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Team Member

1. Kevin Pham
2. Jay Zha
3. Peiying Yang

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Assignment 1 - Select and Assess

FileCompressor

Environment:
System: Windows 10
CPU: i5-6400 2.70GHz
RAM: 8GB 2444Hz
Video card: NVIDIA GTX 1060 3GB

The size of file before compressing is 128MB After:65.2MB (Depend on the file)

Here is the major code to compress a file :

The following image shows that the CompressCore function takes 99.55% of the time to compress a 128MB file.

As the size of file increase, the time that this program spend on compressing a file will increase.

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Assignment 1 Ray Tracing

Environment:
System: Windows 10
CPU: i7-6800K 3.40GHz
RAM: 16GB 2133Hz
Video card: NVIDIA GTX 650

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Assignment 1 Ray Tracing

Environment:
System: Windows 10
CPU: i7-6700HQ 2.60GHz
RAM: 16GB 21337Hz
Video card: NVIDIA GTX 1060 6GB

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Program: raytracing.cpp from scratchpixel.com tutorial on basic raytracing. website along with source code location: [1]

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Compilation

Unix -

      g++ -O2 -o raytrace raytracer.cpp
      raytrace

OSX -

      clang++ -O2 -o raytrace raytracer.cpp
      raytrace

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From the compilation it creates this ppm file

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Running the Flat Profile: gprof -p -b raytrace > raytrace.flt

gives us this :

Flat profile:

Each sample counts as 0.01 seconds.

 %   cumulative   self              self     total           
time   seconds   seconds    calls  us/call  us/call  name    
87.76      0.43     0.43   307200     1.40     1.40  trace(Vec3<float> const&, Vec3<float> const&, std::vector<Sphere, std::allocator<Sphere> > const&, int const&)
12.24      0.49     0.06                             render(std::vector<Sphere, std::allocator<Sphere> > const&)
 0.00      0.49     0.00        4     0.00     0.00  std::vector<Sphere, std::allocator<Sphere> >::_M_insert_aux(__gnu_cxx::__normal_iterator<Sphere*, std::vector<Sphere, std::allocator<Sphere> > >, Sphere const&)
 0.00      0.49     0.00        1     0.00     0.00  _GLOBAL__sub_I__Z3mixRKfS0_S0_

Observation:

From looking at the result of the flat profile we can see that the trace and the render functions take the most time to run.

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Running the call graph: gprof -q -b raytrace > raytrace.clg

Observation: From looking at both the flat profile and the call graph we can see that both the trace and the render functions are the hot spots of the program.

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Possible Parallelizations:

When looking at both the Trace Function and the render function.

Render Function :

void render(const std::vector<Sphere> &spheres) {

   unsigned width = 640, height = 480;
   Vec3f *image = new Vec3f[width * height], *pixel = image;
   float invWidth = 1 / float(width), invHeight = 1 / float(height);
   float fov = 30, aspectratio = width / float(height);
   float angle = tan(M_PI * 0.5 * fov / 180.);
   // Trace rays
   for (unsigned y = 0; y < height; ++y) {    Possible Parallelization  spot
       for (unsigned x = 0; x < width; ++x, ++pixel) {
           float xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;
           float yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;
           Vec3f raydir(xx, yy, -1);
           raydir.normalize();
           *pixel = trace(Vec3f(0), raydir, spheres, 0);
       }
   }
   // Save result to a PPM image (keep these flags if you compile under Windows)
   std::ofstream ofs("./untitled.ppm", std::ios::out | std::ios::binary);
   ofs << "P6\n" << width << " " << height << "\n255\n";
   for (unsigned i = 0; i < width * height; ++i) {
       ofs << (unsigned char)(std::min(float(1), image[i].x) * 255) <<
              (unsigned char)(std::min(float(1), image[i].y) * 255) <<
              (unsigned char)(std::min(float(1), image[i].z) * 255);
   }
   ofs.close();
   delete [] image;

}

In the render function it has a runtime speed of T(n) = o^2.

Trace Function:

Vec3f trace(

   const Vec3f &rayorig,
   const Vec3f &raydir,
   const std::vector<Sphere> &spheres,
   const int &depth)

{

   //if (raydir.length() != 1) std::cerr << "Error " << raydir << std::endl;
   float tnear = INFINITY;
   const Sphere* sphere = NULL;
   // find intersection of this ray with the sphere in the scene
   for (unsigned i = 0; i < spheres.size(); ++i) {
       float t0 = INFINITY, t1 = INFINITY;
       if (spheres[i].intersect(rayorig, raydir, t0, t1)) {
           if (t0 < 0) t0 = t1;
           if (t0 < tnear) {
               tnear = t0;
               sphere = &spheres[i];
           }
       }
   }
   // if there's no intersection return black or background color
   if (!sphere) return Vec3f(2);
   Vec3f surfaceColor = 0; // color of the ray/surfaceof the object intersected by the ray
   Vec3f phit = rayorig + raydir * tnear; // point of intersection
   Vec3f nhit = phit - sphere->center; // normal at the intersection point
   nhit.normalize(); // normalize normal direction
   // If the normal and the view direction are not opposite to each other
   // reverse the normal direction. That also means we are inside the sphere so set
   // the inside bool to true. Finally reverse the sign of IdotN which we want
   // positive.
   float bias = 1e-4; // add some bias to the point from which we will be tracing
   bool inside = false;
   if (raydir.dot(nhit) > 0) nhit = -nhit, inside = true;
   if ((sphere->transparency > 0 || sphere->reflection > 0) && depth < MAX_RAY_DEPTH) {
       float facingratio = -raydir.dot(nhit);
       // change the mix value to tweak the effect
       float fresneleffect = mix(pow(1 - facingratio, 3), 1, 0.1);
       // compute reflection direction (not need to normalize because all vectors
       // are already normalized)
       Vec3f refldir = raydir - nhit * 2 * raydir.dot(nhit);
       refldir.normalize();
       Vec3f reflection = trace(phit + nhit * bias, refldir, spheres, depth + 1);
       Vec3f refraction = 0;
       // if the sphere is also transparent compute refraction ray (transmission)
       if (sphere->transparency) {
           float ior = 1.1, eta = (inside) ? ior : 1 / ior; // are we inside or outside the surface?
           float cosi = -nhit.dot(raydir);
           float k = 1 - eta * eta * (1 - cosi * cosi);
           Vec3f refrdir = raydir * eta + nhit * (eta *  cosi - sqrt(k));
           refrdir.normalize();
           refraction = trace(phit - nhit * bias, refrdir, spheres, depth + 1);
       }
       // the result is a mix of reflection and refraction (if the sphere is transparent)
       surfaceColor = (
           reflection * fresneleffect +
           refraction * (1 - fresneleffect) * sphere->transparency) * sphere->surfaceColor;
   }
   else {
       // it's a diffuse object, no need to raytrace any further
       for (unsigned i = 0; i < spheres.size(); ++i) {
           if (spheres[i].emissionColor.x > 0) {
               // this is a light
               Vec3f transmission = 1;
               Vec3f lightDirection = spheres[i].center - phit;
               lightDirection.normalize();
               for (unsigned j = 0; j < spheres.size(); ++j) {
                   if (i != j) {
                       float t0, t1;
                       if (spheres[j].intersect(phit + nhit * bias, lightDirection, t0, t1)) {
                           transmission = 0;
                           break;
                       }
                   }
               }
               surfaceColor += sphere->surfaceColor * transmission *
               std::max(float(0), nhit.dot(lightDirection)) * spheres[i].emissionColor;
           }
       }
   }
   
   return surfaceColor + sphere->emissionColor;

}

Within this trace function the possible parallelization points would be here :

{

  for (unsigned i = 0; i < spheres.size(); ++i) {
       float t0 = INFINITY, t1 = INFINITY;
       if (spheres[i].intersect(rayorig, raydir, t0, t1)) {
           if (t0 < 0) t0 = t1;
           if (t0 < tnear) {
               tnear = t0;
               sphere = &spheres[i];
           }
       }
   }

} {

   else {
       // it's a diffuse object, no need to raytrace any further
       for (unsigned i = 0; i < spheres.size(); ++i) {
           if (spheres[i].emissionColor.x > 0) {
               // this is a light
               Vec3f transmission = 1;
               Vec3f lightDirection = spheres[i].center - phit;
               lightDirection.normalize();
               for (unsigned j = 0; j < spheres.size(); ++j) {
                   if (i != j) {
                       float t0, t1;
                       if (spheres[j].intersect(phit + nhit * bias, lightDirection, t0, t1)) {
                           transmission = 0;
                           break;
                       }
                   }
               }
               surfaceColor += sphere->surfaceColor * transmission *
               std::max(float(0), nhit.dot(lightDirection)) * spheres[i].emissionColor;
           }
       }
   }
   
   return surfaceColor + sphere->emissionColor;

}

In this function it has a runtime speed of T(n) = O^2.