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Ray Tracer

Team Members

1. Michael Wang, (responsibility tbd)
2. Bruno Pereira, (responsibility tbd)
3. ...

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Progress

Assignment 1

Bruno

For assignment 1 I looked into finding a simple Ray Tracer that could be easily understood by someone with no image processing background and benefit from parallelization.

I found ray tracer that matched the criteria I was looking for at http://scratchapixel.com/assets/Uploads/Lesson001/Source%20Code/raytracer.cpp

Looking into Big O notation I believe this program falls under [f(n) = n ^ 2]

I profiled the ray tracer by modifying trace depths, as seen below:

Depth of 70

Each sample counts as 0.01 seconds.

 %   cumulative   self              self     total
time   seconds   seconds    calls  ms/call  ms/call  name
99.99    517.97   517.97   307200     1.69     1.69  Vec3<float> trace<float>(Vec3<float> const&, Vec3<float> const&, std::vector<Sphere<float>*, std::allocator<Sphere<float>*> > const&, int const&)
 0.01    518.00     0.03                             void render<float>(std::vector<Sphere<float>*, std::allocator<Sphere<float>*> > const&)
 0.00    518.00     0.00        1     0.00     0.00  _GLOBAL__sub_I_main

The program spends nearly 100% of all processing with in its Vec3 trace method, this is a recursive method.

Vec3<T> trace(const Vec3<T> &rayorig, const Vec3<T> &raydir,const std::vector<Sphere<T> *> &spheres, const int &depth)

.......
.......

	if ((sphere->transparency > 0 || sphere->reflection > 0) && depth < MAX_RAY_DEPTH) {

		T facingratio = -raydir.dot(nhit);

		// change the mix value to tweak the effect

		T fresneleffect = mix<T>(pow(1 - facingratio, 3), 1, 0.1);

		Vec3<T> refldir = raydir - nhit * 2 * raydir.dot(nhit);

		refldir.normalize();

		Vec3<T> reflection = trace(phit + nhit * bias, refldir, spheres, depth + 1);

		Vec3<T> refraction = 0;

		if (sphere->transparency) {

			T ior = 1.1, eta = (inside) ? ior : 1 / ior; 

			T cosi = -nhit.dot(raydir);

			T k = 1 - eta * eta * (1 - cosi * cosi);

			Vec3<T> refrdir = raydir * eta + nhit * (eta *  cosi - sqrt(k));

			refrdir.normalize();

			refraction = trace(phit - nhit * bias, refrdir, spheres, depth + 1);

		}

		surfaceColor = (reflection * fresneleffect + refraction * (1 - fresneleffect) * sphere->transparency) * sphere->surfaceColor;

	}
...
...

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

{
	unsigned width = 640, height = 480;

	Vec3<T> *image = new Vec3<T>[width * height], *pixel = image;

	T invWidth = 1 / T(width), invHeight = 1 / T(height);

	T fov = 30, aspectratio = width / T(height);

	T angle = tan(M_PI * 0.5 * fov / T(180));

	// Trace rays

	for (unsigned y = 0; y < height; ++y) {

		for (unsigned x = 0; x < width; ++x, ++pixel) {

			T xx = (2 * ((x + 0.5) * invWidth) - 1) * angle * aspectratio;

			T yy = (1 - 2 * ((y + 0.5) * invHeight)) * angle;

			Vec3<T> raydir(xx, yy, -1);

			raydir.normalize();

			*pixel = trace(Vec3<T>(0), raydir, spheres, 0);

		}
	}

Michael

I have picked the Monte Carlo simulation for this assignment. Source code was from here and was modified to take and argument as the number of iterations and factored out the function which is going to be used for parallelzation.

Runtime for this program O(N) and the results are as follows:

N Iterations	Time (seconds)
1,000,000	0.02
5,000,000	0.24
10,000,000	0.42
50,000,000	2.22
100,000,000	4.75
500,000,000	19.97
1,000,000,000	44.5
5,000,000,000	94.08

Due to the simplicity of the program, all of the time spent was on the calc function below, as iterations increased, the time it takes increases at a linear rate.

Function to parallelize:

void calc(int iterations, int* count){
    double x, y, z;
    for (int i=0;i<iterations;i++){
        x = (double)rand()/RAND_MAX;
        y = (double)rand()/RAND_MAX;
        z = x*x+y*y;
        if (z<=1){
            (*count)++;
        }
    }
}

Assignment 2

Assignment 3