#include <stdio.h>

#include <stdlib.h>

#include <pthread.h>

#include "math-toolkit.h"

#include "primitives.h"

#include "raytracing.h"

#include "idx_stack.h"

#define MAX_REFLECTION_BOUNCES 3

#define MAX_DISTANCE 1000000000000.0

#define MIN_DISTANCE 0.00001

#define SAMPLES 4

#define SQUARE(x) (x * x)

#define MAX(a, b) (a > b ? a : b)

/* @param t t distance

* @return 1 means hit, otherwise 0

*/

static int raySphereIntersection(const point3 ray_e,

const point3 ray_d,

const sphere *sph,

intersection *ip, double *t1)

{

point3 l;

subtract_vector(sph->center, ray_e, l);

double s = dot_product(l, ray_d);

double l2 = dot_product(l, l);

double r2 = sph->radius * sph->radius;

if (s < 0 && l2 > r2)

return 0;

float m2 = l2 - s * s;

if (m2 > r2)

return 0;

float q = sqrt(r2 - m2);

*t1 = (l2 > r2) ? (s - q) : (s + q);

/* p = e + t1 * d */

multiply_vector(ray_d, *t1, ip->point);

add_vector(ray_e, ip->point, ip->point);

subtract_vector(ip->point, sph->center, ip->normal);

normalize(ip->normal);

if (dot_product(ip->normal, ray_d) > 0.0)

multiply_vector(ip->normal, -1, ip->normal);

return 1;

}

/* @return 1 means hit, otherwise 0; */

static int rayRectangularIntersection(const point3 ray_e,

const point3 ray_d,

rectangular *rec,

intersection *ip, double *t1)

{

point3 e01, e03, p;

subtract_vector(rec->vertices[1], rec->vertices[0], e01);

subtract_vector(rec->vertices[3], rec->vertices[0], e03);

cross_product(ray_d, e03, p);

double det = dot_product(e01, p);

/* Reject rays orthagonal to the normal vector.

* I.e. rays parallell to the plane.

*/

if (det < 1e-4)

return 0;

double inv_det = 1.0 / det;

point3 s;

subtract_vector(ray_e, rec->vertices[0], s);

double alpha = inv_det * dot_product(s, p);

if ((alpha > 1.0) || (alpha < 0.0))

return 0;

point3 q;

cross_product(s, e01, q);

double beta = inv_det * dot_product(ray_d, q);

if ((beta > 1.0) || (beta < 0.0))

return 0;

*t1 = inv_det * dot_product(e03, q);

if (alpha + beta > 1.0f) {

/* for the second triangle */

point3 e23, e21;

subtract_vector(rec->vertices[3], rec->vertices[2], e23);

subtract_vector(rec->vertices[1], rec->vertices[2], e21);

cross_product(ray_d, e21, p);

det = dot_product(e23, p);

if (det < 1e-4)

return 0;

inv_det = 1.0 / det;

subtract_vector(ray_e, rec->vertices[2], s);

alpha = inv_det * dot_product(s, p);

if (alpha < 0.0)

return 0;

cross_product(s, e23, q);

beta = inv_det * dot_product(ray_d, q);

if ((beta < 0.0) || (beta + alpha > 1.0))

return 0;

*t1 = inv_det * dot_product(e21, q);

}

if (*t1 < 1e-4)

return 0;

COPY_POINT3(ip->normal, rec->normal);

if (dot_product(ip->normal, ray_d)>0.0)

multiply_vector(ip->normal, -1, ip->normal);

multiply_vector(ray_d, *t1, ip->point);

add_vector(ray_e, ip->point, ip->point);

return 1;

}

static void localColor(color local_color,

const color light_color, double diffuse,

double specular, const object_fill *fill)

{

color ambi = { 0.1, 0.1, 0.1 };

color diff, spec, lightCo, surface;

/* Local Color = ambient * surface +

* light * ( kd * surface * diffuse + ks * specular)

*/

COPY_COLOR(diff, fill->fill_color);

multiply_vector(diff, fill->Kd, diff);

multiply_vector(diff, diffuse, diff);

COPY_COLOR(lightCo, light_color);

multiply_vectors(diff, lightCo, diff);

COPY_COLOR(spec, light_color);

multiply_vector(spec, fill->Ks, spec);

multiply_vector(spec, specular, spec);

COPY_COLOR(surface, fill->fill_color);

multiply_vectors(ambi,surface, ambi);

add_vector(diff, ambi, diff);

add_vector(diff, spec, diff);

add_vector(local_color, diff, local_color);

}

/* @param d direction of the ray into intersection

* @param l direction of intersection to light

* @param n surface normal

*/

static void compute_specular_diffuse(double *diffuse,

double *specular,

const point3 d, const point3 l,

const point3 n, double phong_pow)

{

point3 d_copy, l_copy, middle, r;

/* Calculate vector to eye V */

COPY_POINT3(d_copy, d);

multiply_vector(d_copy, -1, d_copy);

normalize(d_copy);

/* Calculate vector to light L */

COPY_POINT3(l_copy, l);

multiply_vector(l_copy, -1, l_copy);

normalize(l_copy);

/* Calculate reflection direction R */

double tmp = dot_product(n, l_copy);

multiply_vector(n, tmp, middle);

multiply_vector(middle, 2, middle);

subtract_vector(middle, l_copy, r);

normalize(r);

/* diffuse = max(0, dot_product(n, -l)) */

*diffuse = MAX(0, dot_product(n, l_copy));

/* specular = (dot_product(r, -d))^p */

*specular = pow(MAX(0, dot_product(r, d_copy)), phong_pow);

}

/* @param r direction of reflected ray

* @param d direction of primary ray into intersection

* @param n surface normal at intersection

*/

static void reflection(point3 r, const point3 d, const point3 n)

{

/* r = d - 2(d . n)n */

multiply_vector(n, -2.0 * dot_product(d, n), r);

add_vector(r, d, r);

}

/* reference: https://www.opengl.org/sdk/docs/man/html/refract.xhtml */

static void refraction(point3 t, const point3 I, const point3 N,

double n1, double n2)

{

double eta = n1 / n2;

double dot_NI = dot_product(N,I);

double k = 1.0 - eta * eta * (1.0 - dot_NI * dot_NI);

if (k < 0.0 || n2 <= 0.0)

t[0] = t[1] = t[2] = 0.0;

else {

point3 tmp;

multiply_vector(I, eta, t);

multiply_vector(N, eta * dot_NI + sqrt(k), tmp);

subtract_vector(t, tmp, t);

}

}

/* @param i direction of incoming ray, unit vector

* @param r direction of refraction ray, unit vector

* @param normal unit vector

* @param n1 refraction index

* @param n2 refraction index

*

* reference: http://graphics.stanford.edu/courses/cs148-10-summer/docs/2006--degreve--reflection_refraction.pdf

*/

static double fresnel(const point3 r, const point3 l,

const point3 normal, double n1, double n2)

{

/* TIR */

if (length(l) < 0.99)

return 1.0;

double cos_theta_i = -dot_product(r, normal);

double cos_theta_t = -dot_product(l, normal);

double r_vertical_root = (n1 * cos_theta_i - n2 * cos_theta_t) /

(n1 * cos_theta_i + n2 * cos_theta_t);

double r_parallel_root = (n2 * cos_theta_i - n1 * cos_theta_t) /

(n2 * cos_theta_i + n1 * cos_theta_t);

return (r_vertical_root * r_vertical_root +

r_parallel_root * r_parallel_root) / 2.0;

}

/* @param t distance */

static intersection ray_hit_object(const point3 e, const point3 d,

sphere_node *hit_sphere)

{

/* set these to not hit */

*hit_rectangular = NULL;

*hit_sphere = NULL;

point3 biased_e;

multiply_vector(d, t0, biased_e);

add_vector(biased_e, e, biased_e);

double nearest = t1;

intersection result, tmpresult;

for (rectangular_node rec = rectangulars; rec; rec = rec->next) {

if (rayRectangularIntersection(biased_e, d, &(rec->element),

&tmpresult, &t1) && (t1 < nearest)) {

/* hit is closest so far */

*hit_rectangular = rec;

nearest = t1;

result = tmpresult;

}

}

/* check the spheres */

for (sphere_node sphere = spheres; sphere; sphere = sphere->next) {

if (raySphereIntersection(biased_e, d, &(sphere->element),

&tmpresult, &t1) && (t1 < nearest)) {

*hit_sphere = sphere;

*hit_rectangular = NULL;

nearest = t1;

result = tmpresult;

}

}

return result;

}

/* @param d direction of ray

* @param w basic vectors

*/

static void rayConstruction(point3 d, const point3 u, const point3 v,

const point3 w, unsigned int i, unsigned int j,

const viewpoint *view, unsigned int width,

unsigned int height)

{

double xmin = -0.0175;

double ymin = -0.0175;

double xmax = 0.0175;

double ymax = 0.0175;

double focal = 0.05;

point3 u_tmp, v_tmp, w_tmp, s;

double w_s = focal;

double u_s = xmin + ((xmax - xmin) * (float) i / (width - 1));

double v_s = ymax + ((ymin - ymax) * (float) j / (height - 1));

/* s = e + u_s * u + v_s * v + w_s * w */

multiply_vector(u, u_s, u_tmp);

multiply_vector(v, v_s, v_tmp);

multiply_vector(w, w_s, w_tmp);

add_vector(view->vrp, u_tmp, s);

add_vector(s, v_tmp, s);

add_vector(s, w_tmp, s);

/* p(t) = e + td = e + t(s - e) */

subtract_vector(s, view->vrp, d);

normalize(d);

}

static void calculateBasisVectors(point3 u, point3 v, point3 w,

const viewpoint *view)

{

/* w */

COPY_POINT3(w, view->vpn);

normalize(w);

/* u = (t x w) / (|t x w|) */

cross_product(w, view->vup, u);

normalize(u);

/* v = w x u */

cross_product(u, w, v);

normalize(v);

}

/* @brief protect color value overflow */

static void protect_color_overflow(color c)

{

for (int i = 0; i < 3; i++)

if (c[i] > 1.0) c[i] = 1.0;

}

static unsigned int ray_color(const point3 e, double t,

color object_color, int bounces_left)

{

rectangular_node hit_rec = NULL, light_hit_rec = NULL;

sphere_node hit_sphere = NULL, light_hit_sphere = NULL;

double diffuse, specular;

point3 l, _l, r, rr;

object_fill fill;

color reflection_part;

color refraction_part;

/* might be a reflection ray, so check how many times we've bounced */

if (bounces_left == 0) {

SET_COLOR(object_color, 0.0, 0.0, 0.0);

return 0;

}

/* check for intersection with a sphere or a rectangular */

intersection ip= ray_hit_object(e, d, t, MAX_DISTANCE, rectangulars,

&hit_rec, spheres, &hit_sphere);

if (!hit_rec && !hit_sphere)

return 0;

/* pick the fill of the object that was hit */

fill = hit_rec ?

hit_rec->element.rectangular_fill :

hit_sphere->element.sphere_fill;

void *hit_obj = hit_rec ? (void *) hit_rec : (void *) hit_sphere;

/* assume it is a shadow */

SET_COLOR(object_color, 0.0, 0.0, 0.0);

for (light_node light = lights; light; light = light->next) {

/* calculate the intersection vector pointing at the light */

subtract_vector(ip.point, light->element.position, l);

multiply_vector(l, -1, _l);

normalize(_l);

/* check for intersection with an object. use ignore_me

* because we don't care about this normal

*/

ray_hit_object(ip.point, _l, MIN_DISTANCE, length(l),

rectangulars, &light_hit_rec,

spheres, &light_hit_sphere);

/* the light was not block by itself(lit object) */

if (light_hit_rec || light_hit_sphere)

continue;

compute_specular_diffuse(&diffuse, &specular, d, l,

ip.normal, fill.phong_power);

localColor(object_color, light->element.light_color,

diffuse, specular, &fill);

}

reflection(r, d, ip.normal);

double idx = idx_stack_top(stk).idx, idx_pass = fill.index_of_refraction;

if (idx_stack_top(stk).obj == hit_obj) {

idx_stack_pop(stk);

idx_pass = idx_stack_top(stk).idx;

} else {

idx_stack_element e = { .obj = hit_obj,

.idx = fill.index_of_refraction

};

idx_stack_push(stk, e);

}

refraction(rr, d, ip.normal, idx, idx_pass);

double R = (fill.T > 0.1) ?

fresnel(d, rr, ip.normal, idx, idx_pass) :

1.0;

/* totalColor = localColor +

mix((1-fill.Kd) * fill.R * reflection, T * refraction, R)

*/

if (fill.R > 0) {

/* if we hit something, add the color */

int old_top = stk->top;

if (ray_color(ip.point, MIN_DISTANCE, r, stk, rectangulars, spheres,

lights, reflection_part,

bounces_left - 1)) {

multiply_vector(reflection_part, R * (1.0 - fill.Kd) * fill.R,

reflection_part);

add_vector(object_color, reflection_part,

object_color);

}

stk->top = old_top;

}

/* calculate refraction ray */

if ((length(rr) > 0.0) && (fill.T > 0.0) &&

(fill.index_of_refraction > 0.0)) {

normalize(rr);

if (ray_color(ip.point, MIN_DISTANCE, rr, stk,rectangulars, spheres,

lights, refraction_part,

bounces_left - 1)) {

multiply_vector(refraction_part, (1 - R) * fill.T,

refraction_part);

add_vector(object_color, refraction_part,

object_color);

}

}

protect_color_overflow(object_color);

return 1;

}

/* @param background_color this is not ambient light */

void raytracing(void* args)

{

arg *data = (arg*) args;

point3 u, v, w, d;

color object_color = { 0.0, 0.0, 0.0 };

const viewpoint *view = (*data).View;

color back = { 0.0 , 0.1 , 0.1 };

uint8_t *pixels = data->pixels;

int start_j,end_j;

/* Separate to count the pixels */

if(pthread_equal(pthread_self(),THREAD[0])) {

start_j = 0;

end_j = 128;

} else if(pthread_equal(pthread_self(),THREAD[1])) {

start_j = 128;

end_j = 256;

} else if(pthread_equal(pthread_self(),THREAD[2])) {

start_j = 256;

end_j = 384;

} else if(pthread_equal(pthread_self(),THREAD[3])) {

start_j = 384;

end_j = 512;

}

/* calculate u, v, w */

calculateBasisVectors(u, v, w, view);

idx_stack stk;

int factor = sqrt(SAMPLES);

#pragma omp parallel for num_threads(64) \

private(stk), private(d), \

private(object_color)

for (int j = start_j ; j < end_j; j++) {

for (int i = 0 ; i < (*data).row; i++) {

double r = 0, g = 0, b = 0;

/* MSAA */

for (int s = 0; s < SAMPLES; s++) {

idx_stack_init(&stk);

rayConstruction(d, u, v, w,

i * factor + s / factor,

j * factor + s % factor,

view,

(*data).row * factor, (*data).col * factor);

if (ray_color(view->vrp, 0.0, d, &stk,(*data).rectangulars,

(*data).spheres, (*data).lights, object_color,

MAX_REFLECTION_BOUNCES)) {

r += object_color[0];

g += object_color[1];

b += object_color[2];

} else {

r += back[0];

g += back[1];

b += back[2];

}

pixels[((i + (j * (*data).row)) * 3) + 0] = r * 255 / SAMPLES;

pixels[((i + (j * (*data).row)) * 3) + 1] = g * 255 / SAMPLES;

pixels[((i + (j * (*data).row)) * 3) + 2] = b * 255 / SAMPLES;

}

}

}

}