Added indirect illumination.

TODO.org

@@ -1,4 +1,4 @@
-* Features [7/19]
+* Features [8/20]
 
  - [X] Perspective projection
  - [X] Ray-sphere intersection
@@ -20,7 +20,7 @@
  - [X] Specular reflections
  - [X] Transmission
  - [ ] Scene description input files (JSON)
- - [ ] Indirect illumination
+ - [X] Indirect illumination
  - [ ] Russian roulette
  - [ ] Image based lightning
  - [ ] HDR light probes for IBL

directional_light.cpp

@@ -20,12 +20,19 @@ inline float DirectionalLight::distance(vec3 point) {
   return numeric_limits<float>::max();
 }
 
-vec3 DirectionalLight::shade(vec3 normal, Ray & r, float t, Material & m) const {
+vec3 DirectionalLight::diffuse(vec3 normal, Ray & r, float t, Material & m) const {
-  float n_dot_l, r_dot_l;
+  float n_dot_l;
-  vec3 color, ref;
+  vec3 color;
 
   n_dot_l = max(dot(normal, m_position), 0.0f);
-  color += (m.m_diffuse / pi<float>()) * m_diffuse * n_dot_l;
+  color += m_diffuse * n_dot_l;
+
+  return color;
+}
+
+vec3 DirectionalLight::specular(vec3 normal, Ray & r, float t, Material & m) const {
+  float r_dot_l;
+  vec3 color, ref;
 
   ref = reflect(m_position, normal);
   r_dot_l = pow(max(dot(ref, r.m_direction), 0.0f), m.m_shininess);

directional_light.hpp

@@ -20,7 +20,8 @@ public:
 
   virtual vec3 direction(vec3 point);
   virtual float distance(vec3 point);
-  virtual vec3 shade(vec3 normal, Ray & r, float t, Material & m) const;
+  virtual vec3 diffuse(vec3 normal, Ray & r, float t, Material & m) const;
+  virtual vec3 specular(vec3 normal, Ray & r, float t, Material & m) const;
 };
 
 #endif

light.hpp

@@ -19,7 +19,8 @@ public:
 
   virtual vec3 direction(vec3 point) = 0;
   virtual float distance(vec3 point) = 0;
-  virtual vec3 shade(vec3 normal, Ray & r, float t, Material & m) const = 0;
+  virtual vec3 diffuse(vec3 normal, Ray & r, float t, Material & m) const = 0;
+  virtual vec3 specular(vec3 normal, Ray & r, float t, Material & m) const = 0;
 };
 
 #endif

main.cpp

@@ -97,7 +97,7 @@ int main(int argc, char ** argv) {
 
   scene_2(figures, lights, i_model_view);
 
-  tracer = Tracer(g_h, g_w, g_fov);
+  tracer = Tracer(g_h, g_w, g_fov, true);
 
   total = g_h * g_w * g_samples;
 
@@ -137,9 +137,9 @@ int main(int argc, char ** argv) {
   fprintf(out, "P6 %d %d %d ", g_w, g_h, 255);
   for (int i = 0; i < g_h; i++) {
     for (int j = 0; j < g_w; j++) {
-      fputc(static_cast<int>(image[i][j].r * 255.0f), out);
+      fputc(static_cast<int>(pow(image[i][j].r, 1.0f / 2.2f) * 255.0f), out);
-      fputc(static_cast<int>(image[i][j].g * 255.0f), out);
+      fputc(static_cast<int>(pow(image[i][j].g, 1.0f / 2.2f) * 255.0f), out);
-      fputc(static_cast<int>(image[i][j].b * 255.0f), out);
+      fputc(static_cast<int>(pow(image[i][j].b, 1.0f / 2.2f) * 255.0f), out);
     }
   }
   fclose(out);
@@ -229,14 +229,11 @@ static void scene_1(vector<Figure *> & vf, vector<Light *> & vl, mat4x4 & i_mode
 static void scene_2(vector<Figure *> & vf, vector<Light *> & vl, mat4x4 & i_model_view) {
   Sphere * s;
   Plane * p;
+  Disk * d;
   PointLight * l;
 
   s = new Sphere(0.2f, 0.0f, -0.75f, 0.25f);
-  s->m_mat.m_diffuse = vec3(0.0f);
+  s->m_mat.m_diffuse = vec3(1.0f);
-  s->m_mat.m_specular = vec3(0.0f);
-  s->m_mat.m_rho = 0.1f;
-  s->m_mat.m_refract = true;
-  s->m_mat.m_ref_index = 2.33f;
   vf.push_back(static_cast<Figure *>(s));
 
   p = new Plane(vec3(0.0f, -1.0f, 0.0f), vec3(0.0f, 1.0f, 0.0f));
@@ -259,15 +256,38 @@ static void scene_2(vector<Figure *> & vf, vector<Light *> & vl, mat4x4 & i_mode
   p->m_mat.m_diffuse = vec3(1.0f, 0.0f, 1.0f);
   vf.push_back(static_cast<Figure *>(p));
 
-  p = new Plane(vec3(0.0f, 0.0f, 0.1f), vec3(0.0f, 0.0f, -1.0f));
+  p = new Plane(vec3(0.0f, 0.0f, 1.1f), vec3(0.0f, 0.0f, -1.0f));
   p->m_mat.m_diffuse = vec3(1.0f, 1.0f, 1.0f);
   vf.push_back(static_cast<Figure *>(p));
 
-  s = new Sphere(-0.4f, -0.5f, -1.5f, 0.5f);
+  s = new Sphere(-0.5f, -0.5f, -1.5f, 0.5f);
   s->m_mat.m_diffuse = vec3(1.0f, 1.0f, 0.0f);
   s->m_mat.m_rho = 0.9f;
   vf.push_back(static_cast<Figure *>(s));
 
+  s = new Sphere(-0.5f, -0.5f, 0.6f, 0.5f);
+  s->m_mat.m_diffuse = vec3(1.0f, 1.0f, 0.0f);
+  s->m_mat.m_rho = 0.1f;
+  s->m_mat.m_refract = true;
+  s->m_mat.m_ref_index = 1.33f;
+  vf.push_back(static_cast<Figure *>(s));
+
+  d = new Disk(vec3(-0.25f, 1.0f, -1.0f), vec3(1.0f, 0.0f, 0.0f), 0.25f);
+  d->m_mat.m_diffuse = vec3(1.0f);
+  vf.push_back(static_cast<Figure *>(d));
+
+  d = new Disk(vec3(0.25f, 1.0f, -1.0f), vec3(-1.0f, 0.0f, 0.0f), 0.25f);
+  d->m_mat.m_diffuse = vec3(1.0f);
+  vf.push_back(static_cast<Figure *>(d));
+
+  d = new Disk(vec3(0.0f, 1.0f, -1.25f), vec3(0.0f, 0.0f, 1.0f), 0.25f);
+  d->m_mat.m_diffuse = vec3(1.0f);
+  vf.push_back(static_cast<Figure *>(d));
+
+  d = new Disk(vec3(0.0f, 1.0f, -0.75f), vec3(0.0f, 0.0f, -1.0f), 0.25f);
+  d->m_mat.m_diffuse = vec3(1.0f);
+  vf.push_back(static_cast<Figure *>(d));
+
   l = new PointLight();
   l->m_position = vec3(0.0f, 0.9f, -1.0f);
   l->m_diffuse = vec3(1.0f);
@@ -302,7 +322,7 @@ static void scene_3(vector<Figure *> & vf, vector<Light *> & vl, mat4x4 & i_mode
 
   s = new Sphere(2.0f, 0.0f, -2.0f, 1.0f);
   s->m_mat.m_diffuse = vec3(1.0f, 0.0f, 1.0f);
-  s->m_mat.m_rho = 0.6f;
+  s->m_mat.m_rho = 1.0f;
   vf.push_back(static_cast<Figure *>(s));
 
   s = new Sphere(-1.0f, 0.25f, -3.25f, 1.0f);
@@ -311,13 +331,13 @@ static void scene_3(vector<Figure *> & vf, vector<Light *> & vl, mat4x4 & i_mode
   vf.push_back(static_cast<Figure *>(s));
 
   p = new Plane(vec3(0.0f, -1.5f, 0.0f), vec3(0.0f, 1.0f, 0.0f));
-  p->m_mat.m_diffuse = vec3(1.0f, 1.0f, 1.0f);
+  p->m_mat.m_diffuse = vec3(1.0f);
   p->m_mat.m_specular = vec3(0.0f);
   vf.push_back(static_cast<Figure *>(p));
 
   l = new DirectionalLight();
   l->m_position = normalize(vec3(-1.0f, 1.0f, -1.0f));
-  l->m_diffuse = vec3(0.0f, 1.0f, 0.0f);
+  l->m_diffuse = vec3(1.0f, 1.0f, 1.0f);
   l->m_specular = vec3(0.0f, 1.0f, 0.0f);
   vl.push_back(static_cast<Light *>(l));
 
@@ -334,7 +354,7 @@ static void scene_3(vector<Figure *> & vf, vector<Light *> & vl, mat4x4 & i_mode
   vl.push_back(static_cast<Light *>(l));
 
   l = new DirectionalLight();
-  l->m_position = normalize(vec3(0.0f, 1.0f, 0.0f));
+  l->m_position = normalize(vec3(1.0f, 0.0f, 1.0f));
   l->m_diffuse = vec3(0.5f);
   vl.push_back(static_cast<Light *>(l));
 

material.hpp

@@ -14,8 +14,10 @@ public:
   float m_shininess;
   float m_ref_index;
   bool m_refract;
+  float kd;
+  float ks;
 
-  Material(): m_diffuse(vec3(1.0f)), m_specular(vec3(1.0f)), m_rho(0.0f), m_shininess(89.0f), m_ref_index(1.0f), m_refract(false) { }
+  Material(): m_diffuse(vec3(1.0f)), m_specular(vec3(1.0f)), m_rho(0.0f), m_shininess(89.0f), m_ref_index(1.0f), m_refract(false), kd(0.4f), ks(0.4f) { }
 
   Material(const Material & m) {
     m_diffuse = m.m_diffuse;

point_light.cpp

@@ -19,8 +19,8 @@ inline float PointLight::distance(vec3 point) {
   return length(m_position - point);
 }
 
-vec3 PointLight::shade(vec3 normal, Ray & r, float t, Material & m) const {
+vec3 PointLight::diffuse(vec3 normal, Ray & r, float t, Material & m) const {
-  float d, att, n_dot_l, r_dot_l;
+  float d, att, n_dot_l;
   vec3 color, i_pos, l_dir, ref;
 
   i_pos = r.m_origin + t * r.m_direction;
@@ -30,7 +30,20 @@ vec3 PointLight::shade(vec3 normal, Ray & r, float t, Material & m) const {
   att = 1.0f / (m_const_att + (m_lin_att * d) + (m_quad_att * (d * d)));
 
   n_dot_l = max(dot(normal, l_dir), 0.0f);
-  color += att * (m.m_diffuse / pi<float>()) * m_diffuse * n_dot_l;
+  color += att * m_diffuse * n_dot_l;
+
+  return color;
+}
+
+vec3 PointLight::specular(vec3 normal, Ray & r, float t, Material & m) const {
+  float d, att, r_dot_l;
+  vec3 color, i_pos, l_dir, ref;
+
+  i_pos = r.m_origin + t * r.m_direction;
+  l_dir = m_position - i_pos;
+  d = length(l_dir);
+  l_dir = normalize(l_dir);
+  att = 1.0f / (m_const_att + (m_lin_att * d) + (m_quad_att * (d * d)));
 
   ref = reflect(l_dir, normal);
   r_dot_l = pow(max(dot(ref, r.m_direction), 0.0f), m.m_shininess);

point_light.hpp

@@ -24,7 +24,8 @@ public:
 
   virtual vec3 direction(vec3 point);
   virtual float distance(vec3 point);
-  virtual vec3 shade(vec3 normal, Ray & r, float t, Material & m) const;
+  virtual vec3 diffuse(vec3 normal, Ray & r, float t, Material & m) const;
+  virtual vec3 specular(vec3 normal, Ray & r, float t, Material & m) const;
 };
 
 #endif

tracer.cpp

@@ -2,24 +2,19 @@
 #include <limits>
 #include <cstdlib>
 
+#include <glm/gtc/constants.hpp>
+
 #include "tracer.hpp"
 
-#define MAX_RECURSION 9
+#define MAX_RECURSION 3
 #define BIAS 0.000001f
 
 using namespace std;
 
 using std::numeric_limits;
-using glm::normalize;
+using namespace glm;
-using glm::radians;
-using glm::dot;
-using glm::reflect;
-using glm::refract;
-using glm::clamp;
-using glm::tan;
-using glm::sqrt;
 
-static const vec3 BCKG_COLOR = vec3(0.16f, 0.66f, 0.72f);
+static const vec3 BCKG_COLOR = vec3(0.0f);
 
 static inline float random01() {
   return static_cast<float>(rand()) / static_cast<float>(RAND_MAX);
@@ -56,14 +51,15 @@ vec2 Tracer::sample_pixel(int i, int j) const {
 vec3 Tracer::trace_ray(Ray & r, vector<Figure *> & v_figures, vector<Light *> & v_lights, unsigned int rec_level) const {
   float t, _t;
   Figure * _f;
-  vec3 n, color, i_pos, ref;
+  vec3 n, color, i_pos, ref, sample, dir_diff_color, dir_spec_color, ind_color;
   Ray mv_r, sr, rr;
   bool vis;
-  float kr;
+  float kr, r1, r2;
 
   t = numeric_limits<float>::max();
   _f = NULL;
 
+  // Find the closest intersecting surface.
   for (size_t f = 0; f < v_figures.size(); f++) {
     if (v_figures[f]->intersect(r, _t) && _t < t) {
       t = _t;
@@ -71,45 +67,99 @@ vec3 Tracer::trace_ray(Ray & r, vector<Figure *> & v_figures, vector<Light *> &
     }
   }
 
+  // If this ray intersects something:
   if (_f != NULL) {
+    // Take the intersection point and the normal of the surface at that point.
     i_pos = r.m_origin + (t * r.m_direction);
     n = _f->normal_at_int(r, t);
 
-    for (size_t l = 0; l < v_lights.size(); l++) {
+    // Check if the material is not reflective/refractive.
-      vis = true;
+    if( !_f->m_mat.m_refract && _f->m_mat.m_rho == 0.0f) {
-      sr = Ray(v_lights[l]->direction(i_pos), i_pos + n * BIAS);
+      // Calculate the direct lighting.
+      for (size_t l = 0; l < v_lights.size(); l++) {
+	// For every light source
+	vis = true;
 
-      for (size_t f = 0; f < v_figures.size(); f++) {
+	// Cast a shadow ray to determine visibility.
-	if (v_figures[f]->intersect(sr, _t) && _t < v_lights[l]->distance(i_pos)) {
+	sr = Ray(v_lights[l]->direction(i_pos), i_pos + n * BIAS);
-	  vis = false;
+	for (size_t f = 0; f < v_figures.size(); f++) {
-	  break;
+	  if (v_figures[f]->intersect(sr, _t) && _t < v_lights[l]->distance(i_pos)) {
+	    vis = false;
+	    break;
+	  }
 	}
+
+	// Evaluate the shading model accounting for visibility.
+	dir_diff_color += (vis ? 1.0f : 0.0f) * v_lights[l]->diffuse(n, r, t, _f->m_mat);
+	dir_spec_color += (vis ? 1.0f : 0.0f) * v_lights[l]->specular(n, r, t, _f->m_mat);
       }
 
-      color += (vis ? 1.0f : 0.0f) * v_lights[l]->shade(n, r, t, _f->m_mat);
+      // If enabled, calculate indirect lighting contribution.
+      if (indirect_l && rec_level < MAX_RECURSION) {
+	  r1 = random01();
+	  r2 = random01();
+	  sample = sample_hemisphere(r1, r2);
+	  rotate_sample(sample, n);
+	  rr = Ray(normalize(sample), i_pos + (sample * BIAS));
+	  ind_color += r1 * trace_ray(rr, v_figures, v_lights, rec_level + 1) / (1.0f / (2.0f * pi<float>()));
+      }
+
+      color += ((dir_diff_color + ind_color) * (_f->m_mat.m_diffuse / pi<float>())) + dir_spec_color;
+
+    } else {
+      // If the material has reflection/transmission enabled.
+      // Calculate the Fresnel term if the surface is refracting.
+      if (_f->m_mat.m_refract)
+	kr = fresnel(r.m_direction, n, r.m_ref_index, _f->m_mat.m_ref_index);
+      else
+	kr = _f->m_mat.m_rho;
+
+      // Determinte the specular reflection color.
+      if (kr > 0.0f && rec_level < MAX_RECURSION) {
+	rr = Ray(normalize(reflect(r.m_direction, n)), i_pos + n * BIAS);
+	color += _f->m_mat.m_rho * kr * trace_ray(rr, v_figures, v_lights, rec_level + 1);
+      } else if (rec_level >= MAX_RECURSION)
+	return vec3(0.0f);
+
+      // Determine the transmission color.
+      if (_f->m_mat.m_refract && kr < 1.0f && rec_level < MAX_RECURSION) {
+	rr = Ray(normalize(refract(r.m_direction, n, r.m_ref_index / _f->m_mat.m_ref_index)), i_pos - n * BIAS, _f->m_mat.m_ref_index);
+	color += (1.0f - _f->m_mat.m_rho) * (1.0f - kr) * trace_ray(rr, v_figures, v_lights, rec_level + 1);
+      } else if (rec_level >= MAX_RECURSION)
+	return vec3(0.0f);
+
     }
 
-    if (_f->m_mat.m_refract)
+    // Return final color.
-      kr = fresnel(r.m_direction, n, r.m_ref_index, _f->m_mat.m_ref_index);
-    else
-      kr = _f->m_mat.m_rho;
-
-    if (kr > 0.0f && rec_level < MAX_RECURSION) {
-      rr = Ray(normalize(reflect(r.m_direction, n)), i_pos + n * BIAS);
-      color += _f->m_mat.m_rho * kr * trace_ray(rr, v_figures, v_lights, rec_level + 1);
-
-    } else if (rec_level >= MAX_RECURSION)
-      return vec3(BCKG_COLOR);
-
-    if (_f->m_mat.m_refract && kr < 1.0f && rec_level < MAX_RECURSION) {
-      rr = Ray(normalize(refract(r.m_direction, n, r.m_ref_index / _f->m_mat.m_ref_index)), i_pos - n * BIAS, _f->m_mat.m_ref_index);
-      color += (1.0f - _f->m_mat.m_rho) * (1.0f - kr) * trace_ray(rr, v_figures, v_lights, rec_level + 1);
-
-    } else if (rec_level >= MAX_RECURSION)
-      return vec3(BCKG_COLOR);
-
     return clamp(color, 0.0f, 1.0f);
 
   } else
     return vec3(BCKG_COLOR);
 }
+
+/* Helper functions pretty much taken from scratchapixel.com */
+void Tracer::create_coords_system(const vec3 &n, vec3 &nt, vec3 &nb) const {
+  if (abs(n.x) > abs(n.y))
+    nt = normalize(vec3(n.z, 0.0f, -n.x));
+  else
+    nt = normalize(vec3(0.0f, -n.z, n.y));
+  nb = normalize(cross(n, nt));
+}
+
+vec3 Tracer::sample_hemisphere(const float r1, const float r2) const {
+  float sin_t = sqrt(1.0f - (r1 * r1));
+  float phi = 2 * pi<float>() * r2;
+  float x = sin_t * cos(phi);
+  float z = sin_t * sin(phi);
+  return vec3(x, r1, z);
+}
+
+void Tracer::rotate_sample(vec3 & sample, const vec3 & n) const {
+  vec3 nt, nb;
+  mat3 rot_m;
+
+  create_coords_system(n, nt, nb);
+  sample = vec3(sample.x * nb.x + sample.y * n.x + sample.z * nt.x,
+		sample.x * nb.y + sample.y * n.y + sample.z * nt.y,
+		sample.x * nb.z + sample.y * n.z + sample.z * nt.z);
+}

tracer.hpp

@@ -21,15 +21,21 @@ public:
   int m_w;
   float m_fov;
   float m_a_ratio;
+  bool indirect_l;
 
-  Tracer(): m_h(480), m_w(640), m_fov(90.0f), m_a_ratio(640.0f / 480.0f) { }
+  Tracer(): m_h(480), m_w(640), m_fov(90.0f), m_a_ratio(640.0f / 480.0f), indirect_l(false) { }
 
-  Tracer(int h, int w, float fov): m_h(h), m_w(w), m_fov(fov) {
+  Tracer(int h, int w, float fov, bool il): m_h(h), m_w(w), m_fov(fov), indirect_l(il) {
     m_a_ratio = static_cast<float>(w) / static_cast<float>(h);
   };
 
   vec2 sample_pixel(int i, int j) const;
   vec3 trace_ray(Ray & r, vector<Figure *> & v_figures, vector<Light *> & v_lights, unsigned int rec_level) const;
+
+private:
+  void create_coords_system(const vec3 &n, vec3 &nt, vec3 &nb) const;
+  vec3 sample_hemisphere(const float r1, const float r2) const;
+  void rotate_sample(vec3 & sample, const vec3 & n) const;
 };
 
 #endif