Refraction is fully there, with magic fresnel!

Lots of work left to do!

.gitmodules

@@ -1,9 +1,6 @@
 [submodule "external/googletest"]
 	path = external/googletest
 	url = https://github.com/google/googletest.git
-[submodule "external/nanogui"]
-	path = external/nanogui
-	url = https://github.com/Godzil/nanogui.git
 [submodule "external/glfw"]
 	path = external/glfw
 	url = https://github.com/glfw/glfw.git

README.md

@@ -37,3 +37,11 @@ From Chapter 09:
 From Chapter 10:
 
 ![Chapter 10 rendering test](output/ch10_test.png)
+
+From Chapter 11:
+
+![Chapter 11 reflections rendering test](output/ch11_reflection.png)
+
+![Chapter 11 refraction rendering test](output/ch11_refraction.png)
+
+![Chapter 11 rendering test](output/ch11_test.png)

source/camera.cpp

@@ -55,7 +55,7 @@ Ray Camera::rayForPixel(uint32_t pixelX, uint32_t pixelY)
     return Ray(origin, direction);
 }
 
-Canvas Camera::render(World world)
+Canvas Camera::render(World world, uint32_t depth)
 {
     uint32_t x, y;
     Canvas image = Canvas(this->horizontalSize, this->verticalSize);
@@ -65,7 +65,7 @@ Canvas Camera::render(World world)
         for(x = 0; x < this->horizontalSize; x++)
         {
             Ray r = this->rayForPixel(x, y);
-            Tuple colour = world.colourAt(r);
+            Tuple colour = world.colourAt(r, depth);
             image.putPixel(x, y, colour);
         }
     }

source/include/camera.h

@@ -32,7 +32,7 @@ public:
     Camera(uint32_t hsize, uint32_t vsize, double fov);
     void setTransform(Matrix transform);
     Ray rayForPixel(uint32_t pixelX, uint32_t pixelY);
-    Canvas render(World w);
+    Canvas render(World w, uint32_t depth = 5);
 };
 
 #endif /* DORAYME_CAMERA_H */

source/include/intersection.h

@@ -13,18 +13,53 @@
 #include <ray.h>
 
 class Shape;
+class Intersect;
 
 struct Computation
 {
-    Computation(Shape *object, double t, Tuple point, Tuple eyev, Tuple normalv, Tuple overHitP, bool inside) :
+    Computation(Shape *object, double t, Tuple point, Tuple eyev, Tuple normalv, Tuple overHitP,
-          object(object), t(t), hitPoint(point), eyeVector(eyev), normalVector(normalv), inside(inside), overHitPoint(overHitP) { };
+                bool inside, Tuple reflectV = Vector(0, 0, 0), double n1 = 1.0, double n2 = 1.0,
+                Tuple underHitP = Point(0, 0, 0)) :
+          object(object), t(t), hitPoint(point), eyeVector(eyev), normalVector(normalv), inside(inside),
+          overHitPoint(overHitP), underHitPoint(underHitP), reflectVector(reflectV), n1(n1), n2(n2) { };
+
+    double schlick()
+    {
+        /* Find the cos of the angle betzeen the eye and normal vector */
+        double cos = this->eyeVector.dot(this->normalVector);
+        double r0;
+        /* Total internal reflection can only occur when n1 > n2 */
+        if (this->n1 > this->n2)
+        {
+            double n, sin2_t;
+            n = this->n1 / this->n2;
+            sin2_t = (n * n) * (1.0 - (cos * cos));
+            if (sin2_t > 1.0)
+            {
+                return 1.0;
+            }
+            /* Compute the cos of theta */
+            cos = sqrt(1.0 - sin2_t);
+        }
+
+
+        r0 = ((this->n1 - this->n2) / (this->n1 + this->n2));
+        r0 = r0 * r0;
+
+        return r0 + (1 - r0) *  ((1 - cos)*(1 - cos)*(1 - cos)*(1 - cos)*(1 - cos));
+    };
 
     Shape *object;
     double t;
     Tuple hitPoint;
     Tuple overHitPoint;
+    Tuple underHitPoint;
     Tuple eyeVector;
     Tuple normalVector;
+    Tuple reflectVector;
+
+    double n1;
+    double n2;
 
     bool inside;
 };
@@ -39,7 +74,7 @@ public:
     Intersection(double t, Shape *object) : t(t), object(object) { };
     bool nothing() { return (this->object == nullptr); };
 
-    Computation prepareComputation(Ray r);
+    Computation prepareComputation(Ray r, Intersect *xs = nullptr);
 
     bool operator==(const Intersection &b) const { return ((this->t == b.t) && (this->object == b.object)); };
 };

source/include/list.h

@@ -0,0 +1,112 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  List header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_LIST_H
+#define DORAYME_LIST_H
+
+#include <shape.h>
+
+struct ChainList
+{
+    Shape *shape;
+    ChainList *next;
+};
+
+class List
+{
+private:
+    ChainList *head;
+    ChainList *tail;
+    uint32_t count;
+public:
+    List() : head(nullptr), tail(nullptr), count(0) { };
+    ~List()
+    {
+        ChainList *p = this->head;
+        if (p == nullptr) { return; }
+
+        /* clear up the list */
+    }
+
+    Shape *last()
+    {
+        ChainList *p = this->tail;
+        if (p == nullptr) { return nullptr; }
+        return p->shape;
+    }
+
+    void remove(Shape *s)
+    {
+        ChainList *p = this->head;
+        if (p == nullptr) { return; }
+
+        if ((p->next == nullptr) && (p->shape == s))
+        {
+            /* First element */
+            this->tail = nullptr;
+            free(this->head);
+            this->head = nullptr;
+            this->count = 0;
+
+            return;
+        }
+
+        while(p->next != nullptr)
+        {
+            if (p->next->shape == s)
+            {
+                ChainList *found = p->next;
+
+                p->next = p->next->next;
+
+                free(found);
+
+                if (p->next == NULL) { this->tail = p; }
+
+                this->count --;
+                return;
+            }
+            p = p->next;
+        }
+    }
+
+    void append(Shape *s)
+    {
+        ChainList *theNew = (ChainList *)calloc(1, sizeof(ChainList));
+
+        theNew->shape = s;
+
+        ChainList *p = this->tail;
+        this->tail = theNew;
+
+        if (p != nullptr) { p->next = theNew; }
+        else { this->head = theNew; } /* If the tail is empty, it mean the list IS empty. */
+
+        this->count ++;
+    }
+
+    bool isEmpty()
+    {
+        return (this->count == 0);
+    }
+
+    bool doesInclude(Shape *s)
+    {
+        ChainList *p = this->head;
+
+        while(p != nullptr)
+        {
+            if (p->shape == s) { return true; }
+            p = p->next;
+        }
+
+        return false;
+    }
+};
+
+#endif //DORAYME_LIST_H

source/include/material.h

@@ -24,11 +24,15 @@ public:
     double diffuse;
     double specular;
     double shininess;
+    double reflective;
+    double transparency;
+    double refractiveIndex;
 
     Pattern *pattern;
 
 public:
-    Material() : colour(Colour(1, 1, 1)), ambient(0.1), diffuse(0.9), specular(0.9), shininess(200), pattern(nullptr) {};
+    Material() : colour(Colour(1, 1, 1)), ambient(0.1), diffuse(0.9), specular(0.9), shininess(200),
+           reflective(0.0), transparency(0.0), refractiveIndex(1.0), pattern(nullptr) {};
 
     Colour lighting(Light light, Tuple point, Tuple eyeVector, Tuple normalVector, Shape *hitObject, bool inShadow = false);
 
@@ -39,4 +43,5 @@ public:
                                                       (this->colour == b.colour); };
 };
 
+
 #endif /* DORAYME_MATERIAL_H */

source/include/sphere.h

@@ -24,4 +24,11 @@ public:
     /* All sphere are at (0, 0, 0) and radius 1 in the object space */
 };
 
+/* Mostly for test purposes */
+class GlassSphere : public Sphere
+{
+public:
+    GlassSphere() : Sphere() { this->material.transparency = 1.0; this->material.refractiveIndex = 1.5; };
+};
+
 #endif /* DORAYME_SPHERE_H */

source/include/world.h

@@ -40,11 +40,15 @@ public:
     bool objectIsIn(Shape &s);
 
     Shape *getObject(int i) { return this->objectList[i]; };
+    Light *getLight(int i) { return this->lightList[i]; };
 
-    Tuple shadeHit(Computation comps);;
+    Tuple shadeHit(Computation comps, uint32_t depthCount = 4);
-    Tuple colourAt(Ray r);
+    Tuple colourAt(Ray r, uint32_t depthCount = 4);
     bool isShadowed(Tuple point);
 
+    Colour reflectColour(Computation comps, uint32_t depthCount = 4);
+    Colour refractedColour(Computation comps, uint32_t depthCount = 4);
+
     Intersect intersect(Ray r);
 
 };

source/intersection.cpp

@@ -8,9 +8,13 @@
  */
 #include <intersection.h>
 #include <shape.h>
+#include <list.h>
 
-Computation Intersection::prepareComputation(Ray r)
+Computation Intersection::prepareComputation(Ray r, Intersect *xs)
 {
+    double n1 = 1.0;
+    double n2 = 1.0;
+
     Tuple hitP = r.position(this->t);
     Tuple normalV = this->object->normalAt(hitP);
     Tuple eyeV = -r.direction;
@@ -23,6 +27,46 @@ Computation Intersection::prepareComputation(Ray r)
     }
 
     Tuple overHitP = hitP + normalV * getEpsilon();
+    Tuple underHitP = hitP - normalV * getEpsilon();
+    Tuple reflectV = r.direction.reflect(normalV);
+
+    if (xs != nullptr)
+    {
+        List containers;
+        int j, k;
+
+        for(j = 0; j < xs->count(); j++)
+        {
+            Intersection i = (*xs)[j];
+            if (*this == i)
+            {
+                if (!containers.isEmpty())
+                {
+                    n1 = containers.last()->material.refractiveIndex;
+                }
+            }
+
+            if (containers.doesInclude(i.object))
+            {
+                containers.remove(i.object);
+            }
+            else
+            {
+                containers.append(i.object);
+            }
+
+            if (*this == i)
+            {
+                if (!containers.isEmpty())
+                {
+                    n2 = containers.last()->material.refractiveIndex;
+                }
+
+                /* End the loop */
+                break;
+            }
+        }
+    }
 
     return Computation(this->object,
                        this->t,
@@ -30,5 +74,9 @@ Computation Intersection::prepareComputation(Ray r)
                        eyeV,
                        normalV,
                        overHitP,
-                       inside);
+                       inside,
+                       reflectV,
+                       n1,
+                       n2,
+                       underHitP);
 }

source/world.cpp

@@ -92,19 +92,33 @@ Intersect World::intersect(Ray r)
     return ret;
 }
 
-Tuple World::shadeHit(Computation comps)
+Tuple World::shadeHit(Computation comps, uint32_t depthCount)
 {
     /* TODO: Add support for more than one light */
 
     bool isThereAnObstacle = this->isShadowed(comps.overHitPoint);
 
-    return comps.object->material.lighting(*this->lightList[0], comps.overHitPoint, comps.eyeVector,
+    Tuple surface = comps.object->material.lighting(*this->lightList[0], comps.overHitPoint, comps.eyeVector,
             comps.normalVector, comps.object, isThereAnObstacle);
+
+    Tuple reflected = this->reflectColour(comps, depthCount);
+    Tuple refracted = this->refractedColour(comps, depthCount);
+
+    if ((comps.object->material.reflective > 0) && (comps.object->material.transparency > 0))
+    {
+        double reflectance = comps.schlick();
+
+        return surface + reflected * reflectance + refracted * (1 - reflectance);
+
+    }
+
+    return surface + reflected + refracted;
 }
 
-Tuple World::colourAt(Ray r)
+Tuple World::colourAt(Ray r, uint32_t depthCount)
 {
-    Intersection hit = this->intersect(r).hit();
+    Intersect allHits = this->intersect(r);
+    Intersection hit = allHits.hit();
 
     if (hit.nothing())
     {
@@ -112,7 +126,7 @@ Tuple World::colourAt(Ray r)
     }
     else
     {
-        return this->shadeHit(hit.prepareComputation(r));
+        return this->shadeHit(hit.prepareComputation(r, &allHits), depthCount);
     }
 }
 
@@ -134,3 +148,40 @@ bool World::isShadowed(Tuple point)
 
     return false;
 }
+
+Colour World::reflectColour(Computation comps, uint32_t depthCount)
+{
+    if ((depthCount == 0) || (comps.object->material.reflective == 0))
+    {
+        return Colour(0, 0, 0);
+    }
+
+    /* So it is reflective, even just a bit. Let'sr reflect the ray! */
+    Ray reflectedRay = Ray(comps.overHitPoint, comps.reflectVector);
+
+    Tuple hitColour = this->colourAt(reflectedRay, depthCount - 1);
+    hitColour = hitColour * comps.object->material.reflective;
+
+    return Colour(hitColour.x, hitColour.y, hitColour.z);
+}
+
+Colour World::refractedColour(Computation comps, uint32_t depthCount)
+{
+    double nRatio = comps.n1 / comps.n2;
+    double cos_i = comps.eyeVector.dot(comps.normalVector);
+    double sin2_t = (nRatio*nRatio) * (1 - cos_i * cos_i);
+
+    if ((sin2_t > 1 ) || (depthCount == 0) || (comps.object->material.transparency == 0))
+    {
+        return Colour(0, 0, 0);
+    }
+
+    double cos_t = sqrt(1.0 - sin2_t);
+    Tuple direction = comps.normalVector * (nRatio * cos_i - cos_t) - comps.eyeVector * nRatio;
+
+    Ray refractedRay = Ray(comps.underHitPoint, direction);
+
+    Tuple hitColour = this->colourAt(refractedRay, depthCount - 1) * comps.object->material.transparency;
+
+    return Colour(hitColour.x, hitColour.y, hitColour.z);
+}

tests/CMakeLists.txt

@@ -44,8 +44,26 @@ target_include_directories(ch10_test PUBLIC ../source/include)
 target_sources(ch10_test PRIVATE ch10_test.cpp)
 target_link_libraries(ch10_test rayonnement)
 
+add_executable(ch11_reflection)
+target_include_directories(ch11_reflection PUBLIC ../source/include)
+target_sources(ch11_reflection PRIVATE ch11_reflection.cpp)
+target_link_libraries(ch11_reflection rayonnement)
+
+add_executable(ch11_refraction)
+target_include_directories(ch11_refraction PUBLIC ../source/include)
+target_sources(ch11_refraction PRIVATE ch11_refraction.cpp)
+target_link_libraries(ch11_refraction rayonnement)
+
+add_executable(ch11_test)
+target_include_directories(ch11_test PUBLIC ../source/include)
+target_sources(ch11_test PRIVATE ch11_test.cpp)
+target_link_libraries(ch11_test rayonnement)
+
 add_test(NAME Chapter05_Test COMMAND $<TARGET_FILE:ch5_test>)
 add_test(NAME Chapter06_Test COMMAND $<TARGET_FILE:ch6_test>)
 add_test(NAME Chapter07_Test COMMAND $<TARGET_FILE:ch7_test>)
 add_test(NAME Chapter09_Test COMMAND $<TARGET_FILE:ch9_test>)
 add_test(NAME Chapter10_Test COMMAND $<TARGET_FILE:ch10_test>)
+add_test(NAME Chapter11_Reflection COMMAND $<TARGET_FILE:ch11_reflection>)
+add_test(NAME Chapter11_Refraction COMMAND $<TARGET_FILE:ch11_refraction>)
+add_test(NAME Chapter11_Test COMMAND $<TARGET_FILE:ch11_test>)

tests/ch10_test.cpp

@@ -1,6 +1,6 @@
 /*
  *  DoRayMe - a quick and dirty Raytracer
- *  Render test for chapter 5 "Put it together".
+ *  Render test for chapter 10
  *
  *  Created by Manoël Trapier
  *  Copyright (c) 2020 986-Studio.
@@ -79,7 +79,7 @@ int main()
     w.addLight(&light);
 
     /* Set the camera */
-    Camera camera = Camera(100, 50, M_PI / 3);
+    Camera camera = Camera(1920, 1080, M_PI / 3);
     camera.setTransform(viewTransform(Point(0, 1.5, -5),
                                       Point(0, 1, 0),
                                       Vector(0, 1, 0)));

tests/ch11_reflection.cpp

@@ -0,0 +1,117 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Render test for reflection in chapter 11.
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <world.h>
+#include <light.h>
+#include <sphere.h>
+#include <plane.h>
+#include <material.h>
+#include <colour.h>
+#include <canvas.h>
+#include <camera.h>
+
+#include <pattern.h>
+#include <strippattern.h>
+#include <gradientpattern.h>
+#include <checkerspattern.h>
+#include <ringpattern.h>
+
+#include <transformation.h>
+
+int main()
+{
+    /* First we need to construct the world */
+    Plane floor = Plane();
+    floor.material.specular = 0;
+    floor.material.pattern = new RingPattern(Colour(1, 0.9, 0.9), Colour(1, 0.2, 0.2));
+    floor.material.reflective = 0.1;
+
+    Plane wall = Plane();
+    wall.material.specular = 0;
+    wall.material.pattern = new StripPattern(Colour(1, 0.9, 0.9), Colour(1, 0.2, 0.2));
+    wall.material.pattern->setTransform(translation(0, 0, 1) * rotationY(M_PI/4));
+    wall.setTransform(translation(0, 0, 5) * rotationX(M_PI/2));
+
+    Sphere middle = Sphere();
+    middle.setTransform(translation(-0.7, 1, 0.6));
+    middle.material.diffuse = 0.7;
+    middle.material.specular = 0.3;
+    middle.material.pattern = new StripPattern(Colour(0.1, 1, 0.5), Colour(0, 0.2, 0.2));
+    middle.material.pattern->setTransform((rotationZ(M_PI/4) * rotationY(M_PI/5) * scaling(0.2, 0.2, 0.2)));
+
+    Sphere right = Sphere();
+    right.setTransform(translation(1.5, 0.5, -0.5) * scaling(0.5, 0.5, 0.5));
+    right.material.diffuse = 0.7;
+    right.material.specular = 0.3;
+    right.material.pattern = new StripPattern(Colour(0.5, 1, 0.1), Colour(0, 0, 0));
+    right.material.pattern->setTransform((scaling(0.1, 0.1, 0.1)));
+    right.material.reflective = 0.1;
+
+    Sphere left = Sphere();
+    left.setTransform(translation(-1.5, 0.33, -0.75) * scaling(0.33, 0.33, 0.33));
+    left.material.diffuse = 0.7;
+    left.material.specular = 0.3;
+    left.material.pattern = new GradientPattern(Colour(1, 0.8, 0.1), Colour(0.1, 0.1, 1));
+    left.material.pattern->setTransform(translation(1.5, 0, 0) * scaling(2.1, 2, 2) * rotationY(-M_PI/4));
+
+    Sphere fourth = Sphere();
+    fourth.setTransform(translation(.5, 0.25, 0.4) * scaling(0.3, 0.3, 0.3));
+    fourth.material.diffuse = 0.7;
+    fourth.material.specular = 0.3;
+    fourth.material.pattern = new CheckersPattern(Colour(0.1, 0.8, 0.1), Colour(0.8, 1, 0.8));
+    fourth.material.pattern->setTransform( scaling(0.2, 0.2, 0.2));
+    fourth.material.reflective = 0.4;
+
+    World w = World();
+
+    w.addObject(&floor);
+    w.addObject(&wall);
+    w.addObject(&middle);
+    w.addObject(&left);
+    w.addObject(&right);
+    w.addObject(&fourth);
+
+    /* Add some more reflective spheres */
+    Sphere ref1 = Sphere();
+    ref1.setTransform(translation(1, 1, .4) * scaling(0.2, 0.2, 0.2));
+    ref1.material.reflective = 1;
+    ref1.material.colour = Colour(0.3, 0.7, 0.6);
+    w.addObject(&ref1);
+
+    Sphere ref2 = Sphere();
+    ref2.setTransform(translation(1.5, 2, -.8) * scaling(0.2, 0.2, 0.2));
+    ref2.material.reflective = 1;
+    ref2.material.specular = 0.5;
+    ref2.material.colour = Colour(0.3, 0.3, 0.3);
+    w.addObject(&ref2);
+
+    Sphere ref3 = Sphere();
+    ref3.setTransform(translation(-2, 1.678, .4) * scaling(0.4, 0.4, 0.4));
+    ref3.material.reflective = 1;
+    ref3.material.specular = 0.5;
+    w.addObject(&ref3);
+
+    /* Add light */
+    Light light = Light(POINT_LIGHT, Point(-10, 10, -10), Colour(1, 1, 1));
+
+    w.addLight(&light);
+
+    /* Set the camera */
+    Camera camera = Camera(100, 50, M_PI / 3);
+    camera.setTransform(viewTransform(Point(0, 1.5, -5),
+                                      Point(0, 1, 0),
+                                      Vector(0, 1, 0)));
+
+    /* Now render it */
+    Canvas image = camera.render(w);
+
+    image.SaveAsPNG("ch11_reflection.png");
+
+
+    return 0;
+}

tests/ch11_refraction.cpp

@@ -0,0 +1,71 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Render test for reflection in chapter 11.
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <world.h>
+#include <light.h>
+#include <sphere.h>
+#include <plane.h>
+#include <material.h>
+#include <colour.h>
+#include <canvas.h>
+#include <camera.h>
+
+#include <pattern.h>
+#include <strippattern.h>
+#include <gradientpattern.h>
+#include <checkerspattern.h>
+#include <ringpattern.h>
+
+#include <transformation.h>
+
+int main()
+{
+    World w = World();
+
+    /* First we need to construct the world */
+    Plane floor = Plane();
+    floor.material.pattern = new CheckersPattern(Colour(1, 1, 1), Colour(0, 0, 0));
+    floor.setTransform(translation(0, -10, 0));
+    w.addObject(&floor);
+
+
+    Sphere glassBall = Sphere();
+    glassBall.material.shininess = 300;
+    glassBall.material.transparency = 1;
+    glassBall.material.reflective = 1;
+    glassBall.material.refractiveIndex = 1.52;
+    glassBall.material.diffuse = 0.1;
+    w.addObject(&glassBall);
+
+    Sphere airBall = Sphere();
+    airBall.setTransform(scaling(0.5, 0.5, 0.5));
+    airBall.material.shininess = 300;
+    airBall.material.transparency = 1;
+    airBall.material.reflective = 1;
+    airBall.material.refractiveIndex = 1.0009;
+    airBall.material.diffuse = 0.1;
+    w.addObject(&airBall);
+
+   /* Add light */
+    Light light = Light(POINT_LIGHT, Point(20, 10, 0), Colour(0.7, 0.7, 0.7));
+    w.addLight(&light);
+
+    /* Set the camera */
+    Camera camera = Camera(100, 100, M_PI / 3);
+
+    camera.setTransform(viewTransform(Point(0, 2.5, 0),
+                                      Point(0, 0, 0),
+                                      Vector(1, 0, 0)));
+
+    /* Now render it */
+    Canvas image = camera.render(w);
+
+    image.SaveAsPNG("ch11_refraction.png");
+
+    return 0;
+}

tests/ch11_test.cpp

@@ -0,0 +1,160 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Render test for reflection in chapter 11.
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <world.h>
+#include <light.h>
+#include <sphere.h>
+#include <plane.h>
+#include <material.h>
+#include <colour.h>
+#include <canvas.h>
+#include <camera.h>
+
+#include <pattern.h>
+#include <strippattern.h>
+#include <gradientpattern.h>
+#include <checkerspattern.h>
+#include <ringpattern.h>
+
+#include <transformation.h>
+
+int main()
+{
+    World w = World();
+
+    Material wallMaterial = Material();
+    wallMaterial.pattern = new StripPattern(Colour(0.45, 0.45, 0.45), Colour(0.55, 0.55, 0.55));
+    wallMaterial.pattern->setTransform( scaling(0.25, 0.25, 0.25) * rotationY(1.5708));
+    wallMaterial.ambient = 0;
+    wallMaterial.diffuse = 0.4;
+    wallMaterial.specular = 0;
+    wallMaterial.reflective = 0.3;
+
+    /* ----------------------------- */
+
+    /* The flood */
+    Plane floor = Plane();
+    floor.setTransform(rotationY(0.31415));
+    floor.material.pattern = new CheckersPattern(Colour(0.35, 0.35, 0.35), Colour(0.65, 0.65, 0.65));
+    floor.material.specular = 0;
+    floor.material.reflective = 0.4;
+    w.addObject(&floor);
+
+    /* the ceiling */
+    Plane ceiling = Plane();
+    ceiling.setTransform(translation(0, 5, 0));
+    ceiling.material.colour = Colour(0.8, 0.8, 0.8);
+    ceiling.material.ambient = 0.3;
+    ceiling.material.specular = 0;
+    w.addObject(&ceiling);
+
+    /* West wall */
+    Plane westWall = Plane();
+    westWall.setTransform( translation(-5, 0, 0) * rotationZ(1.5708) * rotationY(1.5708));
+    westWall.setMaterial(wallMaterial);
+    w.addObject(&westWall);
+
+    /* east wall */
+    Plane eastWall = Plane();
+    eastWall.setTransform( translation(5, 0, 0) * rotationZ(1.5708) * rotationY(1.5708));
+    eastWall.setMaterial(wallMaterial);
+    w.addObject(&eastWall);
+
+    /* north wall */
+    Plane northWall = Plane();
+    northWall.setTransform( translation(0, 0, 5) * rotationX(1.5708));
+    northWall.setMaterial(wallMaterial);
+    w.addObject(&northWall);
+
+    /* south wall */
+    Plane southWall = Plane();
+    southWall.setTransform( translation(0, 0, -5) * rotationX(1.5708));
+    southWall.setMaterial(wallMaterial);
+    w.addObject(&southWall);
+
+    /* ----------------------------- */
+
+    /* Background balls */
+    Sphere bg1 = Sphere();
+    bg1.setTransform(translation(4.6, 0.4, 1) * scaling(0.4, 0.4, 0.4));
+    bg1.material.colour = Colour(0.8, 0.5, 0.3);
+    bg1.material.shininess = 50;
+    w.addObject(&bg1);
+
+    Sphere bg2 = Sphere();
+    bg2.setTransform(translation(4.7, 0.3, 0.4) * scaling(0.3, 0.3, 0.3));
+    bg2.material.colour = Colour(0.9, 0.4, 0.5);
+    bg2.material.shininess = 50;
+    w.addObject(&bg2);
+
+    Sphere bg3 = Sphere();
+    bg3.setTransform(translation(-1, 0.5, 4.5) * scaling(0.5, 0.5, 0.5));
+    bg3.material.colour = Colour(0.4, 0.9, 0.6);
+    bg3.material.shininess = 50;
+    w.addObject(&bg3);
+
+    Sphere bg4 = Sphere();
+    bg4.setTransform(translation(-1.7, 0.3, 4.7) * scaling(0.3, 0.3, 0.3));
+    bg4.material.colour = Colour(0.4, 0.6, 0.9);
+    bg4.material.shininess = 50;
+    w.addObject(&bg4);
+
+    /* Forground balls */
+
+    /* Red sphere */
+    Sphere redBall = Sphere();
+    redBall.setTransform(translation(-0.6, 1, 0.6));
+    redBall.material.colour = Colour(1, 0.3, 0.2);
+    redBall.material.shininess = 5;
+    redBall.material.specular = 0.4;
+    w.addObject(&redBall);
+
+    /* blue glass ball */
+    Sphere blueGlassBall = Sphere();
+    blueGlassBall.setTransform(translation(0.6, 0.7, -0.6) * scaling(0.7, 0.7, 0.7));
+    blueGlassBall.material.colour = Colour(0, 0, 0.2);
+    blueGlassBall.material.ambient = 0;
+    blueGlassBall.material.diffuse = 0.4;
+    blueGlassBall.material.specular = 0.9;
+    blueGlassBall.material.shininess = 300;
+    blueGlassBall.material.transparency = 0.9;
+    blueGlassBall.material.refractiveIndex = 1.5;
+    w.addObject(&blueGlassBall);
+
+    /* green glass ball */
+    Sphere greenGlassBall = Sphere();
+    greenGlassBall.setTransform(translation(-0.7, 0.5, -0.8) * scaling(0.5, 0.5, 0.5));
+    greenGlassBall.material.colour = Colour(0, 0.2, 0);
+    greenGlassBall.material.ambient = 0;
+    greenGlassBall.material.diffuse = 0.4;
+    greenGlassBall.material.specular = 0.9;
+    greenGlassBall.material.shininess = 300;
+    greenGlassBall.material.transparency = 0.9;
+    greenGlassBall.material.refractiveIndex = 1.5;
+    w.addObject(&greenGlassBall);
+
+    /* ----------------------------- */
+
+    /* Add light */
+    Light light = Light(POINT_LIGHT, Point(-4.9, 4.9, -1), Colour(1, 1, 1));
+    w.addLight(&light);
+
+    /* Set the camera */
+    Camera camera = Camera(400, 100, 1.152);
+    camera.setTransform(viewTransform(Point(-2.6, 1.5, -3.9),
+                                      Point(-0.6, 1, -0.8),
+                                      Vector(0, 1, 0)));
+
+    /* Now render it */
+    Canvas image = camera.render(w);
+
+    image.SaveAsPNG("ch11_test.png");
+
+
+    return 0;
+}

tests/ch6_test.cpp

@@ -1,6 +1,6 @@
 /*
  *  DoRayMe - a quick and dirty Raytracer
- *  Render test for chapter 5 "Put it together".
+ *  Render test for chapter 6 "Put it together".
  *
  *  Created by Manoël Trapier
  *  Copyright (c) 2020 986-Studio.

tests/ch7_test.cpp

@@ -1,6 +1,6 @@
 /*
  *  DoRayMe - a quick and dirty Raytracer
- *  Render test for chapter 5 "Put it together".
+ *  Render test for chapter 7 "Put it together".
  *
  *  Created by Manoël Trapier
  *  Copyright (c) 2020 986-Studio.

tests/ch9_test.cpp

@@ -1,6 +1,6 @@
 /*
  *  DoRayMe - a quick and dirty Raytracer
- *  Render test for chapter 5 "Put it together".
+ *  Render test for chapter 9.
  *
  *  Created by Manoël Trapier
  *  Copyright (c) 2020 986-Studio.

tests/intersect_test.cpp

@@ -9,6 +9,7 @@
 #include <intersect.h>
 #include <intersection.h>
 #include <sphere.h>
+#include <plane.h>
 #include <transformation.h>
 #include <gtest/gtest.h>
 
@@ -190,3 +191,115 @@ TEST(IntersectTest, The_hit_should_offset_the_point)
     ASSERT_LT(comps.overHitPoint.z, -getEpsilon() / 2);
     ASSERT_GT(comps.hitPoint.z, comps.overHitPoint.z);
 }
+
+TEST(IntersectTest, Precomputing_the_reflection_vector)
+{
+    Plane s = Plane();
+    Ray r = Ray(Point(0, 1, -1), Vector(0, -sqrt(2) / 2, sqrt(2) / 2));
+    Intersection i = Intersection(sqrt(2), &s);
+
+    Computation comps = i.prepareComputation(r);
+
+    ASSERT_EQ(comps.reflectVector, Vector(0, sqrt(2) / 2, sqrt(2) / 2));
+}
+
+TEST(IntersectTest, Finding_n1_and_n2_at_various_intersections)
+{
+    int i;
+    double n1_res[6] = { 1.0, 1.5, 2.0, 2.5, 2.5, 1.5 };
+    double n2_res[6] = { 1.5, 2.0, 2.5, 2.5, 1.5, 1.0 };
+
+    GlassSphere A = GlassSphere();
+    A.setTransform(scaling(2, 2, 2));
+    A.material.refractiveIndex = 1.5;
+
+    GlassSphere B = GlassSphere();
+    B.setTransform(translation(0, 0, -0.25));
+    B.material.refractiveIndex = 2.0;
+
+    GlassSphere C = GlassSphere();
+    C.setTransform(translation(0, 0, 0.25));
+    C.material.refractiveIndex = 2.5;
+
+    Ray r = Ray(Point(0, 0, -4), Vector(0, 0, 1));
+    Intersect xs = Intersect();
+    xs.add(Intersection(2.0, &A));
+    xs.add(Intersection(2.75, &B));
+    xs.add(Intersection(3.25, &C));
+    xs.add(Intersection(4.75, &B));
+    xs.add(Intersection(5.25, &C));
+    xs.add(Intersection(6, &A));
+
+    for(i = 0; i < xs.count(); i++)
+    {
+        Intersection inter = xs[i];
+        Computation comps = inter.prepareComputation(r, &xs);
+        ASSERT_EQ(comps.n1, n1_res[i]);
+        ASSERT_EQ(comps.n2, n2_res[i]);
+    }
+}
+
+TEST(IntersectTest, The_under_point_is_offset_below_the_surface)
+{
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    GlassSphere shape = GlassSphere();
+    shape.setTransform(translation(0, 0, 1));
+
+    Intersection i = Intersection(5, &shape);
+    Intersect xs = Intersect();
+    xs.add(i);
+
+    Computation comps = i.prepareComputation(r, &xs);
+
+    ASSERT_TRUE(double_equal(comps.underHitPoint.z, getEpsilon() / 2));
+    ASSERT_LT(comps.hitPoint.z, comps.underHitPoint.z);
+}
+
+TEST(IntersectTest, The_Schlick_approximation_under_total_internal_reflection)
+{
+    GlassSphere shape = GlassSphere();
+
+    Ray r = Ray(Point(0, 0, sqrt(2)/2), Vector(0, 1, 0));
+    Intersect xs = Intersect();
+    xs.add(Intersection(-sqrt(2)/2, &shape));
+    xs.add(Intersection(sqrt(2)/2, &shape));
+
+    Computation comps = xs[1].prepareComputation(r, &xs);
+    double reflectance = comps.schlick();
+
+    ASSERT_EQ(reflectance, 1.0);
+}
+
+TEST(IntersectTest, The_Schlick_approximation_with_a_perpendicular_viewing_angle)
+{
+    GlassSphere shape = GlassSphere();
+
+    Ray r = Ray(Point(0, 0, 0), Vector(0, 1, 0));
+    Intersect xs = Intersect();
+    xs.add(Intersection(-1, &shape));
+    xs.add(Intersection(1, &shape));
+
+    Computation comps = xs[1].prepareComputation(r, &xs);
+    double reflectance = comps.schlick();
+
+    ASSERT_TRUE(double_equal(reflectance, 0.04));
+}
+
+TEST(IntersectTest, The_Schlick_approximation_with_small_angle_and_n2_gt_n1)
+{
+    GlassSphere shape = GlassSphere();
+
+    Ray r = Ray(Point(0, 0.99, -2), Vector(0, 0, 1));
+    Intersect xs = Intersect();
+    xs.add(Intersection(1.8589, &shape));
+
+    Computation comps = xs[0].prepareComputation(r, &xs);
+    double reflectance = comps.schlick();
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00001);
+
+    ASSERT_TRUE(double_equal(reflectance, 0.48873));
+
+    set_equal_precision(FLT_EPSILON);
+}

tests/material_test.cpp

@@ -107,3 +107,18 @@ TEST(MaterialTest, Lighting_with_the_surface_in_shadow)
 
     ASSERT_EQ(result, Colour(0.1, 0.1, 0.1));
 }
+
+TEST(MaterialTest, Reflectivity_for_the_default_material)
+{
+    Material m = Material();
+
+    ASSERT_EQ(m.reflective, 0);
+}
+
+TEST(MaterialTest, Transparency_and_refractive_index_for_the_default_material)
+{
+    Material m = Material();
+
+    ASSERT_EQ(m.transparency, 0.0);
+    ASSERT_EQ(m.refractiveIndex, 1.0);
+}

tests/sphere_test.cpp

@@ -199,3 +199,12 @@ TEST(SphereTest, A_sphere_may_be_assigned_a_material)
 
     ASSERT_EQ(s.material, m);
 }
+
+TEST(SphereTest, A_helper_for_producing_a_sphere_with_a_glassy_material)
+{
+    GlassSphere s = GlassSphere();
+
+    ASSERT_EQ(s.transformMatrix, Matrix4().identity());
+    ASSERT_EQ(s.material.transparency, 1.0);
+    ASSERT_EQ(s.material.refractiveIndex, 1.5);
+}

tests/world_test.cpp

@@ -12,8 +12,10 @@
 #include <material.h>
 #include <transformation.h>
 #include <worldbuilder.h>
+#include <testpattern.h>
 #include <math.h>
 #include <gtest/gtest.h>
+#include <plane.h>
 
 
 TEST(WorldTest, Creating_a_world)
@@ -168,3 +170,260 @@ TEST(WorldTest, Shade_hit_is_given_an_intersection_in_shadow)
 
     ASSERT_EQ(c, Colour(0.1, 0.1, 0.1));
 };
+
+TEST(WorldTest, The_reflected_colour_for_a_non_reflective_material)
+{
+    World w = DefaultWorld();
+    Ray r = Ray(Point(0, 0, 0), Vector(0, 0, 1));
+
+    Shape *shape = w.getObject(1); /* The second object */
+    shape->material.ambient = 1; /* We use this to get a predictable colour */
+
+    Intersection i = Intersection(1, shape);
+
+    Computation comps = i.prepareComputation(r);
+    Colour colour = w.reflectColour(comps);
+
+    ASSERT_EQ(colour, Colour(0, 0, 0));
+}
+
+TEST(WorldTest, The_reflected_colour_for_a_reflective_material)
+{
+    World w = DefaultWorld();
+    Plane shape = Plane();
+    shape.material.reflective = 0.5;
+    shape.setTransform(translation(0, -1, 0));
+    w.addObject(&shape);
+
+    Ray r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2));
+
+    Intersection i = Intersection(sqrt(2), &shape);
+
+    Computation comps = i.prepareComputation(r);
+    Colour colour = w.reflectColour(comps);
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00002);
+
+    ASSERT_EQ(colour, Colour(0.19032, 0.2379, 0.14274));
+
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(WorldTest, Shade_hit_with_a_reflective_material)
+{
+    World w = DefaultWorld();
+    Plane shape = Plane();
+    shape.material.reflective = 0.5;
+    shape.setTransform(translation(0, -1, 0));
+    w.addObject(&shape);
+
+    Ray r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2));
+
+    Intersection i = Intersection(sqrt(2), &shape);
+
+    Computation comps = i.prepareComputation(r);
+    Tuple colour = w.shadeHit(comps);
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00005);
+
+    ASSERT_EQ(colour, Colour(0.87677, 0.92436, 0.82918));
+
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(WorldTest, Colour_at_with_mutually_reflective_surfaces)
+{
+    World w = World();
+
+    Light l = Light(POINT_LIGHT, Point(0, 0, 0), Colour(1, 1, 1));
+
+    w.addLight(&l);
+
+    Plane lower = Plane();
+    lower.material.reflective = 1;
+    lower.setTransform(translation(0, -1, 0));
+
+    Plane higher = Plane();
+    higher.material.reflective = 1;
+    higher.setTransform(translation(0, 1, 0));
+
+    w.addObject(&lower);
+    w.addObject(&higher);
+
+    Ray r = Ray(Point(0, 0, 0), Vector(0, 1, 0));
+
+    /* It should just exit, we don't care about the actual colour */
+    w.colourAt(r);
+
+    SUCCEED();
+}
+
+TEST(WorldTest, The_reflected_colour_at_the_maximum_recursion_depth)
+{
+    World w = DefaultWorld();
+    Plane shape = Plane();
+    shape.material.reflective = 0.5;
+    shape.setTransform(translation(0, -1, 0));
+    w.addObject(&shape);
+
+    Ray r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2));
+    Intersection i = Intersection(sqrt(2), &shape);
+
+    Computation comps = i.prepareComputation(r);
+    Tuple colour = w.reflectColour(comps, 0);
+
+    /* Temporary lower the precision */
+    ASSERT_EQ(colour, Colour(0, 0, 0));
+}
+
+TEST(WorldTest, The_refracted_colour_with_an_opaque_surface)
+{
+    World w = DefaultWorld();
+    Shape *shape = w.getObject(0);
+
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    Intersect xs = Intersect();
+    xs.add(Intersection(4, shape));
+    xs.add(Intersection(6, shape));
+
+    Computation comps = xs[0].prepareComputation(r, &xs);
+    Colour c = w.refractedColour(comps, 5);
+
+    ASSERT_EQ(c, Colour(0, 0, 0));
+}
+
+TEST(WorldTest, The_refracted_colour_at_the_maximum_recursive_depth)
+{
+    World w = DefaultWorld();
+    Shape *shape = w.getObject(0);
+
+    shape->material.transparency = 1.0;
+    shape->material.refractiveIndex = 1.5;
+
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    Intersect xs = Intersect();
+    xs.add(Intersection(4, shape));
+    xs.add(Intersection(6, shape));
+
+    Computation comps = xs[0].prepareComputation(r, &xs);
+    Colour c = w.refractedColour(comps, 0);
+
+    ASSERT_EQ(c, Colour(0, 0, 0));
+}
+
+TEST(WorldTest, The_refracted_colour_under_total_internal_reflection)
+{
+    World w = DefaultWorld();
+    Shape *shape = w.getObject(0);
+
+    shape->material.transparency = 1.0;
+    shape->material.refractiveIndex = 1.5;
+
+    Ray r = Ray(Point(0, 0, sqrt(2)/2), Vector(0, 1, 0));
+    Intersect xs = Intersect();
+    xs.add(Intersection(-sqrt(2)/2, shape));
+    xs.add(Intersection(sqrt(2)/2, shape));
+
+    Computation comps = xs[1].prepareComputation(r, &xs);
+    Colour c = w.refractedColour(comps, 5);
+
+    ASSERT_EQ(c, Colour(0, 0, 0));
+}
+
+TEST(WorldTest, The_refracted_coloud_with_a_refracted_ray)
+{
+    World w = DefaultWorld();
+
+    Shape *A = w.getObject(0);
+    A->material.ambient = 1.0;
+    A->material.pattern = new TestPattern();
+
+    Shape *B = w.getObject(1);
+    B->material.transparency = 1.0;
+    B->material.refractiveIndex = 1.5;
+
+    Ray r = Ray(Point(0, 0, 0.1), Vector(0, 1, 0));
+    Intersect xs = Intersect();
+    xs.add(Intersection(-0.9899, A));
+    xs.add(Intersection(-0.4899, B));
+    xs.add(Intersection(0.4899, B));
+    xs.add(Intersection(0.9899, A));
+
+    Computation comps = xs[2].prepareComputation(r, &xs);
+    Colour c = w.refractedColour(comps, 5);
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00005);
+
+    ASSERT_EQ(c, Colour(0, 0.99888, 0.04725));
+
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(WorldTest, Shade_hit_with_a_transparent_material)
+{
+    World w = DefaultWorld();
+
+    Plane floor = Plane();
+    floor.setTransform(translation(0, -1, 0));
+    floor.material.transparency = 0.5;
+    floor.material.refractiveIndex = 1.5;
+    w.addObject(&floor);
+
+    Sphere ball = Sphere();
+    ball.material.colour = Colour(1, 0, 0);
+    ball.material.ambient = 0.5;
+    ball.setTransform(translation(0, -3.5, -0.5));
+    w.addObject(&ball);
+
+    Ray r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2));
+    Intersect xs = Intersect();
+    xs.add(Intersection(sqrt(2), &floor));
+
+    Computation comps = xs[0].prepareComputation(r, &xs);
+
+    Tuple c = w.shadeHit(comps, 5);
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00001);
+
+    ASSERT_EQ(c, Colour(0.93642, 0.68642, 0.68642));
+
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(WorldTest, Shade_hit_with_a_reflective_transparent_material)
+{
+    World w = DefaultWorld();
+
+    Ray r = Ray(Point(0, 0, -3), Vector(0, -sqrt(2)/2, sqrt(2)/2));
+
+    Plane floor = Plane();
+    floor.setTransform(translation(0, -1, 0));
+    floor.material.transparency = 0.5;
+    floor.material.reflective = 0.5;
+    floor.material.refractiveIndex = 1.5;
+    w.addObject(&floor);
+
+    Sphere ball = Sphere();
+    ball.material.colour = Colour(1, 0, 0);
+    ball.material.ambient = 0.5;
+    ball.setTransform(translation(0, -3.5, -0.5));
+    w.addObject(&ball);
+
+    Intersect xs = Intersect();
+    xs.add(Intersection(sqrt(2), &floor));
+
+    Computation comps = xs[0].prepareComputation(r, &xs);
+
+    Tuple c = w.shadeHit(comps, 5);
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00001);
+
+    ASSERT_EQ(c, Colour(0.93391, 0.69643, 0.69243));
+
+    set_equal_precision(FLT_EPSILON);
+}