the device (GPU VRAM)

// allocate memory on the CUDA device (GPU VRAM)
cudaMalloc(&output_d, width * height * sizeof(float3));

// dim3 is CUDA specific type, block and grid are required to schedule CUDA threads over streaming multiprocessors
dim3 block(8, 8, 1);
dim3 grid(width / block.x, height / block.y, 1);

printf("CUDA initialised.\nStart rendering...\n");

// schedule threads on device and launch CUDA kernel from host
render_kernel <<< grid, block >>>(output_d);

// copy results of computation from device back to host
cudaMemcpy(output_h, output_d, width * height *sizeof(float3), cudaMemcpyDeviceToHost);

// free CUDA memory


// Write image to PPM file, a very simple image file format
FILE *f = fopen("smallptcuda.ppm", "w");
fprintf(f, "P3\n%d %d\n%d\n", width, height, 255);
for (int i = 0; i < width*height; i++) // loop over pixels, write RGB values
fprintf(f, "%d %d %d ", toInt(output_h[i].x),

printf("Saved image to 'smallptcuda.ppm'\n");

delete[] output_h;

Optionally, the following 3D vector algebra functions can be inserted at the top of the file instead of #including "cutil_math.h". Instead of creating a Vector3D class (with 3 floats), CUDA's built-in float3 type is used instead as built-in types have automated memory alignment and provide higher for performance. The "__host__ __device__" keywords in front of the functions allow them to run on both the CPU and GPU.

// 3D vector algebra from cutil_math.h
struct float3 {float x, y, z;};
typedef struct float3 float3;
// add
inline __host__ __device__ float3 operator+(float3 a, float3 b){return make_float3(a.x + b.x, a.y + b.y, a.z + b.z);}
inline __host__ __device__ void operator+=(float3 &a, float3 b){a.x += b.x; a.y += b.y; a.z += b.z;}
inline __host__ __device__ float3 operator+(float3 a, float b){return make_float3(a.x + b, a.y + b, a.z + b);}
inline __host__ __device__ float3 operator+(float b, float3 a){return make_float3(b + a.x, b + a.y, b + a.z);}
inline __host__ __device__ void operator+=(float3 &a, float b){a.x += b; a.y += b; a.z += b;}
// subtract
inline __host__ __device__ float3 operator-(float3 a, float3 b){return make_float3(a.x - b.x, a.y - b.y, a.z - b.z);}
inline __host__ __device__ void operator-=(float3 &a, float3 b){a.x -= b.x; a.y -= b.y; a.z -= b.z;}
inline __host__ __device__ float3 operator-(float3 a, float b){return make_float3(a.x - b, a.y - b, a.z - b);}
inline __host__ __device__ float3 operator-(float b, float3 a){return make_float3(b - a.x, b - a.y, b - a.z);}
inline __host__ __device__ void operator-=(float3 &a, float b){a.x -= b; a.y -= b; a.z -= b;}
// multiply
inline __host__ __device__ float3 operator*(float3 a, float3 b){return make_float3(a.x * b.x, a.y * b.y, a.z * b.z);}
inline __host__ __device__ void operator*=(float3 &a, float3 b){a.x *= b.x; a.y *= b.y; a.z *= b.z;}
inline __host__ __device__ float3 operator*(float3 a, float b){return make_float3(a.x * b, a.y * b, a.z * b);}
inline __host__ __device__ float3 operator*(float b, float3 a){return make_float3(b * a.x, b * a.y, b * a.z);}
inline __host__ __device__ void operator*=(float3 &a, float b){a.x *= b; a.y *= b; a.z *= b;}
// divide
inline __host__ __device__ float3 operator/(float3 a, float3 b){return make_float3(a.x / b.x, a.y / b.y, a.z / b.z);}
inline __host__ __device__ void operator/=(float3 &a, float3 b){a.x /= b.x; a.y /= b.y; a.z /= b.z;}
inline __host__ __device__ float3 operator/(float3 a, float b){return make_float3(a.x / b, a.y / b, a.z / b);}
inline __host__ __device__ void operator/=(float3 &a, float b){a.x /= b; a.y /= b; a.z /= b;}
inline __host__ __device__ float3 operator/(float b, float3 a){return make_float3(b / a.x, b / a.y, b / a.z);}
// min
inline __host__ __device__ float3 fminf(float3 a, float3 b){return make_float3(fminf(a.x, b.x), fminf(a.y, b.y), fminf(a.z, b.z));}
// max
inline __host__ __device__ float3 fmaxf(float3 a, float3 b){return make_float3(fmaxf(a.x, b.x), fmaxf(a.y, b.y), fmaxf(a.z, b.z));}
// lerp
inline __device__ __host__ float3 lerp(float3 a, float3 b, float t){return a + t*(b - a);}
// clamp value v between a and b
inline __device__ __host__ float clamp(float f, float a, float b){return fmaxf(a, fminf(f, b));}
inline __device__ __host__ float3 clamp(float3 v, float a, float b){return make_float3(clamp(v.x, a, b), clamp(v.y, a, b), clamp(v.z, a, b));}
inline __device__ __host__ float3 clamp(float3 v, float3 a, float3 b){return make_float3(clamp(v.x, a.x, b.x), clamp(v.y, a.y, b.y), clamp(v.z, a.z, b.z));}
// dot product
inline __host__ __device__ float dot(float3 a, float3 b){return a.x * b.x + a.y * b.y + a.z * b.z;}
// length
inline __host__ __device__ float length(float3 v){return sqrtf(dot(v, v));}
// normalize
inline __host__ __device__ float3 normalize(float3 v){float invLen = rsqrtf(dot(v, v));return v * invLen;}
// floor
inline __host__ __device__ float3 floorf(float3 v){return make_float3(floorf(v.x), floorf(v.y), floorf(v.z));}
// frac
inline __host__ __device__ float fracf(float v){return v - floorf(v);}
inline __host__ __device__ float3 fracf(float3 v){return make_float3(fracf(v.x), fracf(v.y), fracf(v.z));}
// fmod
inline __host__ __device__ float3 fmodf(float3 a, float3 b){return make_float3(fmodf(a.x, b.x), fmodf(a.y, b.y), fmodf(a.z, b.z));}
// absolute value
inline __host__ __device__ float3 fabs(float3 v){return make_float3(fabs(v.x), fabs(v.y), fabs(v.z));}
// reflect
//returns reflection of incident ray I around surface normal N
// N should be normalized, reflected vector's length is equal to length of I
inline __host__ __device__ float3 reflect(float3 i, float3 n){return i - 2.0f * n * dot(n, i);}
// cross product
inline __host__ __device__ float3 cross(float3 a, float3 b){return make_float3(a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x);}

In this example, it's pretty easy to turn C/C++ code into CUDA code (CUDA is a subset of the C language). The differences with the CPU version of smallpt are as follows:

  • smallpt's 3D Vector struct is replaced by CUDA's built-in float3 type (linear algebra vector functions for float3 are defined in cutil_math.h)
  • CUDA specific keyword __device__ before functions that should run on the GPU and are only callable from the GPU
  • CUDA specific keyword __global__ in front of the kernel that is called from the host (CPU) and which runs in parallel on all CUDA threads
  • a custom random number generator that runs on the GPU
  • as GPUs don't handle recursion well, the radiance function needs to be converted from a recursive function to an iterative function (see Richie Sam's blogpost or Karl Li's slides for more details) with a fixed number of bounces (Russian roulette could be implemented here to terminate paths with a certain probability, but I took it out for simplicity)
  • in a CPU raytracer, you loop over each pixel of the image with two nested loops (one for image rows and one for image columns). On the GPU the loops are replaced by a kernel which runs for each pixel in parallel. A global thread index is computed instead from the grid dimensions, block dimensions and local thread index. See http://www.3dgep.com/introduction-to-cuda-using-visual-studio-2008/ for more details
  • the main() function calls CUDA specific functions to allocate memory on the CUDA device (cudaMalloc()), launch the CUDA kernel using the "<<< grid, block >>>" syntax and copy the results (in this case the rendered image) from the GPU back to the CPU, where the image is saved in PPM format (a supersimple image format)

When running the code above, we get the following image (1024 samples per pixel, brute force path tracing):

Path traced color bleeding rendered entirely on the GPU! On my laptop's GPU (Geforce 840M) it renders about 24x faster than the multithreaded CPU version (laptop Core-i7 clocked at 2.00 Ghz). The neat thing here is that it only took about 100 lines (if you take out the comments) to get path tracing working on the GPU. The beauty lies in its simplicity.

Even though the path tracing code already works well, it is actually very unoptimized and there are many techniques to speed it up:

  • explicit light sampling (or next event estimation): sample the light source directly instead of using brute force path tracing. This makes an enormous difference in reducing noise.
  • jittered sampling (also called stratified sampling): instead of sampling a pixel randomly, divide the pixel up into a number of layers (strata) in which random sampling is performed. According to Peter Shirley's book this way of sampling (which is partly structured and partly random) is one of the most important noise reduction methods
  • better random number generators
  • various importance sampling strategies: this code already performs cosine weighted importance sampling for diffuse rays, favouring rays with directions that are closer to the normal (as they contribute more to the final image). See http://www.rorydriscoll.com/2009/01/07/better-sampling/.  
  • ray tracing acceleration structures: kd-trees, octrees, grids, bounding volume hierarchies provide massive speedups

GPU specific optimisations (see http://www.3dgep.com/optimizing-cuda-applications/ and Karl Li's course slides linked below):
  • using shared memory and registers whenever possible is many times faster than using global/local memory
  • memory alignment for coalesced reads from GPU memory
  • thread compaction: since CUDA launches a kernel in groups of 32 threads in parallel ("warps"), threads taking different code paths can give rise to thread divergence which reduces the GPU's occupancy. Thread compaction aims to mitigate the effects of thread divergence by bundling threads following similar code paths

I plan to cover the following topics (with CUDA implementations) in upcoming tutorials whenever I find some time:
  • an interactive viewport camera with progressive rendering, 
  • textures (and bump mapping), 
  • environment lighting, 
  • acceleration structures,  
  • triangles and triangle meshes
  • building more advanced features on top of Aila and Laine's GPU ray tracing framework which is also used by Blender's Cycles GPU renderer
  • dissecting some code snippets from Cycles GPU render or SmallLuxGPU 

References used:

GPU path tracing tutorial 2: interactive triangle mesh path tracing

While the tutorial from the previous post was about path tracing simple scenes made of spheres, this tutorial will focus on how to build a very simple path tracer with support for loading and rendering triangle meshes. Instead of rendering the entire image in the background and saving it to a file as was done in the last tutorial, this path tracer displays an interactive viewport which shows progressively rendered updates. This way we can see the rendered image from the first pass and watch it converge to a noise free result (which can take some time in the case of path tracing triangle meshes without using acceleration structures).

For this tutorial I decided to modify the code of a real-time CUDA ray tracer developed by Peter Trier from the Alexandra Institute in 2009 (described in this blog post), because it's very compact, does not use any external libraries (except for CUDA-OpenGL interoperability) and provides a simple obj loader for triangle meshes. I modified the ray tracing kernel to handle path tracing (without recursion) using the path tracing code from the previous tutorial, added support for perfectly reflective and refractive materials (like glass) based on the code of smallpt. The random number generator from the previous post has been replaced with CUDA's own random number generation library provided by curand(), which is less prone to patterns at low sample rates and has more uniform distribution properties. The seed calculation is based on a trick described in a post on RichieSam's blog.

Features of this path tracer

- primitive types: supports spheres, boxes and triangles/triangle meshes
- material types: support for perfectly diffuse, perfectly reflective and perfectly refractive materials
- progressive rendering
- interactive viewport displaying intermediate rendering results

Scratch-a-Pixel has some excellent lessons on ray tracing triangles and triangle meshes, which discuss barycentric coordinates, backface culling and the fast Muller-Trumbore ray/triangle intersection algorithm that is also used in the code for this tutorial:

- ray tracing triangles: http://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-rendering-a-triangle

- ray tracing polygon meshes: http://www.scratchapixel.com/lessons/3d-basic-rendering/ray-tracing-polygon-mesh

The code is one big CUDA file with lots of comments and can be found on my Github repository.

Github repository link: https://github.com/straaljager/GPU-path-tracing-tutorial-2 

Some screenshots

Performance optimisations

- triangle edges are precomputed to speed up ray intersection computation and triangles are stored as (first vertex, edge1, edge2)
- ray/triangle intersection uses the fast Muller-Trumbore technique
- triangle data is stored in the GPU's texture memory which is cached and is a bit faster than global memory because fetching data from textures is accelerated in hardware. The texture cache is also optimized for 2D spatial locality, so threads that access addresses in texture memory that are close together in 2D will achieve best performance. 
- triangle data is aligned in float4s (128 bits) for coalesced memory access, maximising memory throughput,  (see https://docs.nvidia.com/cuda/cuda-c-programming-guide/#device-memory-accesses and http://blog.spectralstudios.net/raytracing/realtime-raytracing-part-3/#more-573)
- for expensive functions (such as sin() and sqrt()), compute fast approximations using single precision intrinsic math functions such as __sinf(), __powf(), __fdividef(): these functions are performed in hardware by the special function units (SFU) on the GPU and are much faster than the standard divide and sin/cos functions at the cost of precision and robustness in corner cases (see https://docs.nvidia.com/cuda/cuda-c-programming-guide/#intrinsic-functions
- to speed up the ray tracing an axis aligned bounding box is created around the triangle mesh. Only rays hitting this box are intersected with the mesh. Without this box,  all rays would have to be tested against every triangle for intersection, which is unbearably slow.

In the next tutorial, we'll have a look at implementing an acceleration structure, which speeds up the rendering by several orders of magnitude. This blog post provides  a good overview of the most recent research in ray tracing acceleration structures for the GPU. There will also be an interactive camera to allow real-time navigation through the scene with depth of field and supersampled anti-aliasing (and there are still lots of optimisations). 


GPU path tracing tutorial 3: GPU-friendly Acceleration Structures. Now you're cooking with GAS!

(In case you were wondering, my pun-loving girlfriend came up with the title for this post). This tutorial is the longest, but most crucial one so far and deals with the implementation ray tracing acceleration structure that can be traversed on the GPU. The code from the previous tutorial works okay for simple triangle meshes with less then 10,000 triangles, but since render times grow linearly or O(n)with the complexity of the scene (each ray needs to test every primitive in the scene for intersection), anything above that number becomes unfeasible. To address this issue, ray tracing researchers came up with several acceleration structures such as grids, octrees, binary space partitioning trees (BSP trees), kd-trees and BVHs (bounding volume hierarchy), allowing render times to scale logarithmically or O(log n) instead of linearly with scene complexity, a huge improvement in speed and efficiency. Acceleration structures are by far the most important ingredient to building a fast ray tracer and an enormous amount of research has gone into improving and refining the algorithms to build and traverse them, both on the CPU on the GPU (the latter since 2006, around the same time unified shader architecture was introduced on GPUs). 

Scratch-a-Pixel (again) has a great introduction to acceleration structures for ray tracing (grids and bounding volume hierarchies) that includes example code: http://www.scratchapixel.com/lessons/advanced-rendering/introduction-acceleration-structure. Peter Shirley's "Realistic Ray Tracing" book also contains a good description and implementation of a BVH with C++ code.

An overview of the latest state-of-the-art research in acceleration structures for GPUs can be found in this blogpost on Robbin Marcus' blog: http://robbinmarcus.blogspot.co.nz/2015/10/real-time-raytracing-part-2.html

This tutorial focuses on the implementation of a BVH acceleration structure on the GPU, and comes with complete annotated source code for BVH construction (on the CPU) and BVH traversal (on the GPU using CUDA). The reason for choosing a BVH over a grid or kd-tree is because BVHs map better to modern GPU architectures and have also been shown to be the acceleration structure which allows the fastest build and render times (see for example https://anteru.net/research/quantitative-analysis-of-voxel-raytracing-acceleration-structures/). Another reason for choosing BVHs is that they are conceptually simple and easy to implement. The Nvidia research paper "Understanding the efficiency of ray traversal on GPUs" by Aila and Laine comes with open source code that contains a highly optimised BVH for CUDA path tracers which was used in Cycles, Blender's GPU path tracing renderer (http://wiki.blender.org/index.php/Dev:Source/Render/Cycles/BVH).

The code in this tutorial is based on a real-time CUDA ray tracer developed by Thanassis Tsiodras, which can be found on http://users.softlab.ntua.gr/~ttsiod/cudarenderer-BVH.html and which I converted to support path tracing instead. The BVH from this renderer is already quite fast and relatively easy to understand.

For the purpose of clarity and to keep the code concise (as there's quite a lot of code required for BVH construction), I removed quite a few nice features from Thanassis' code which are not essential for this tutorial, such as multithreaded BVH building on the CPU (using SSE intrinsics), various render modes (like point rendering), backface culling, a scheme to divide the image in rendertiles in Morton order (along a space filling Z-curve) and some clever workarounds to deal with CUDA's limitations such as separate templated kernels for shadow rays and ambient occlusion. 

One of the more tricky parts of implementing a BVH for ray tracing on the GPU is how to store the BVH structure and BVH node data in a GPU friendly format. CPU ray tracers store a BVH as a hierarchical structure starting with the root node, which contains pointers to its child nodes (in case of an inner node) or pointers to triangles (in case of a leaf node). Since a BVH is built recursively, the child nodes in turn contain pointers to their own child nodes and this keeps on going until the leaf nodes are reached. This process involves lots of pointers which might point to scattered locations in memory, a scenario which is not ideal for the GPU. GPUs like coherent, memory aligned datastructures such as indexable arrays that avoid the use of too many pointers. In this tutorial, the BVH data (such as nodes, triangle data, triangle indices, precomputed intersection data) are therefore stored in flat one-dimensonal arrays (storing elements in depth first order by recursively traversing the BVH), which can be easily digested by CUDA and are stored on the GPU in either global memory or texture memory in the form of CUDA textures (hardware cached). The BVH in this tutorial is using CUDA texture memory, since global memory on older GPUs is not cached (as opposed to texture memory). Since the introduction of Fermi however, global memory is also cached and the performance difference when using one or the other is hardly noticeable.  

In order to avoid wasting time by rebuilding the BVH every time the program is run, the BVH is built only once and stored in a file. For this to work, the BVH data is converted to a cache-friendly format which takes up as little memory space as possible (but the compactness of the data makes it also harder to read). A clever scheme is used to store BVH leaf nodes and inner nodes using the same data structure: instead of using a separate struct for leaf nodes and inner nodes, both types of nodes occupy the same memory space (using a union), which stores either two child indices to the left and right child when dealing with an inner node or a start index into the list of triangles and a triangle count in case of a leaf node. To distinguish between a leaf node and an inner node, the highest bit of the triangle count variable is set to 1 for a leaf node. The renderer can then determine at runtime if it has intersected an inner node or a leaf node by checking the highest bit (with a bitwise AND operation).  

A lot of the triangle intersection data (such as triangle edges, barycentric coordinates, dot products between vertices and edge planes) is precomputed at the scene initialisation stage and stored. Since modern GPUs have much more raw compute power than memory bandwidth, it would be interesting to know whether fetching the precomputed data from memory is faster or slower compared to computing that data directly on the GPU. 

The following is a high level explanation of the algorithm for top-down BVH construction (on the CPU) and traversal (on the GPU). The BVH in this code is built according to the surface area heuristic and uses binning to find the best splitting plane. The details of the BVH algorithm can be found in the following papers:

"On fast construction of SAH based Bounding Volume Hierarchies" by Ingo Wald, 2007. This paper is a must read in order to understand what the code is doing.

- "Ray tracing deformable scenes using dynamic Bounding Volume Hierarchies" by Wald, Boulos and Shirley, 2007

- "On building fast kd-trees for ray tracing, and on doing that in O(N log N)" by Wald and Havran, 2006

Overview of algorithm for building the BVH on the CPU

- the main() function (in main.cpp) calls prepCUDAscene(), which in turn calls UpdateBoundingVolumeHierarchy()

- UpdateBoundingVolumeHierarchy() checks if there is already a BVH for the scene stored (cached) in a file and loads that one or builds a new BVH by calling CreateBVH()

- CreateBVH():
  1. computes a bbox (bounding box) for every triangle and calculate the bounds (top and bottom)
  2. initialises a "working list" bbox to contain all the triangle bboxes
  3. expands the bounds of the working list bbox so it encompasses all triangles in the scene by looping over all the triangle bboxes
  4. computes each triangle bbox centre and adds the triangle bbox to the working list
  5. passes the working list to Recurse(), which builds the BVH tree structure
  6. returns the BVH root node
Recurse() recursively builds the BVH tree from top (rootnode) to bottom using binning, finding optimal split planes for each depth. It divides the work bounding box into a number of equally sized "bins" along each axis, chooses the axis and splitting plane resulting in the least cost (determined by the surface area heuristic or SAH: the larger the surface area of a bounding box, the costlier it is to raytrace) and finding the bbox with the minimum surface area:
  1. Check if the working list contains less then 4 elements (triangle bboxes) in which case create a leaf node and push each triangle to a triangle list
  2. Create an inner node if the working list contains 4 or more elements
  3. Divide node further into smaller nodes
  4. Start by finding the working list bounds (top and bottom)
  5. Loop over all bboxes in current working list, expanding/growing the working list bbox
  6. find surface area of bounding box by multiplying the dimensions of the working list's bounding box
  7. The current bbox has a cost C of N (number of triangles) * SA (Surface Area) or C = N * SA
  8. Loop over all three axises (X, Y, Z) to find best splitting plane using "binning"
  9. Binning: try splitting the current axis at a uniform distance (equidistantly spaced planes) in "bins" of size "step" that gets smaller the deeper we go: size of "sampling grid": 1024 (depth 0), 512 (depth 1), etc
  10. For each bin (equally spaced bins of size "step"), initialise a left and right bounding box 
  11. For each test split (or bin), allocate all triangles in the current work list based on their bbox centers (this is a fast O(N) pass, no triangle sorting needed): if the center of the triangle bbox is smaller than the test split value, put the triangle in the left bbox, otherwise put the triangle in the right bbox. Count the number of triangles in the left and right bboxes.
  12. Now use the Surface Area Heuristic to see if this split has a better "cost": calculate the surface area of the left and right bbox and calculate the total cost by multiplying the surface area of the left and right bbox by the number of triangles in each. Keep track of cheapest split found so far.
  13. At the end of this loop (which runs for every "bin" or "sample location"), we should have the best splitting plane, best splitting axis and bboxes with minimal traversal cost
  14. If we found no split to improve the cost, create a BVH leaf, otherwise create a BVH inner node with L and R child nodes. Split with the optimal value we found above.
  15. After selection of the best split plane, distribute each of the triangles into the left or right child nodes based on their bbox center
  16. Recursively build the left and right child nodes (do step 1 - 16)
  17. When all recursive function calls have finished, the end result of Recurse() is the root node of the BVH
Once the BVH has been created, we can copy its data into a memory saving, cache-friendly format (CacheFriendlyBVHNode occupies exactly 32 bytes, i.e. a cache-line) by calling CreateCFBVH(). which recursively counts the triangles and bounding boxes and stores them in depth first order in one-dimensional arrays by calling PopulateCacheFriendlyBVH()

The data of the cache friendly BVH is copied to the GPU in CUDA global memory by prepCUDAscene() (using the cudaMalloc() and cudaMemcpy() functions). Once the data is in global memory it's ready to be used by the renderer, but the code is taking it one step further and binds the BVH data to CUDA textures for performance reasons (texture memory is cached, although global memory is also cached since Fermi). The texture binding is done by cudarender() (in cuda_pathtracer.cu) which calls cudaBindTexture(). After this stage, all scene data is now ready to be rendered (rays traversing the BVH and intersecting triangles).

Overview of algorithm for traversing the BVH on the GPU

- after cudarenderer() has bound the data to CUDA textures with cudaBindTexture() the first time it's being called, it launches the CoreLoopPathTracingKernel() which runs in parallel over all pixels to render a frame.
- CoreLoopPathTracingKernel() computes a primary ray starting from the interactive camera view (which can differ each frame) and calls path_trace() to calculate the ray bounces 
- path_trace() first tests all spheres in the scene for intersection and then tests if the ray intersects any triangles by calling BVH_IntersectTriangles() which traverses the BVH.
- BVH_IntersectTriangles():
  1. initialise a stack to keep track of all the nodes the ray has traversed
  2. while the stack is not empty, pop a BVH node from the stack and decrement the stack index
  3. fetch the data associated with this node (indices to left and right child nodes for inner nodes or start index in triangle list + triangle count for leaf nodes)
  4. determine if the node is a leaf node or triangle node by examining the highest bit of the count variable
  5. if inner node, test ray for intersection with AABB (axis aligned bounding box) of node --> if intersection, push left and right child node indices on the stack, and go back to step 2 (pop next node from the stack)
  6. if leaf node, loop over all the triangles in the node (determined by the start index in the list of triangle indices and the triangle count), 
  7. for each triangle in the node, fetch the index, center, normal and precomputed intersection data and check for intersection with the ray
  8. if ray intersects triangle, keep track of the closest hit
  9. recursively traverse the left and right child nodes, if any (do step 2 - 9)
  10. after all recursive calls have finished, the end result returned by the function is a bool based on the index of the closest hit triangle (true if index is not -1)
- after the ray has been tested for intersection with the scene, compute the colour of the ray by multiplying with the colour of the intersected object, calculate the direction of the next ray in the path according to the material BRDF and accumulate the colours of the subsequent path segments (see GPU path tracing tutorial 1).

In addition to the BVH, I added an interactive camera based on the interactive CUDA path tracer code from Yining Karl Li and Peter Kutz (https://github.com/peterkutz/GPUPathTracer). The camera's view direction and position can be changed interactively with mouse and keyboard (a new orthornormal basis for the camera is computed each frame). The camera produces an antialiased image by jittering the primary ray directions. By allowing primary rays to start randomly on a simulated disk shaped lens instead of from a point. a camera aperture (the opening in the diaphragm) with focal plane can be simulated, providing a cool, photographic depth-of-field effect. The focal distance can also be adjusted interactively.

The material system for this tutorial allows five basic materials: ideal diffuse, ideal specular, ideal refractive, Phong metal (based on code from Peter Shirley's "Realistic Ray Tracing" book) with a hardcoded exponent and a coat (acrylic) material (based on Karl Li and Peter Kutz' CUDA path tracer).

CUDA/C++ code (on GitHub)

The code for this tutorial can be found at https://github.com/straaljager/GPU-path-tracing-tutorial-3/ I've added plenty of comments throughout the code, but if some steps aren't clear, let me know. Detailed compilation instructions for Windows and Visual Studio are in the readme file: https://github.com/straaljager/GPU-path-tracing-tutorial-3/blob/master/README.md

I'll provide a downloadable executable once a find a good website to upload it to (Google code is no longer an option). 

Screenshots produced with the code from this tutorial (Stanford Dragon and Happy Buddha .ply models from the Stanford 3D scanning repository)

Glossy Stanford dragon model (871,000 triangles)

Happy Buddha model (1,088,000 triangles) with Phong metal material

The next tutorial will add even more speed: I'll dive deeper into the highly optimised BVH acceleration structure for GPU traversal from Aila and Laine, which uses spatial splitting to build higher quality (and faster) trees. It's also the framework that the GPU part of Blender Cycles is using.

Other features for upcoming tutorials are support for textures, sun and sky lighting, environment lighting, more general and accurate materials using Fresnel, area light support, direct light sampling and multiple importance sampling.


- CUDA based sphere path tracer by Peter Kutz and Yining Karl Li
Overview of state-of-the-art acceleration structures for GPU ray tracing by Robbin Marcus
- "Realistic Ray Tracing" by P. Shirley

Free introductory minibook on ray tracing

Peter Shirley has just released "Ray tracing, the next week", a free book on Amazon for anyone who wants to learn how to code a basic path tracer in C: http://psgraphics.blogspot.be/2016/03/new-ray-tracing-mini-book-is-out.html

"Ray tracing the next week" is a follow-up to another mini-book by Shirley, "Ray tracing in one weekend" which was released only last month and covers the very basics of a ray tracer including ray-sphere intersection, path tracing of diffuse, metal and dielectric materials, anti-aliasing, positionable camera and depth-of-field. The Kindle edition is available for free when downloaded within the next five days (until 11 March). The book is excellent for people who quickly want to dive into coding a path tracer from scratch without being overwhelmed by theoretical details. It covers more advanced features such as solid textures, image textures, participating media, motion blur, instancing, and BVH acceleration structures and comes with source code snippets (using C plus classes and operator overloading, easily portable to CUDA). The code even contains some simple but clever optimisation tricks which are not published in any other ray tracing books.

Start your engines: source code for FireRays (AMD's high performance OpenCL based GPU ray tracing framework) available

AMD has just released the full source code of FireRays, their OpenCL based GPU renderer which was first available as a SDK library since August 2015 (see http://raytracey.blogspot.co.nz/2015/08/firerays-amds-opencl-based-high.html). This is an outstanding move by AMD which significantly lowers the threshold for developers to enter the GPU rendering arena and create an efficient OpenCL based path tracing engine that is able to run on hardware from AMD, Intel and Nvidia without extra effort. 

Here's an ugly sample render of FireRays provided by AMD:

And an old video from one of the developers:

Nvidia open sourced their high performance CUDA based ray tracing framework in 2009, but hasn't updated it since 2012 (presumably due to the lack of any real competition from AMD in this area) and has since focused more on developing OptiX, a CUDA based closed source ray tracing library. Intel open sourced Embree in 2011, which is being actively developed and updated with new features and performance improvements. They even released another open source high performance ray tracer for scientific visualisation called OSPRay.

FireRays seems to have some advanced features such as ray filtering, geometry and ray masking (to make certain objects invisible to the camera or selectively ignore effects like shadows and reflections) and support for volumetrics. Hopefully AMD will also release some in-depth documentation and getting started tutorials in order to maximise adoption of this new technology among developers who are new to GPU ray tracing.

Real-time path traced Quake 2

Last week, Edd Biddulph released the code and some videos of a very impressive project he's working on: a real-time path traced version of Quake 2 running on OpenGL 3.3.

Project link with videos: http://amietia.com/q2pt.html
Full source code on Github: https://github.com/eddbiddulph/yquake2/tree/pathtracing

Quake 2, now with real-time indirect lighting and soft shadows
The path tracing engine behind this project is quite astonishing when you consider the number of lightsources in the level and the amount of dynamic characters (each with a unique pose) that are updated every single frame. I had a very interesting talk with Edd on some of the features of his engine, revealing that he used a lot of clever optimisations (some of which are taking advantage of the specific properties of the Quake 2 engine). 

Copying Edd's answers here:
Why Quake 2 instead of Quake 3
I chose Quake 2 because it has area lightsources and the maps were designed with multiple-bounce lighting in mind. As far as I know, Quake 3 was not designed this way and didn't even have area lightsources for the baked lighting. Plus Quake 2's static geometry was still almost entirely defined by a binary space partitioning tree (BSP) and I found that traversing a BSP is pretty easy in GLSL and seems to perform quite well, although I haven't made any comparisons to other approaches. Quake 3 has a lot more freeform geometry such as tessellated Bezier surfaces so it doesn't lend itself so well to special optimisations. I'm a big fan of both games of course :)

How the engine updates dynamic objects
All dynamic geometry is inserted into a single structure which is re-built from scratch on every frame. Each node is an axis-aligned bounding box and has a 'skip pointer' to skip over the children. I make a node for each triangle and build the structure bottom-up after sorting the leaf nodes by morton code for spatial coherence. I chose this approach because the implementation is simple both for building and traversing, the node hierarchy is quite flexible, and building is fast although the whole CPU side is single-threaded for now (mostly because Quake 2 is single-threaded of course). I'm aware that the lack of ordered traversal results in many more ray-triangle intersection tests than are necessary, but there is little divergence and low register usage since the traversal is stackless.

How to keep noise to a minimum when dealing with so many lights
The light selection is a bit more tricky. I divided lightsources into two categories - regular and 'skyportals'. A skyportal is just a light-emitting surface from the original map data which has a special texture applied, which indicates to the game that the skybox should be drawn there. Each leaf in the BSP has two lists of references to lightsources. The first list references regular lightsources which are potentially visible from the leaf according to the PVS (potentially visible set) tables. The second list references skyportals which are contained within the leaf. At an intersection point the first list is used to trace shadow rays and make explicit samples of lightsources, and the second list is used to check if the intersection point is within a skyportal surface. If it's within a skyportal then there is a contribution of light from the sky. This way I can perform a kind of offline multiple importance sampling (MIS) because skyportals are generally much larger than regular lights. For regular lights of course I use importance sampling, but I believe the weight I use is more approximate than usual because it's calculated always from the center of the lightsource rather than from the real sample position on the light.

One big point about the lights right now is that the pointlights that the original game used are being added as 4 triangular lightsources arranged in a tetrahedron so they tend to make quite a performance hit. I'd like to try adding a whole new type of lightsource such as a spherical light to see if that works out better.

Ray tracing specific optimisations
I'm making explicit light samples by tracing shadow rays directly towards points on the lightsources. MIS isn't being performed in the shader, but I'm deciding offline whether a lightsource should be sampled explicitly or implicitly.

Which parts of the rendering process use rasterisation
I use hardware rasterisation only for the primary rays and perform the raytracing in the same pass for the following reasons:
  • Translucent surfaces can be lit and can receive shadows identically to all other surfaces.
  • Hardware anti-aliasing can be used, of course.
  • Quake 2 sorts translucent BSP surfaces and draws them in a second pass, but it doesn't do this for entities (the animated objects) so I would need to change that design and I consider this too intrusive and likely to break something. One of my main goals was to preserve the behaviour of Q2's own renderer.
  • I'm able to eliminate overdraw by making a depth-only pre-pass which even uses the same GL buffers that the raytracer uses so it has little overhead except for a trick that I had to make since I packed the three 16-bit triangle indices for the raytracer into two 32-bit elements (this was necessary due to OpenGL limitations on texture buffer objects).
  • It's nice that I don't need to manage framebuffer stuff and design a good g-buffer format.
The important project files containing the path tracing code
If you want to take a look at the main parts that I wrote, stick to src/client/refresh/r_pathtracing.c and src/client/refresh/pathtracer.glsl. The rest of my changes were mostly about adding various GL extensions and hooking in my stuff to the old refresh subsystem (Quake 2's name for the renderer). I apologise that r_pathtracing.c is such a huge file, but I did try to comment it nicely and refactoring is already on my huge TODO list. The GLSL file is converted into a C header at build time by stringifyshaders.sh which is at the root of the codebase.

More interesting tidbits
- This whole project is only made practical by the fact that the BSP files still contain surface emission data despite the game itself making no use of it at all. This is clearly a by-product of keeping the map-building process simple, and it's a very fortunate one!
- The designers of the original maps sometimes placed pointlights in front of surface lights to give the appearence that they are glowing or emitting light at their sides like a fluorescent tube diffuser. This looks totally weird in my pathtracer so I have static pointlights disabled by default. They also happen to go unused by the original game, so it's also fortunate that they still exist among the map data. 
- The weapon that is viewed in first-person is drawn with a 'depth hack' (it's literally called RF_DEPTHHACK), in which the range of depth values is reduced to prevent the weapon poking in to walls. Unfortunately the pathtracer's representation would still poke in to walls because it needs the triangles in worldspace, and this would cause the tip of the weapon to turn black (completely in shadow). I worked around this by 'virtually' scaling down the weapon for the pathtracer. This is one of the many ways in which raytracing turns out to be tricky for videogames, but I'm sure there can always be elegant solutions.
If you want to mess around with the path traced version of Quake 2 yourself (both AMD and Nvidia cards are supported as the path tracer uses OpenGL), simply follow these steps:
  • on Windows, follow the steps under section 2.3 in the readme file (link: https://github.com/eddbiddulph/yquake2/blob/pathtracing/README). Lots of websites still offer the Quake 2 demo for download (e.g. http://www.ausgamers.com/files/download/314/quake-2-demo)
  • download and unzip the Yamagi Quake 2 source code with path tracing from https://github.com/eddbiddulph/yquake2
  • following the steps under section 2.6 of the readme file, download and extract the premade MinGW build environment, run MSYS32, navigate to the source directory with the makefile, "make" the release build and replace the files "q2ded.exe", "quake2.exe" and "baseq2\game.dll" in the Quake 2 game installation with the freshly built ones
  • start the game by double clicking "quake2", open the Quake2 console with the ~ key (under the ESC key), type "gl_pt_enable 1", hit Enter and the ~ key to close the console
  • the game should now run with path tracing

Edd also said he's also planning to add new special path tracing effects (such as light emitting particles from the railgun) and implementing more optimisations to reduce the path tracing noise.

GPU path tracing tutorial 4: Optimised BVH building, faster traversal and intersection kernels and HDR environment lighting

For this tutorial, I've implemented a couple of improvements based on the high performance GPU ray tracing framework of Timo Aila, Samuli Laine and Tero Karras (Nvidia research) which is described in their 2009 paper "Understanding the efficiency of ray traversal on GPUs" and the 2012 addendum to the original paper which contains specifically hand tuned kernels for Fermi and Kepler GPUs (which also works on Maxwell). The code for this framework is open source and can be found at the Google code repository (which is about to be phased out) or on GitHub. The ray tracing kernels are thoroughly optimised and deliver state-of-the-art performance (the code from this tutorial is 2-3 times faster than the previous one).  For that reason, they are also used in the production grade CUDA path tracer Cycles:

- wiki.blender.org/index.php/Dev:Source/Render/Cycles/BVH

- github.com/doug65536/blender/blob/master/intern/cycles/kernel/kernel_bvh.h

- github.com/doug65536/blender/blob/master/intern/cycles/kernel/kernel_bvh_traversal.h

The major improvements from this framework are:

- Spatial split BVH: this BVH building method is based on Nvidia's "Spatial splits in bounding volume hierarchies" paper by Martin Stich. It aims to reduce BVH node overlap (a high amount of node overlap lowers ray tracing performance) by combining the object splitting strategy of regular BVH building (according to a surface area heuristic or SAH) with the space splitting method of kd-tree building. The algorithm determines for each triangle whether "splitting" it (by creating duplicate references to the triangle and storing them in its overlapping nodes) lowers the cost of ray/node intersections compared to the "unsplit" case. The result is a very high quality acceleration structure with ray traversal performance which on average is significantly higher than (or in the worst case equal to) a regular SAH BVH.

- Woop ray/triangle intersection: this algorithm is explained in "Real-time ray tracing of dynamic scenes on an FPGA chip". It basically transforms each triangle in the mesh to a unit triangle with vertices (0, 0, 0), (1, 0, 0) and (0, 1, 0). During rendering, a ray is transformed into "unit triangle space" using a triangle specific affine triangle transformation and intersected with the unit triangle, which is a much simpler computation.

- Hand optimised GPU ray traversal and intersection kernels:  these kernels use a number of specific tricks to minimise thread divergence within a warp (a warp is a group of 32 SIMD threads which operate in lockstep, i.e. all threads within a warp must execute the same instructions). Thread divergence occurs when one or more threads within a warp follow a different code execution branch, which (in the absolute worst case) could lead to a scenario where only one thread is active while the other 31 threads in the warp are idling, waiting for it to finish. Using "persistent threads" aims to mitigate this problem: when a predefined number of CUDA threads within a warp is idling, the GPU will dynamically fetch new work for these threads in order to increase compute occupancy. The persistent threads feature is used in the original framework. To keep things simple for this tutorial, it has not been implemented as it requires generating and buffering batches of rays, but it is relatively easy to add. Another optimisation to increase SIMD efficiency in a warp is postponing ray/triangle intersection tests until all threads in the same warp have found a leaf node. Robbin Marcus wrote a very informative blogpost about these specific optimisations. In addition to these tricks, the Kepler kernel also uses the GPUs video instructions to perform min/max operations (see "renderkernel.cu" at the top).

Other new features:
- a basic OBJ loader which triangulates n-sided faces (n-gons, triangle fans)
- simple HDR environment map lighting, which for simplicity does not use any filtering (hence the blockiness) or importance sampling yet. The code is based on http://blog.hvidtfeldts.net/index.php/2012/10/image-based-lighting/

Some renders with the code from this tutorial (the "Roman Settlement" city scene was created by LordGood and converted from a SketchUp model, also used by Mitsuba Render. The HDR maps are available at the HDR Labs website):


Source code
The tutorial's source code can be found at github.com/straaljager/GPU-path-tracing-tutorial-4

For clarity, I've tried to simplify the code where possible, keeping the essential improvements provided by the framework and cutting out the unnecessary parts. I have also added clarifying comments to the most difficult code parts where appropriate. There is quite a lot of new code, but the most important and interesting files are:

- SplitBVHBuilder.cpp contains the algorithm for building BVH with spatial splits
- CudaBVH.cppshows the particular layout in which the BVH nodes are stored and Woop's triangle transformation method
- renderkernel.cudemonstrates two methods of ray/triangle intersection: a regular ray/triangle intersection algorithm similar to the one in GPU path tracing tutorial 3, denoted as DEBUGintersectBVHandTriangles() and a method using Woop's ray/triangle intersection named intersectBVHandTriangles()  

A downloadable demo (which requires an Nvidia GPU) is available from

Working with and learning this ray tracing framework was a lot of fun, head scratching and cursing (mostly the latter). It has given me a deeper appreciation for both the intricacies and strengths of GPUs and taught me a multitude of ways of how to optimise Cuda code to maximise performance (even to the level of assembly/PTX). I recommend anyone who wants to build a GPU renderer to sink their teeth in it (the source code in this tutorial should make it easier to digest the complexities). It keeps astounding me what GPUs are capable of and how much they have evolved in the last decade. 

The next tutorial(s) will cover direct lighting, physical sky, area lights, textures and instancing.  I've also had a few requests from people who are new to ray tracing for a more thorough explanation of the code from previous tutorials. At some point (when time permits), I hope to create tutorials with illustrations and pseudocode of all the concepts covered.

OpenCL path tracing tutorial 1: Firing up OpenCL

This is the first tutorial in a new series of GPU path tracing tutorials which will focus on OpenCL based rendering. The first few tutorials will cover the very basics of getting started with OpenCL and OpenCL based ray tracing and path tracing of simple scenes. Follow-up tutorials will use a cut-down version of AMD's RadeonRays framework (the framework formerly known as FireRays), to start from as a basis to add new features in a modular manner. The goal is to incrementally work up to include all the features of RadeonRays, a full-featured GPU path tracer. The Radeon Rays source also forms the basis of AMD's Radeon ProRender Technology (which will also be integrated as a native GPU renderer in an upcoming version of Maxon's Cinema4D).  In the end, developers that are new to rendering should be able to code up their own GPU renderer and integrate it into their application. 

Why OpenCL?

The major benefit of OpenCL is its platform independence, meaning that the same code can run on CPUs and GPUs made by AMD, Nvidia and Intel (in theory at least, in practice there are quite a few implementation differences between the various platforms). The tutorials in this series should thus run on any PC, regardless of GPU vendor (moreover a GPU is not even required to run the program). 

Another advantage of OpenCL is that it can use all the available CPU and GPUs in a system simultaneously to accelerate parallel workloads (such as rendering or physics simulations).

In order to achieve this flexibility, some boiler plate code is required which selects an OpenCL platform (e.g. AMD or Nvidia) and one or more OpenCL devices (CPUs or GPUs). In addition, the OpenCL source must be compiled at runtime (unless the platform and device are known in advance), which adds some initialisation time when the program is first run.

OpenCL execution model quick overview

This is a superquick overview OpenCL execution model, just enough to get started (there are plenty of more exhaustive sources on OpenCL available on the web). 

In order to run an OpenCL program, the following structures are required (and are provided by the OpenCL API):
  • Platform: which vendor (AMD/Nvidia/Intel)
  • Device: CPU, GPU, APU or integrated GPU
  • Context: the runtime interface between the host (CPU) and device (GPU or CPU) which manages all the OpenCL resources (programs, kernels, command queue, buffers). It receives and distributes kernels and transfers data.
  • Program: the entire OpenCL program (one or more kernels and device functions)
  • Kernel: the starting point into the OpenCL program, analogous to the main() function in a CPU program. Kernels are called from the host (CPU). They represent the basic units of executable code that run on an OpenCL device and are preceded by the keyword "__kernel"
  • Command queue: the command queue allows kernel execution commands to be sent to the device (execution can be in-order or out-of-order)
  • Memory objects: buffers and images
These structures are summarised in the diagram below (slide from AMD's Introduction to OpenCL programming):

OpenCL execution model

OpenCL memory model quick overview

The full details of the memory model are beyond the scope of this first tutorial, but we'll cover the basics here to get some understanding on how a kernel is executed on the device. 

There are four levels of memory on an OpenCL device, forming a memory hierarchy (from large and slow to tiny and fast memory):
  • Global memory (similar to RAM): the largest but also slowest form of memory, can be read and written to by all work items (threads) and all work groups on the device and can also be read/written by the host (CPU).
  • Constant memory: a small chunk of global memory on the device, can be read by all work items on the device (but not written to) and can be read/written by the host. Constant memory is slightly faster than global memory.
  • Local memory (similar to cache memory on the CPU): memory shared among work items in the same work group (work items executing together on the same compute unit are grouped into work groups). Local memory allows work items belonging to the same work group to share results. Local memory is much faster than global memory (up to 100x).
  • Private memory (similar to registers on the CPU): the fastest type of memory. Each work item (thread) has a tiny amount of private memory to store intermediate results that can only be used  by that work item

First OpenCL program

With the obligatory theory out of the way, it's time to dive into the code. To get used to the OpenCL syntax, this first program will be very simple (nothing earth shattering yet): the code will just add the corresponding elements of two floating number arrays together in parallel (all at once).

In a nutshell, what happens is the following:
  1. Initialise the OpenCL computing environment: create a platform, device, context, command queue, program and kernel and set up the kernel arguments
  2. Create two floating point number arrays on the host side and copy them to the OpenCL device
  3. Make OpenCL perform the computation in parallel (by determining global and local worksizes and launching the kernel)
  4. Copy the results of the computation from the device to the host
  5. Print the results to the console
To keep the code simple and readable, there is minimal error checking, the "cl" namespace is used for the OpenCL structures and the OpenCL kernel source is provided as a string in the CPU code. 

The code contains plenty of comments to clarify the new syntax:

// Getting started with OpenCL tutorial 
// by Sam Lapere, 2016, http://raytracey.blogspot.com
// Code based on http://simpleopencl.blogspot.com/2013/06/tutorial-simple-start-with-opencl-and-c.html

#include <iostream>
#include <vector>
#include <CL\cl.hpp> // main OpenCL include file

usingnamespace cl;
usingnamespace std;

void main()
// Find all available OpenCL platforms (e.g. AMD, Nvidia, Intel)
vector<Platform> platforms;

// Show the names of all available OpenCL platforms
cout << "Available OpenCL platforms: \n\n";
for (unsignedint i = 0; i < platforms.size(); i++)
cout << "\t"<< i + 1 << ": "<< platforms[i].getInfo<CL_PLATFORM_NAME>() << endl;

// Choose and create an OpenCL platform
cout << endl << "Enter the number of the OpenCL platform you want to use: ";
unsignedint input = 0;
cin >> input;
// Handle incorrect user input
while (input < 1 || input > platforms.size()){
cin.clear(); //clear errors/bad flags on cin
cin.ignore(cin.rdbuf()->in_avail(), '\n'); // ignores exact number of chars in cin buffer
cout << "No such platform."<< endl << "Enter the number of the OpenCL platform you want to use: ";
cin >> input;

Platform platform = platforms[input - 1];

// Print the name of chosen OpenCL platform
cout << "Using OpenCL platform: \t"<< platform.getInfo<CL_PLATFORM_NAME>() << endl;

// Find all available OpenCL devices (e.g. CPU, GPU or integrated GPU)
vector<Device> devices;
platform.getDevices(CL_DEVICE_TYPE_ALL, &devices);

// Print the names of all available OpenCL devices on the chosen platform
cout << "Available OpenCL devices on this platform: "<< endl << endl;
for (unsignedint i = 0; i < devices.size(); i++)
cout << "\t"<< i + 1 << ": "<< devices[i].getInfo<CL_DEVICE_NAME>() << endl;

// Choose an OpenCL device
cout << endl << "Enter the number of the OpenCL device you want to use: ";
input = 0;
cin >> input;
// Handle incorrect user input
while (input < 1 || input > devices.size()){
cin.clear(); //clear errors/bad flags on cin
cin.ignore(cin.rdbuf()->in_avail(), '\n'); // ignores exact number of chars in cin buffer
cout << "No such device. Enter the number of the OpenCL device you want to use: ";
cin >> input;

Device device = devices[input - 1];

// Print the name of the chosen OpenCL device
cout << endl << "Using OpenCL device: \t"<< device.getInfo<CL_DEVICE_NAME>() << endl << endl;

// Create an OpenCL context on that device.
// the context manages all the OpenCL resources
Context context = Context(device);


// the OpenCL kernel in this tutorial is a simple program that adds two float arrays in parallel
// the source code of the OpenCL kernel is passed as a string to the host
// the "__global" keyword denotes that "global" device memory is used, which can be read and written
// to by all work items (threads) and all work groups on the device and can also be read/written by the host (CPU)

constchar* source_string =
" __kernel void parallel_add(__global float* x, __global float* y, __global float* z){ "
" const int i = get_global_id(0); "// get a unique number identifying the work item in the global pool
" z[i] = y[i] + x[i]; "// add two arrays

// Create an OpenCL program by performing runtime source compilation
Program program = Program(context, source_string);

// Build the program and check for compilation errors
cl_int result = program.build({ device }, "");
if (result) cout << "Error during compilation! ("<< result << ")"<< endl;

// Create a kernel (entry point in the OpenCL source program)
// kernels are the basic units of executable code that run on the OpenCL device
// the kernel forms the starting point into the OpenCL program, analogous to main() in CPU code
// kernels can be called from the host (CPU)
Kernel kernel = Kernel(program, "parallel_add");

// Create input data arrays on the host (= CPU)
constint numElements = 10;
float cpuArrayA[numElements] = { 0.0f, 1.0f, 2.0f, 3.0f, 4.0f, 5.0f, 6.0f, 7.0f, 8.0f, 9.0f };
float cpuArrayB[numElements] = { 0.1f, 0.2f, 0.3f, 0.4f, 0.5f, 0.6f, 0.7f, 0.8f, 0.9f, 1.0f };
float cpuOutput[numElements] = {}; // empty array for storing the results of the OpenCL program

// Create buffers (memory objects) on the OpenCL device, allocate memory and copy input data to device.
// Flags indicate how the buffer should be used e.g. read-only, write-only, read-write
Buffer clBufferA = Buffer(context, CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR, numElements * sizeof(cl_int), cpuArrayA);
Buffer clBufferB = Buffer(context, CL_MEM_READ_ONLY | CL_MEM_COPY_HOST_PTR, numElements * sizeof(cl_int), cpuArrayB);
Buffer clOutput = Buffer(context, CL_MEM_WRITE_ONLY, numElements * sizeof(cl_int), NULL);

// Specify the arguments for the OpenCL kernel
// (the arguments are __global float* x, __global float* y and __global float* z)
kernel.setArg(0, clBufferA); // first argument
kernel.setArg(1, clBufferB); // second argument
kernel.setArg(2, clOutput); // third argument

// Create a command queue for the OpenCL device
// the command queue allows kernel execution commands to be sent to the device
CommandQueue queue = CommandQueue(context, device);

// Determine the global and local number of "work items"
// The global work size is the total number of work items (threads) that execute in parallel
// Work items executing together on the same compute unit are grouped into "work groups"
// The local work size defines the number of work items in each work group
// Important: global_work_size must be an integer multiple of local_work_size
std::size_t global_work_size = numElements;
std::size_t local_work_size = 10; // could also be 1, 2 or 5 in this example
// when local_work_size equals 10, all ten number pairs from both arrays will be added together in one go

// Launch the kernel and specify the global and local number of work items (threads)
queue.enqueueNDRangeKernel(kernel, NULL, global_work_size, local_work_size);

// Read and copy OpenCL output to CPU
// the "CL_TRUE" flag blocks the read operation until all work items have finished their computation
queue.enqueueReadBuffer(clOutput, CL_TRUE, 0, numElements * sizeof(cl_float), cpuOutput);

// Print results to console
for (int i = 0; i < numElements; i++)
cout << cpuArrayA[i] << " + "<< cpuArrayB[i] << " = "<< cpuOutput[i] << endl;


Compiling instructions(for Visual Studio on Windows)

To compile this code, it's recommended to download and install the AMD App SDK (this works for systems with GPUs or CPUs from AMD, Nvidia and Intel, even if your system doesn't have an AMD CPU or GPU installed) since Nvidia's OpenCL implementation is no longer up-to-date.
    1. Start an empty Console project in Visual Studio (any recent version should work, including Express and Community) and set to Release mode 
    2. Add the SDK include path to the "Additional Include Directories" (e.g. "C:\Program Files (x86)\AMD APP SDK\2.9-1\include") 
    3. In Linker > Input, add "opencl.lib" to "Additional Dependencies" and add the OpenCL lib path to "Additional Library Directories"  (e.g. "C:\Program Files (x86)\AMD APP SDK\2.9-1\lib\x86")
    4. Add the main.cpp file (or create a new file and paste the code) and build the project

      Download binaries

      The executable (Windows only) for this tutorial is available at 

      It runs on CPUs and/or GPUs from AMD, Nvidia and Intel.

      Useful References

      - "A gentle introduction to OpenCL":

      - "Simple start with OpenCL":

      - Anteru's blogpost, Getting started with OpenCL (uses old OpenCL API)
      - AMD introduction to OpenCL programming:

      Up next

      In the next tutorial we'll start rendering an image with OpenCL.

      OpenCL path tracing tutorial 2: path tracing spheres

      This tutorial consists of two parts: the first part will describe how to ray trace one sphere using OpenCL, while the second part covers path tracing of a scene made of spheres. The tutorial will be light on ray tracing/path tracing theory (there are plenty of excellent resources available online such as Scratch-a-Pixel) and will focus instead on the practical implementation of rendering algorithms in OpenCL.The end result will be a rendered image featuring realistic light effects such as indirect lighting, diffuse colour bleeding and soft shadows, all achieved with just a few lines of code:

      Part 1: Ray tracing a sphere

      Computing a test image on the OpenCL device

      The host (CPU) sets up the OpenCL environment and launches the OpenCL kernel which will be executed on the OpenCL device (GPU or CPU) in parallel. Each work item (or thread) on the device will calculate one pixel of the image. There will thus be as many work items in the global pool as there are pixels in the image. Each work item has a unique ID which distinguishes from all other work items in the global pool of threads and which is obtained with get_global_id(0)

      The X- and Y-coordinates of each pixel can be computed by using that pixel's unique work item ID:
      • x-coordinate: divide by the image width and take the remainder
      • y-coordinate: divide by the image width
      By remapping the x and y coordinates from the [0 to width] range for x and [0 to height] range for y to the range [0 - 1] for both, and plugging those values in the red and green channels repsectively yields the following gradient image (the image is saved in ppm format which can be opened with e.g. IrfanView of Gimp):

      The OpenCL code to generate this image:

      __kernel void render_kernel(__global float3* output, int width, int height)
      constint work_item_id = get_global_id(0); /* the unique global id of the work item for the current pixel */
      int x = work_item_id % width; /* x-coordinate of the pixel */
      int y = work_item_id / width; /* y-coordinate of the pixel */
      float fx = (float)x / (float)width; /* convert int to float in range [0-1] */
      float fy = (float)y / (float)height; /* convert int to float in range [0-1] */
      output[work_item_id] = (float3)(fx, fy, 0); /* simple interpolated colour gradient based on pixel coordinates */

      Now let's use the OpenCL device for some ray tracing.

      Ray tracing a sphere with OpenCL

      We first define a Ray and a Sphere struct in the OpenCL code:

      A Ray has 
      • an origin in 3D space (3 floats for x, y, z coordinates) 
      • a direction in 3D space (3 floats for the x, y, z coordinates of the 3D vector)
      A Sphere has 
      • a radius
      • a position in 3D space (3 floats for x, y, z coordinates), 
      • an object colour (3 floats for the Red, Green and Blue channel) 
      • an emission colour (again 3 floats for each of the RGB channels)

      struct Ray{
      float3 origin;
      float3 dir;

      struct Sphere{
      float radius;
      float3 pos;
      float3 emi;
      float3 color;

      Camera ray generation

      Rays are shot from the camera (which is in a fixed position for this tutorial) through an imaginary grid of pixels into the scene, where they intersect with 3D objects (in this case spheres). For each pixel in the image, we will generate one camera ray (also called primary rays, view rays or eye rays) and follow or trace it into the scene. For camera rays, the ray origin is the camera position and the ray direction is the vector connecting the camera and the pixel on the screen.

      Source: Wikipedia

      The OpenCL code for generating a camera ray:

      struct Ray createCamRay(constint x_coord, constint y_coord, constint width, constint height){

      float fx = (float)x_coord / (float)width; /* convert int in range [0 - width] to float in range [0-1] */
      float fy = (float)y_coord / (float)height; /* convert int in range [0 - height] to float in range [0-1] */

      /* calculate aspect ratio */
      float aspect_ratio = (float)(width) / (float)(height);
      float fx2 = (fx - 0.5f) * aspect_ratio;
      float fy2 = fy - 0.5f;

      /* determine position of pixel on screen */
      float3 pixel_pos = (float3)(fx2, -fy2, 0.0f);

      /* create camera ray*/
      struct Ray ray;
      ray.origin = (float3)(0.0f, 0.0f, 40.0f); /* fixed camera position */
      ray.dir = normalize(pixel_pos - ray.origin);

      return ray;

      Ray-sphere intersection

      To find the intersection of a ray with a sphere, we need the parametric equation of a line, which denotes the distance from the ray origin to the intersection point along the ray direction with the parameter "t"

      intersection point = ray origin + ray direction * t

      The equation of a sphere follows from the Pythagorean theorem in 3D (all points on the surface of a sphere are located at a distance of radius r from its center): 

      (sphere surface point - sphere center)2 = radius2 

      Combining both equations 

      (ray origin + ray direction * t)2 = radius2

      and expanding the equation in a quadratic equation of form ax2 + bx + c = 0 where 

      • a = (ray direction) . (ray direction)  
      • b = 2 * (ray direction) . (ray origin to sphere center) 
      • c = (ray origin to sphere center) . (ray origin to sphere center) - radius2 
      yields solutions for t (the distance to the point where the ray intersects the sphere) given by the quadratic formula−b ± √ b2− 4ac / 2a (where b2 - 4acis called the discriminant).

      There can be zero (ray misses sphere), one (ray grazes sphere at one point) or two solutions (ray fully intersects sphere at two points). The distance t can be positive (intersection in front of ray origin) or negative (intersection behind ray origin). The details of the mathematical derivation are explained in this Scratch-a-Pixel article.

      The ray-sphere intersection algorithm is optimised by omitting the "a" coefficient in the quadratic formula, because its value is the dot product of the normalised ray direction with itself which equals 1. Taking the square root of the discriminant (an expensive function) can only be performed when the discriminant is non-negative.

      bool intersect_sphere(conststruct Sphere* sphere, conststruct Ray* ray, float* t)
      float3 rayToCenter = sphere->pos - ray->origin;

      /* calculate coefficients a, b, c from quadratic equation */

      /* float a = dot(ray->dir, ray->dir); // ray direction is normalised, dotproduct simplifies to 1 */
      float b = dot(rayToCenter, ray->dir);
      float c = dot(rayToCenter, rayToCenter) - sphere->radius*sphere->radius;
      float disc = b * b - c; /* discriminant of quadratic formula */

      /* solve for t (distance to hitpoint along ray) */

      if (disc < 0.0f) return false;
      else *t = b - sqrt(disc);

      if (*t < 0.0f){
      *t = b + sqrt(disc);
      if (*t < 0.0f) return false;

      elsereturn true;

      Scene initialisation

      For simplicity, in this first part of the tutorial the scene will be initialised on the device in the kernel function (in the second part the scene will be initialised on the host and passed to OpenCL which is more flexible and memory efficient, but also requires to be more careful with regards to memory alignment and the use of memory address spaces). Every work item will thus have a local copy of the scene (in this case one sphere).

      __kernel void render_kernel(__global float3* output, int width, int height)
      constint work_item_id = get_global_id(0); /* the unique global id of the work item for the current pixel */
      int x_coord = work_item_id % width; /* x-coordinate of the pixel */
      int y_coord = work_item_id / width; /* y-coordinate of the pixel */

      /* create a camera ray */
      struct Ray camray = createCamRay(x_coord, y_coord, width, height);

      /* create and initialise a sphere */
      struct Sphere sphere1;
      sphere1.radius = 0.4f;
      sphere1.pos = (float3)(0.0f, 0.0f, 3.0f);
      sphere1.color = (float3)(0.9f, 0.3f, 0.0f);

      /* intersect ray with sphere */
      float t = 1e20;
      intersect_sphere(&sphere1, &camray, &t);

      /* if ray misses sphere, return background colour
      background colour is a blue-ish gradient dependent on image height */
      if (t > 1e19){
      output[work_item_id] = (float3)(fy * 0.1f, fy * 0.3f, 0.3f);

      /* if ray hits the sphere, it will return the sphere colour*/
      output[work_item_id] = sphere1.color;

      Running the ray tracer 

      Now we've got everything we need to start ray tracing! Let's begin with a plain colour sphere. When the ray misses the sphere, the background colour is returned:

      A more interesting sphere with cosine-weighted colours, giving the impression of front lighting.

      To achieve this effect we need to calculate the angle between the ray hitting the sphere surface and the normal at that point. The sphere normal at a specific intersection point on the surface is just the normalised vector (with unit length) going from the sphere center to that intersection point.

              float3 hitpoint = camray.origin + camray.dir * t;
      float3 normal = normalize(hitpoint - sphere1.pos);
      float cosine_factor = dot(normal, camray.dir) * -1.0f;

      output[work_item_id] = sphere1.color * cosine_factor;

      Adding some stripe pattern by multiplying the colour with the sine of the height:

      Screen-door effect using sine functions for both x and y-directions

      Showing the surface normals (calculated in the code snippet above) as colours:

      Source code


      Download demo (works on AMD, Nvidia and Intel)

      The executable demo will render the above images.


      Part 2: Path tracing spheres

      Very quick overview of ray tracing and path tracing

      The following section covers the background of the ray tracing process in a very simplified way, but should be sufficient to understand the code in this tutorial. Scratch-a-Pixel provides a much more detailed explanation of ray tracing.  

      Ray tracing is a general term that encompasses ray casting, Whitted ray tracing, distribution ray tracing and path tracing. So far, we have only traced rays from the camera (so called "camera rays", "eye rays" or "primary rays") into the scene, a process called ray casting, resulting in plainly coloured images with no lighting. In order to achieve effects like shadows and reflections, new rays must be generated at the points where the camera rays intersect with the scene. These secondary rays can be shadow rays, reflection rays, transmission rays (for refractions), ambient occlusion rays or diffuse interreflection rays (for indirect lighting/global illumination). For example, shadow rays used for direct lighting are generated to point directly towards a light source while reflection rays are pointed in (or near) the direction of the reflection vector. For now we will skip direct lighting to generate shadows and go straight to path tracing, which is strangely enough easier to code, creates more realistic and prettier pictures and is just more fun.

      In (plain) path tracing, rays are shot from the camera and bounce off the surface of scene objects in a random direction (like a high-energy bouncing ball), forming a chain of random rays connected together into a path. If the path hits a light emitting object such as a light source, it will return a colour which depends on the surface colours of all the objects encountered so far along the path, the colour of the light emitters, the angles at which the path hit a surface and the angles at which the path bounced off a surface. These ideas form the essence of the "rendering equation", proposed in a paper with the same name by Jim Kajiya in 1986.

      Since the directions of the rays in a path are generated randomly, some paths will hit a light source while others won't, resulting in noise ("variance" in statistics due to random sampling). The noise can be reduced by shooting many random paths per pixel (= taking many samples) and averaging the results.

      Implementation of (plain) path tracing in OpenCL       

      The code for the path tracer is based on smallpt from Kevin Beason and is largely the same as the ray tracer code from part 1 of this tutorial, with some important differences on the host side:

      - the scene is initialised on the host (CPU) side, which requires a host version of the Sphere struct. Correct memory alignment in the host struct is very important to avoid shifting of values and wrongly initialised variables in the OpenCL struct, especially when  using OpenCL's built-in data types such as float3 and float4. If necessary, the struct should be padded with dummy variables to ensure memory alignment (the total size of the struct must be a multiple of the size of float4).

      struct Sphere
      cl_float radius;
      cl_float dummy1;
      cl_float dummy2;
      cl_float dummy3;
      cl_float3 position;
      cl_float3 color;
      cl_float3 emission;

      - the scene (an array of spheres) is copied from the host to the OpenCL device into global memory (using CL_MEM_READ_WRITE) or constant memory (using CL_MEM_READ_ONLY

      // initialise scene
      constint sphere_count = 9;
      Sphere cpu_spheres[sphere_count];

      // Create buffers on the OpenCL device for the image and the scene
      cl_output = Buffer(context, CL_MEM_WRITE_ONLY, image_width * image_height * sizeof(cl_float3));
      cl_spheres = Buffer(context, CL_MEM_READ_ONLY, sphere_count * sizeof(Sphere));
      queue.enqueueWriteBuffer(cl_spheres, CL_TRUE, 0, sphere_count * sizeof(Sphere), cpu_spheres);

      - explicit memory management: once the scene is on the device, its pointer can be passed on to other device functions preceded by the keyword "__global" or "__constant".

      - the host code automatically determines the local size of the kernel work group (the number of work items or "threads" per work group) by calling the OpenCL function kernel.getWorkGroupInfo(device)

      The actual path tracing function

      - iterative path tracing function: since OpenCL does not support recursion, the trace() function traces paths iteratively (instead of recursively) using a loop with a fixed number of bounces (iterations), representing path depth.

      - each path starts off with an "accumulated colour" initialised to black and a "mask colour" initialised to pure white. The mask colour "collects" surface colours along its path by multiplication. The accumulated colour accumulates light from emitters along its path by adding emitted colours multiplied by the mask colour.

      - generating random ray directions: new rays start at the hitpoint and get shot in a random direction by sampling a random point on the hemisphere above the surface hitpoint. For each new ray, a local orthogonal uvw-coordinate system and two random numbers are generated: one to pick a random value on the horizon for the azimuth, the other for the altitude (with the zenith being the highest point)

      - diffuse materials: the code for this tutorial only supports diffuse materials, which reflect incident light almost uniformly in all directions (in the hemisphere above the hitpoint)

      - cosine-weighted importance sampling: because diffuse light reflection is not truly uniform, the light contribution from rays that are pointing away from the surface plane and closer to the surface normal is greater. Cosine-weighted importance sampling favours rays that are pointing away from the surface plane by multiplying their colour with the cosine of the angle between the surface normal and the ray direction.

      - while ray tracing can get away with tracing only one ray per pixel to render a good image (more are needed for anti-aliasing and blurry effects like depth-of-field and glossy reflections), the inherently noisy nature of path tracing requires tracing of many paths per pixel (samples per pixel) and averaging the results to reduce noise to an acceptable level.

      float3 trace(__constant Sphere* spheres, const Ray* camray, constint sphere_count, constint* seed0, constint* seed1){

      Ray ray = *camray;

      float3 accum_color = (float3)(0.0f, 0.0f, 0.0f);
      float3 mask = (float3)(1.0f, 1.0f, 1.0f);

      for (int bounces = 0; bounces < 8; bounces++){

      float t; /* distance to intersection */
      int hitsphere_id = 0; /* index of intersected sphere */

      /* if ray misses scene, return background colour */
      if (!intersect_scene(spheres, &ray, &t, &hitsphere_id, sphere_count))
      return accum_color += mask * (float3)(0.15f, 0.15f, 0.25f);

      /* else, we've got a hit! Fetch the closest hit sphere */
      Sphere hitsphere = spheres[hitsphere_id]; /* version with local copy of sphere */

      /* compute the hitpoint using the ray equation */
      float3 hitpoint = ray.origin + ray.dir * t;

      /* compute the surface normal and flip it if necessary to face the incoming ray */
      float3 normal = normalize(hitpoint - hitsphere.pos);
      float3 normal_facing = dot(normal, ray.dir) < 0.0f ? normal : normal * (-1.0f);

      /* compute two random numbers to pick a random point on the hemisphere above the hitpoint*/
      float rand1 = 2.0f * PI * get_random(seed0, seed1);
      float rand2 = get_random(seed0, seed1);
      float rand2s = sqrt(rand2);

      /* create a local orthogonal coordinate frame centered at the hitpoint */
      float3 w = normal_facing;
      float3 axis = fabs(w.x) > 0.1f ? (float3)(0.0f, 1.0f, 0.0f) : (float3)(1.0f, 0.0f, 0.0f);
      float3 u = normalize(cross(axis, w));
      float3 v = cross(w, u);

      /* use the coordinte frame and random numbers to compute the next ray direction */
      float3 newdir = normalize(u * cos(rand1)*rand2s + v*sin(rand1)*rand2s + w*sqrt(1.0f - rand2));

      /* add a very small offset to the hitpoint to prevent self intersection */
      ray.origin = hitpoint + normal_facing * EPSILON;
      ray.dir = newdir;

      /* add the colour and light contributions to the accumulated colour */
      accum_color += mask * hitsphere.emission;

      /* the mask colour picks up surface colours at each bounce */
      mask *= hitsphere.color;

      /* perform cosine-weighted importance sampling for diffuse surfaces*/
      mask *= dot(newdir, normal_facing);

      return accum_color;

      A screenshot made with the code above (also see the screenshot at the top of this post). Notice the colour bleeding (bounced colour reflected from the floor onto the spheres), soft shadows and lighting coming from the background.

      Source code


      Downloadable demo (for AMD, Nvidia and Intel platforms, Windows only)


      Useful resources

      - Scratch-a-pixel is an excellent free online resource to learn about the theory behind ray tracing and path tracing. Many code samples (in C++) are also provided. This article gives a great introduction to global illumination and path tracing.

      - smallpt by Kevin Beason is a great little CPU path tracer in 100 lines code. It of formed the inspiration for the Cornell box scene and for many parts of the OpenCL code 

      Up next

      The next tutorial will cover the implementation of an interactive OpenGL viewport with a progressively refining image and an interactive camera with anti-aliasing and depth-of-field.

      Wanted: GPU rendering developers

      I'm working for an international company with very large (<Trump voice>"YUUUUUGE"<\Trump voice>) industry partners.

      We are currently looking for excellent developers with experience in GPU rendering (path tracing) for a new project.

      Our ideal candidates have either a:
      • Bachelor in Computer Science, Computer/Software Engineering or Physics with a minimum of 2 years of work experience in a relevant field, or
      • Master in Computer Science, Computer/Software Engineering or Physics, or
      • PhD in a relevant field
      and a strong interest in physically based rendering and ray tracing.

      Self-taught programmers are encouraged to apply if they meet the following requirements:
      • you breathe rendering and have Monte Carlo simulations running through your blood
      • you have a copy of PBRT (www.pbrt.org, version 3 was released just last week) on your bedside table
      • provable experience working with open source rendering frameworks such as PBRT, LuxRender, Cycles, AMD RadeonRays or with a commercial renderer will earn you extra brownie points
      • 5+ years of experience with C++
      • experience with CUDA or OpenCL
      • experience with version control systems and working on large projects
      • proven rendering track record (publications, Github projects, blog)

      Other requirements:
      • insatiable hunger to innovate
      • a "can do" attitude
      • strong work ethic and focus on results
      • continuous self-learner
      • work well in a team
      • work independently and able to take direction
      • ability to communicate effectively
      • comfortable speaking English
      • own initiatives and original ideas are highly encouraged
      • willing to relocate to New Zealand

      What we offer:
      • unique location in one of the most beautiful and greenest countries in the world
      • be part of a small, high-performance team 
      • competitive salary
      • jandals, marmite and hokey pokey ice cream

      For more information, contact me at sam.lapere@live.be

      If you are interested, send your CV and cover letter to sam.lapere@live.be. Applications will close on 16 December or when we find the right people. (update: spots are filling up quickly so we advanced the closing date with five days)

      OpenCL path tracing tutorial 3: OpenGL viewport, interactive camera and defocus blur

      Just a link to the source code on Github for now, I'll update this post with a more detailed description when I find a bit more time:

       Part 1Setting up an OpenGL window


      Part 2Adding an interactive camera, depth of field and progressive rendering


      Thanks to Erich Loftis and Brandon Miles for useful tips on improving the generation of random numbers in OpenCL to avoid the distracting artefacts (showing up as a sawtooth pattern) when using defocus blur (still not perfect but much better than before).

      The next tutorial will cover rendering of triangles and triangle meshes.

      Web developer wanted

      Our project is making great strides and we're currently looking for a top notch web developer to join our team.

      Candidates for this role should have:

      - a Bachelor of Computer Science 
      - a minimum of 4 years of working experience with front-end and back-end web development (e.g. Node.js/npm, Rails, Go, Django, Ember.js, Angular.js, React.js, Bootstrap, jQuery)
      - UI design skills are a plus
      - an unbounded passion for and hands-on experience with real-time and offline 3D graphics
      - creative and original problem solving skills
      - unrelentless hunger to learn more and become an expert in your field
      - ability to work independently
      - be highly efficient, motivated, perfectionist and driven with heaps of initiative and
      - New Zealand residency or be keen on moving to NZ (we consider remote contractor work if you are one of a kind)

       Send your cover letter and CV with a link to your portfolio or Github page to sam.lapere@live.be
      Applications will close on 21 March.

      Virtual reality

      Cycles, the fastest GPU renderer thanks to new denoising algorithms

      Cycles is Blender's native CPU/GPU renderer, originally created in early 2011 by Brecht van Lommel (who left the Blender Institute in 2014 to work on Solid Angle's Arnold, which was acquired last year by the innovation crushing Autodesk Corp.). In the past six years, it has slowly but steadily become a fully featured production ready renderer including motion blur, hair/fur rendering, OpenVDB volume rendering, Disney's OpenSubDiv and Principled PBR shader, GGX microfacet distribution, AOVs (arbitrary output volumes or render passes), filmic tonemapping and support for Alembic scene importing.

      A video showing the stunning realism that can be achieved with Cycles:

      Even though Cycles has been open source since the beginning, the Blender Institute decided in August 2013 to change the license for the Cycles source code from a restrictive GPL license to a permissive Apache 2.0 license, which allows Cycles to be integrated into commercial projects.

      Although Cycles started out as an unbiased renderer, it quickly adopted many biased tricks to drastically cut down rendertimes such as clamping the bounces for different types of rays, blurry filters for glossy surfaces and switching over to shooting ambient occlusion rays after a certain number of bounces is reached.  

      In recent months, Lukas Stockner, one of Cycles' developers (who was also responsible for adding light portals and IES light profile support) implemented a few remarkable noise reduction algorithms based on very recent research, which will certainly turn many rendering heads. Two features in particular have been added that reduce rendertimes by 8 times on average: scramble distance (which takes the randomness out of sampling and traces rays in a fully coherent way) and a noise filtering algorithm based on "weigthed local regression". The noise filter has been in development for over a year and has been available in experimental Cycles builds for beta-testing. It's currently under final review and is ready to be released into the Cycles master branch any day. The Blender community is going wild and for good reason. The new denoiser delivers exceptional results, preserving details in textures at very low sample rates and rendertimes:

      Full HD render (1920x1080 resolution). Rendertime: 1m 24s
      Fully denoised at 50 samples on a single GTX 1070.
      Image from the Blender Artists forum
      Final denoised and colour corrected render, 1m25s (from BlenderArtists forum)
      The new version of Cycles with built-in denoising will run on both CPU and GPUs from Nvidia and AMD. Experimental builds for CUDA and OpenCL are available here.

      Experimental OpenCL/CUDA build Release notes:
      • OpenCL & Cuda GPU Denoise System (this is Lukas' latest denoise code system) 
      • Cuda & OpenCL supported
      • GPU Denoise Multi-GPU Support (even in viewport, definitely works for Cuda but not tested with multiple OpenCL GPUs)
      • Scramble Distance added for Sobol and multi-jitter (works on CPU & GPU) Also added to supported features render tab
      • Blue Noise Dithered Sobol with scramble distance
      • Thread Divergence Sort Reduction patch (gives 30% speedup in classroom and 8% in Barcelona scene)
      More information on the denoising algorithm can be found in this thread on the Blender Artists forum and Lukas Stockner's Wiki page:

      Experimental Cycles denoising build thread


      With this groundbreaking denoiser, Cycles leapfrogs all other GPU renderers, and will soon be making the dream of ultrafast photoreal rendering happen for anyone.  

      Practical light field rendering tutorial with Cycles

      This week Google announced "Seurat", a novel surface lightfield rendering technology which would enable "real-time cinema-quality, photorealistic graphics" on mobile VR devices, developed in collaboration with ILMxLab:

      The technology captures all light rays in a scene by pre-rendering it from many different viewpoints. During runtime, entirely new viewpoints are created by interpolating those viewpoints on-the-fly resulting in photoreal reflections and lighting in real-time (http://www.roadtovr.com/googles-seurat-surface-light-field-tech-graphical-breakthrough-mobile-vr/).

      At almost the same time, Disney released a paper called "Real-time rendering with compressed animated light fields", demonstrating the feasibility of rendering a Pixar quality 3D movie in real-time where the viewer can actually be part of the scene and walk in between scene elements or characters (according to a predetermined camera path):

      Light field rendering in itself is not a new technique and has actually been around for more than 20 years, but has only recently become a viable rendering technique. The first paper was released at Siggraph 1996 ("Light field rendering" by Mark Levoy and Pat Hanrahan) and the method has since been incrementally improved by others. The Stanford university compiled an entire archive of light fields to accompany the Siggraph paper from 1996 which can be found at http://graphics.stanford.edu/software/lightpack/lifs.html. A more up-to-date archive of photography-based light fields can be found at http://lightfield.stanford.edu/lfs.html

      One of the first movies that showed a practical use for light fields is The Matrix from 1999, where an array of cameras firing at the same time (or in rapid succession) made it possible to pan around an actor to create a super slow motion effect ("bullet time"):

      Bullet time in The Matrix (1999)

      Rendering the light field

      Instead of attempting to explain the theory behind light fields (for which there are plenty of excellent online sources), the main focus of this post is to show how to quickly get started with rendering a synthetic light field using Blender Cycles and some open-source plug-ins. If you're interested in a crash course on light fields, check out Joan Charmant's video tutorial below, which explains the basics of implementing a light field renderer:

      The following video demonstrates light fields rendered with Cycles:

      Rendering a light field is actually surprisingly easy with Blender's Cycles and doesn't require much technical expertise (besides knowing how to build the plugins). For this tutorial, we'll use a couple of open source plug-ins:

      1) The first one is the light field camera grid add-on for Blender made by Katrin Honauer and Ole Johanssen from the Heidelberg University in Germany: 

      This plug-in sets up a camera grid in Blender and renders the scene from each camera using the Cycles path tracing engine. Good results can be obtained with a grid of 17 by 17 cameras with a distance of 10 cm between neighbouring cameras. For high quality, a 33-by-33 camera grid with an inter-camera distance of 5 cm is recommended.

      3-by-3 camera grid with their overlapping frustrums

      2) The second tool is the light field encoder and WebGL based light field viewer, created by Michal Polko, found at https://github.com/mpk/lightfield (build instructions are included in the readme file).

      This plugin takes in all the images generated by the first plug-in and compresses them by keeping some keyframes and encoding the delta in the remaining intermediary frames. The viewer is WebGL based and makes use of virtual texturing (similar to Carmack's mega-textures) for fast, on-the-fly reconstruction of new viewpoints from pre-rendered viewpoints (via hardware accelerated bilinear interpolation on the GPU).

      Results and Live Demo

      A live online demo of the light field with the dragon can be seen here: 

      You can change the viewpoint (within the limits of the original camera grid) and refocus the image in real-time by clicking on the image.  

      I rendered the Stanford dragon using a 17 by 17 camera grid and distance of 5 cm between adjacent cameras. The light field was created by rendering the scene from 289 (17x17) different camera viewpoints, which took about 6 minutes in total (about 1 to 2 seconds rendertime per 512x512 image on a good GPU). The 289 renders are then highly compressed (for this scene, the 107 MB large batch of 289 images was compressed down to only 3 MB!). 

      A depth map is also created at the same time an enables on-the-fly refocusing of the image, by interpolating information from several images, 

      A later tutorial will add a bit more freedom to the camera, allowing for rotation and zooming.

      Beta testers wanted

      In the past several months, we have been developing a novel ultrafast photorealistic rendering application and we're almost ready to unleash our beast onto the world. In our humble opinion, we think our innovative, pioneering and revolutionary tech is going to be groundbreaking, earth-shaking, paradigm-shifting, status quo defying, industry-disrupting and transmogrifying, and be greater than the Second Coming of Sliced Bread! In short, we think it's going to be rather good.

      We're currently looking for some outstanding beta-testers who have extensive experience with one of the following 3d modeling packages:

      - 3ds Max
      - Maya
      - Cinema 4D
      - Modo
      - Blender
      - LightWave 3D
      - SketchUp

      and a ray tracing based rendering engine like V-Ray, Corona, Cycles or similar.

      The perfect candidate has also won or been nominated for a Montgomery Burns Award for Outstanding Achievement in the Field of Excellence.

      To apply, send an email with a link to your artist portfolio to sam.lapere@live.be (people with low frustration tolerance need not apply).

      Towards real-time path tracing: An Efficient Denoising Algorithm for Global Illumination

      July is a great month for rendering enthusiasts: there's of course Siggraph, but the most exciting conference is High Performance Graphics, which focuses on (real-time) ray tracing. One of the more interesting sounding papers is titled: "Towards real-time path tracing: An Efficient Denoising Algorithm for Global Illumination" by Mara, McGuire, Bitterli and Jarosz, which was released a couple of days ago. The paper, video and source code can be found at

      We propose a hybrid ray-tracing/rasterization strategy for realtime rendering enabled by a fast new denoising method. We factor global illumination into direct light at rasterized primary surfaces and two indirect lighting terms, each estimated with one pathtraced sample per pixel. Our factorization enables efficient (biased) reconstruction by denoising light without blurring materials. We demonstrate denoising in under 10 ms per 1280×720 frame, compare results against the leading offline denoising methods, and include a supplement with source code, video, and data.

      While the premise of the paper sounds incredibly exciting, the results are disappointing. The denoising filter does a great job filtering almost all the noise (apart from some noise which is still visible in reflections), but at the same it kills pretty much all the realism that path tracing is famous for, producing flat and lifeless images. Even the first Crysis from 10 years ago (the first game with SSAO) looks distinctly better. I don't think applying such aggressive filtering algorithms to a path tracer will convince game developers to make the switch to path traced rendering anytime soon. A comparison with ground truth reference images (rendered to 5000 samples or more) is also lacking from some reason. 

      At the same conference, a very similar paper will be presented titled "Spatiotemporal Variance-Guided Filtering: Real-Time Reconstruction for Path-Traced Global Illumination". 

      We introduce a reconstruction algorithm that generates a temporally stable sequence of images from one path-per-pixel global illumination. To handle such noisy input, we use temporal accumulation to increase the effective sample count and spatiotemporal luminance variance estimates to drive a hierarchical, image-space wavelet filter. This hierarchy allows us to distinguish between noise and detail at multiple scales using luminance variance.  
      Physically-based light transport is a longstanding goal for real-time computer graphics. While modern games use limited forms of ray tracing, physically-based Monte Carlo global illumination does not meet their 30 Hz minimal performance requirement. Looking ahead to fully dynamic, real-time path tracing, we expect this to only be feasible using a small number of paths per pixel. As such, image reconstruction using low sample counts is key to bringing path tracing to real-time. When compared to prior interactive reconstruction filters, our work gives approximately 10x more temporally stable results, matched references images 5-47% better (according to SSIM), and runs in just 10 ms (+/- 15%) on modern graphics hardware at 1920x1080 resolution.
      It's going to be interesting to see if the method in this paper produces more convincing results that the other paper. Either way HPG has a bunch more interesting papers which are worth keeping an eye on.

      Shiny Toy pathmarcher on Shadertoy

      Excellent computer graphics developers wanted

      Our team is expanding. We're currently looking for a developer with the following skills and experience:

      - Bachelor, Master or PhD in Computer Science or similar field
      - Specialisation in computer graphics
      - (Constructive) Solid experience with parametric and non-parametric 3D modelling algorithms
      - Strong mathematical background (especially linear algebra + multivariable calculus)
      - Very good command of C++11 and OpenGL
      - Web development experience desirable
      - Love for learning cutting edge experimental languages and frameworks
      - Flexible, can-do attitude
      - Perfectionist attitude and obsessed with quality
      - Be part of a very fast moving team
      - Keen to move, live and work in New Zealand

      If you think you fit the above requirements, send your CV to sam.lapere@live.be