main.cpp

/*
Based on https://www.scratchapixel.com/lessons/3d-basic-rendering/introduction-to-ray-tracing/how-does-it-work
I decided to add threading. One day we may see a GPU implementation.
This works as an excellent motivation for parallelism 
*/

#include <cstdlib>
#include <cstdio>
#include <cmath>
#include <fstream>
#include <vector>
#include <iostream>
#include <cassert>
#include <algorithm>
#include <omp.h>
#include <chrono>

#if defined __linux__ || defined __APPLE__
// Not compiled on windows
# else
// Need to define some things for Windows
#define M_PI 3.141592653589793
#endif

#define MAX_RAY_DEPTH 10

template<typename T>
class Vec3{
	public:
    T x, y, z; 
    Vec3() : x(T(0)), y(T(0)), z(T(0)) {} 
    Vec3(T xx) : x(xx), y(xx), z(xx) {} 
    Vec3(T xx, T yy, T zz) : x(xx), y(yy), z(zz) {} 

    T length2() const { return x * x + y * y + z * z; } 
    T length() const { return sqrt(length2()); } 

	Vec3<T> operator * (const T &f) const { return Vec3<T>(x * f, y * f, z * f); } 
    Vec3<T> operator * (const Vec3<T> &v) const { return Vec3<T>(x * v.x, y * v.y, z * v.z); } 
    
	T dot(const Vec3<T> &v) const { return x * v.x + y * v.y + z * v.z; } 
    
	Vec3<T> operator - (const Vec3<T> &v) const { return Vec3<T>(x - v.x, y - v.y, z - v.z); } 
    Vec3<T> operator + (const Vec3<T> &v) const { return Vec3<T>(x + v.x, y + v.y, z + v.z); } 
    
	Vec3<T>& operator += (const Vec3<T> &v) { x += v.x, y += v.y, z += v.z; return *this; } 
    Vec3<T>& operator *= (const Vec3<T> &v) { x *= v.x, y *= v.y, z *= v.z; return *this; } 
    
	Vec3<T> operator - () const { return Vec3<T>(-x, -y, -z); } 
	
	Vec3& normalize(){
		T nor2 = length2();
		if (nor2 > 0){
			T invNor = 1/sqrt(nor2);
			x *= invNor, y *= invNor, z *= invNor;
		}
		return *this;
	}

	friend std::ostream & operator << (std::ostream &os, const Vec3<T> &v)
    {
        os << "[" << v.x << " " << v.y << " " << v.z << "]";
        return os;
    }
};

typedef Vec3<float> Vec3f;

class Sphere{
public:
	Vec3f center;
	float radius, radius2;
	Vec3f surfaceColor, emissionColor;
	float transparency, reflection;
    Sphere( 
        const Vec3f &c, 
        const float &r, 
        const Vec3f &sc, 
        const float &refl = 0, 
        const float &transp = 0, 
        const Vec3f &ec = 0) : 
        center(c), radius(r), radius2(r * r), surfaceColor(sc), emissionColor(ec), 
        transparency(transp), reflection(refl) 
    { /* empty */ }

    bool intersect(const Vec3f &rayorig, const Vec3f &raydir, float &t0, float &t1) const {
        Vec3f l = center - rayorig;
        float tca = l.dot(raydir);
        if (tca < 0) return false;
        float d2 = l.dot(l) - tca * tca;
        if (d2 > radius2) return false;
        float thc = sqrt(radius2 - d2);
        t0 = tca - thc;
        t1 = tca + thc;
        
        return true;
    }
}; 

float mix(const float &a, const float &b, const float &mix){
	return b * mix + a * (1 - mix);
}

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;
}

void render(const std::vector<Sphere> &spheres){
	unsigned width = 5120, height = 2880;
	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 the rays
    auto start = std::chrono::high_resolution_clock::now();
    #pragma omp parallel for collapse(2) //Will not work with MSVC. Need to unroll loop manually.
	for(unsigned y = 0; y < height; ++y){
		for(unsigned x = 0; x < width; ++x){
			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);
			++pixel;
		}
    }
    auto finish = std::chrono::high_resolution_clock::now();
    std::chrono::duration<double> elapsed = finish - start;
    //std::cout << "Rays traced, now writing to file" << std::endl;
    std::cout << "Elapsed time: " << elapsed.count() << std::endl;
    // 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; 
}

int main(int argc, char **argv){
	srand(42);
	std::vector<Sphere> spheres;
	// position, radius, surface color, reflectivity, transparency, emission color
	spheres.push_back(Sphere(Vec3f(0.0, -10000, -20), 10000, Vec3f(0.20, 0.20, 0.20), 0, 0.0));
	spheres.push_back(Sphere(Vec3f(0.0,      0, -20),     4, Vec3f(1.00, 0.32, 0.36), 0.5, 0.5));
	spheres.push_back(Sphere(Vec3f(4.0,     -1, -15),     2, Vec3f(0.90, 0.76, 0.46), 0.5, 0.0));
	spheres.push_back(Sphere(Vec3f(5.0,      0, -25),     3, Vec3f(0.65, 0.77, 0.97), 1, 0.0));
	spheres.push_back(Sphere(Vec3f(-5.5,     0, -15),     3, Vec3f(0.90, 0.90, 0.90), 1, 0.0));

	// light

	spheres.push_back(Sphere(Vec3f( 0.0,     20, -30),    3, Vec3f(0.00, 0.00, 0.00), 0, 0.0, Vec3f(3)));
	render(spheres);

	return 0;
}