Add Chapter 5 "putting it together" example.

A bit more clean (on the code side)

CMakeLists.txt

@@ -6,17 +6,6 @@ project(DoRayMe)
 
 set(CMAKE_CXX_STANDARD 11)
 
-
-#Add external projects that directly need to be builded
-ExternalProject_Add(googletest
-        SOURCE_DIR        "${CMAKE_CURRENT_SOURCE_DIR}/external/googletest"
-        BINARY_DIR        "${CMAKE_CURRENT_BINARY_DIR}/external/googletest"
-        CONFIGURE_COMMAND ""
-        BUILD_COMMAND     ""
-        INSTALL_COMMAND   ""
-        TEST_COMMAND      ""
-)
-
 # LodePNG don't make a .a or .so, so let's build a library here
 add_library(LodePNG STATIC)
 set(LODEPNG_INCLUDE_FOLDER ${CMAKE_CURRENT_SOURCE_DIR}/external/lodepng)
@@ -25,5 +14,11 @@ target_sources(LodePNG PRIVATE external/lodepng/lodepng.cpp external/lodepng/lod
 
 # Main app
 add_subdirectory(source)
-# Unit Tests
-add_subdirectory(tests)
+
+option(PACKAGE_TESTS "Build the tests" ON)
+if(PACKAGE_TESTS)
+    enable_testing()
+    include(GoogleTest)
+	 add_subdirectory("${PROJECT_SOURCE_DIR}/external/googletest" "external/googletest")
+    add_subdirectory(tests)
+endif()

source/CMakeLists.txt

@@ -3,8 +3,11 @@
 # First most is build as a library
 add_library(rayonnement STATIC)
 
-set(RAY_HEADERS include/tuples.h include/math_helper.h include/colour.h include/canvas.h)
-set(RAY_SOURCES tuples.cpp math_helper.cpp colour.cpp canvas.cpp)
+set(RAY_HEADERS include/tuple.h include/math_helper.h include/colour.h include/canvas.h
+        include/matrix.h include/transformation.h include/intersect.h include/intersection.h
+        include/object.h include/ray.h include/sphere.h)
+set(RAY_SOURCES tuple.cpp math_helper.cpp colour.cpp canvas.cpp matrix.cpp transformation.cpp intersect.cpp
+        objects/object.cpp objects/ray.cpp objects/sphere.cpp)
 
 target_include_directories(rayonnement PUBLIC include)
 target_sources(rayonnement PRIVATE ${RAY_HEADERS} ${RAY_SOURCES})

source/include/colour.h

@@ -9,7 +9,7 @@
 #ifndef DORAYME_COLOUR_H
 #define DORAYME_COLOUR_H
 
-#include <tuples.h>
+#include <tuple.h>
 
 class Colour : public Tuple
 {

source/include/intersect.h

@@ -0,0 +1,29 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Intersect header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_INTERSECT_H
+#define DORAYME_INTERSECT_H
+
+#include <stdint.h>
+#include <intersection.h>
+
+class Intersect
+{
+private:
+    Intersection *list;
+    uint32_t num;
+    uint32_t allocated;
+public:
+    Intersect();
+    void add(Intersection i);
+    int count() { return this->num; };
+    Intersection operator[](const int p) { return this->list[p]; }
+    Intersection hit();
+};
+
+#endif //DORAYME_INTERSECT_H

source/include/intersection.h

@@ -0,0 +1,29 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Intersection header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_INTERSECTION_H
+#define DORAYME_INTERSECTION_H
+
+#include <stdlib.h>
+
+class Object;
+
+class Intersection
+{
+public:
+    double t;
+    Object *object;
+
+public:
+    Intersection(double t, Object *object) : t(t), object(object) { };
+    bool nothing() { return (this->object == nullptr); };
+
+    bool operator==(const Intersection &b) const { return ((this->t == b.t) && (this->object == b.object)); };
+};
+
+#endif //DORAYME_INTERSECTION_H

source/include/math_helper.h

@@ -10,6 +10,11 @@
 #ifndef DORAYME_MATH_HELPER_H
 #define DORAYME_MATH_HELPER_H
 
+#include <math.h>
+
+void set_equal_precision(double v);
 bool double_equal(double a, double b);
 
+double deg_to_rad(double deg);
+
 #endif //DORAYME_MATH_HELPER_H

source/include/matrix.h

@@ -0,0 +1,67 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Matrix header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_MATRIX_H
+#define DORAYME_MATRIX_H
+
+#include <tuple.h>
+
+class Matrix
+{
+protected:
+    /* 4x4 is the default */
+    double data[4*4];
+    int size;
+
+public:
+    Matrix(int size = 4);
+    Matrix(double values[], int size);
+
+    double get(int x, int y) const { return this->data[this->size * x + y]; };
+    void set(int x, int y, double v) { this->data[this->size * x + y] = v; };
+
+    Matrix identity();
+    Matrix transpose();
+    double determinant();
+    Matrix submatrix(int row, int column);
+    Matrix inverse();
+    double minor(int row, int column) { return this->submatrix(row, column).determinant(); }
+    double cofactor(int row, int column) { return (((column+row)&1)?-1:1) * this->minor(row, column); }
+    bool operator==(const Matrix &b) const;
+    bool operator!=(const Matrix &b) const;
+
+    bool isInvertible() { return this->determinant() != 0; }
+
+    Matrix operator*(const Matrix &b) const;
+    Tuple operator*(const Tuple &b) const;
+};
+
+class Matrix4: public Matrix
+{
+public:
+    Matrix4() : Matrix(4) { };
+    Matrix4(double values[]) : Matrix(values, 4) { };
+};
+
+class Matrix3 : public Matrix
+{
+public:
+    Matrix3() : Matrix(3) { };
+    Matrix3(double values[]) : Matrix(values, 3) { };
+};
+
+class Matrix2 : public Matrix
+{
+private:
+    using Matrix::data;
+public:
+    Matrix2() : Matrix(2) { };
+    Matrix2(double values[]) : Matrix(values, 2) { };
+};
+
+#endif /* DORAYME_MATRIX_H */

source/include/object.h

@@ -0,0 +1,35 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Object header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_OBJECT_H
+#define DORAYME_OBJECT_H
+
+class Object;
+
+#include <ray.h>
+#include <tuple.h>
+#include <matrix.h>
+#include <intersect.h>
+
+/* Base class for all object that can be presented in the world */
+class Object
+{
+public:
+    Matrix transformMatrix;
+    Matrix inverseTransform;
+
+public:
+    Object();
+
+    virtual Intersect intersect(Ray r);
+    void setTransform(Matrix transform);
+    Ray transform(Ray r) {  return Ray(this->transformMatrix * r.origin, this->transformMatrix * r.direction); };
+    Ray invTransform(Ray r) {  return Ray(this->inverseTransform * r.origin, this->inverseTransform * r.direction); };
+};
+
+#endif //DORAYME_OBJECT_H

source/include/ray.h

@@ -0,0 +1,25 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Ray header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_RAY_H
+#define DORAYME_RAY_H
+
+#include <tuple.h>
+
+class Ray
+{
+public:
+    Tuple direction;
+    Tuple origin;
+
+    Ray(Tuple origin, Tuple direction) : origin(origin), direction(direction) { };
+
+    Tuple position(double t) { return this->origin + this->direction * t; };
+};
+
+#endif //DORAYME_RAY_H

source/include/sphere.h

@@ -0,0 +1,23 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Sphere header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_SPHERE_H
+#define DORAYME_SPHERE_H
+
+#include <object.h>
+#include <ray.h>
+#include <intersect.h>
+
+class Sphere : public Object
+{
+public:
+    /* All sphere are at (0, 0, 0) and radius 1 in the object space */
+    virtual Intersect intersect(Ray r);
+};
+
+#endif //DORAYME_SPHERE_H

source/include/transformation.h

@@ -0,0 +1,24 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Transformation header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_TRANSFORMATION_H
+#define DORAYME_TRANSFORMATION_H
+
+#include <matrix.h>
+
+Matrix translation(double x, double y, double z);
+
+Matrix scaling(double x, double y, double z);
+
+Matrix rotation_x(double angle);
+Matrix rotation_y(double angle);
+Matrix rotation_z(double angle);
+
+Matrix shearing(double Xy, double Xx, double Yx, double Yz, double Zx, double Zy);
+
+#endif /* DORAYME_TRANSFORMATION_H */

source/include/tuple.h

@@ -6,8 +6,8 @@
  *  Copyright (c) 2020 986-Studio.
  *
  */
-#ifndef DORAYME_TUPLES_H
-#define DORAYME_TUPLES_H
+#ifndef DORAYME_TUPLE_H
+#define DORAYME_TUPLE_H
 
 #include <math_helper.h>
 
@@ -41,6 +41,8 @@ public:
     double magnitude();
     Tuple normalise();
     double dot(const Tuple &b);
+
+    Tuple cross(const Tuple &b) const;
 };
 
 class Point: public Tuple
@@ -53,7 +55,6 @@ class Vector: public Tuple
 {
 public:
     Vector(double x, double y, double z) : Tuple(x, y, z, 0.0) {};
-    Vector cross(const Vector &b) const;
 };
 
-#endif /* DORAYME_TUPLES_H */
+#endif /*DORAYME_TUPLE_H*/

source/intersect.cpp

@@ -0,0 +1,54 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Intersect implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <stdlib.h>
+#include <math_helper.h>
+#include <intersect.h>
+
+#include <float.h>
+
+#define MIN_ALLOC (2)
+
+Intersect::Intersect()
+{
+    this->allocated = MIN_ALLOC;
+    this->list = (Intersection *)calloc(sizeof(Object *), MIN_ALLOC);
+    this->num = 0;
+}
+
+void Intersect::add(Intersection i)
+{
+    if ((this->num + 1) < this->allocated)
+    {
+        this->allocated *= 2;
+        this->list = (Intersection *)realloc(this->list, sizeof(Object *) * this->allocated);
+    }
+    this->list[this->num++] = i;
+}
+
+Intersection Intersect::hit()
+{
+    int i;
+    double minHit = DBL_MAX;
+    uint32_t curHit = -1;
+    for(i = 0; i < this->num; i++)
+    {
+        if ((this->list[i].t >= 0) && (this->list[i].t < minHit))
+        {
+            curHit = i;
+            minHit = this->list[i].t;
+        }
+    }
+
+    if (curHit == -1)
+    {
+        return Intersection(0, nullptr);
+    }
+
+    return this->list[curHit];
+}

source/math_helper.cpp

@@ -11,7 +11,19 @@
 #include <float.h>
 #include <math_helper.h>
 
+static double current_precision = FLT_EPSILON;
+
+void set_equal_precision(double v)
+{
+    current_precision = v;
+}
+
 bool double_equal(double a, double b)
 {
-    return fabs(a - b) < DBL_EPSILON;
+    return fabs(a - b) < current_precision;
 }
+
+double deg_to_rad(double deg)
+{
+   return deg * M_PI / 180.;
+}

source/matrix.cpp

@@ -0,0 +1,201 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Matrix implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+
+#include <stdio.h>
+#include <matrix.h>
+#include <tuple.h>
+#include <math_helper.h>
+
+Matrix::Matrix(int width)
+{
+    int i;
+
+    this->size = width;
+
+    for(i = 0; i < width*width; i++)
+    {
+        this->data[i] = 0;
+    }
+};
+
+Matrix::Matrix(double values[], int width)
+{
+    int x, y;
+
+    this->size = width;
+
+    for(y = 0; y < this->size; y++)
+    {
+        for (x = 0 ; x < this->size ; x++)
+        {
+            this->data[this->size * x + y] = values[this->size * x + y];
+        }
+    }
+};
+
+bool Matrix::operator==(const Matrix &b) const
+{
+    int i;
+    if (this->size != b.size)
+    {
+        /* If they are not the same size don't even bother */
+        return false;
+    }
+
+    for(i = 0; i < this->size*this->size; i++)
+    {
+        if (!double_equal(this->data[i], b.data[i]))
+        {
+            return false;
+        }
+    }
+
+    return true;
+}
+
+bool Matrix::operator!=(const Matrix &b) const
+{
+    int i;
+    if (this->size != b.size)
+    {
+        /* If they are not the same size don't even bother */
+        return true;
+    }
+
+    for(i = 0; i < this->size*this->size; i++)
+    {
+        if (!double_equal(this->data[i], b.data[i]))
+        {
+            return true;
+        }
+    }
+    return false;
+}
+
+Matrix Matrix::operator*(const Matrix &b) const
+{
+    int x, y, k;
+    Matrix ret = Matrix(this->size);
+
+    if (this->size == b.size)
+    {
+        for (y = 0 ; y < this->size ; y++)
+        {
+            for (x = 0 ; x < this->size ; x++)
+            {
+                double v = 0;
+                for (k = 0 ; k < this->size ; k++)
+                {
+                    v += this->get(x, k) * b.get(k, y);
+                }
+                ret.set(x, y, v);
+            }
+        }
+    }
+    return ret;
+}
+
+Tuple Matrix::operator*(const Tuple &b) const
+{
+    return Tuple(b.x * this->get(0, 0) + b.y * this->get(0, 1) + b.z * this->get(0, 2) + b.w * this->get(0, 3),
+                 b.x * this->get(1, 0) + b.y * this->get(1, 1) + b.z * this->get(1, 2) + b.w * this->get(1, 3),
+                 b.x * this->get(2, 0) + b.y * this->get(2, 1) + b.z * this->get(2, 2) + b.w * this->get(2, 3),
+                 b.x * this->get(3, 0) + b.y * this->get(3, 1) + b.z * this->get(3, 2) + b.w * this->get(3, 3));
+}
+
+Matrix Matrix::identity()
+{
+    int i;
+    for(i = 0; i < this->size; i++)
+    {
+        this->set(i, i, 1);
+    }
+    return *this;
+}
+
+Matrix Matrix::transpose()
+{
+    int x, y;
+    Matrix ret = Matrix(this->size);
+    for (y = 0 ; y < this->size ; y++)
+    {
+        for (x = 0 ; x < this->size ; x++)
+        {
+            ret.set(y, x, this->get(x, y));
+        }
+    }
+    return ret;
+}
+
+Matrix Matrix::submatrix(int row, int column)
+{
+    int i, j;
+    int x = 0, y = 0;
+    Matrix ret = Matrix(this->size - 1);
+    for (i = 0 ; i < this->size ; i++)
+    {
+        if (i == row)
+        {
+            /* Skip that row */
+            continue;
+        }
+        y = 0;
+        for (j = 0 ; j < this->size ; j++)
+        {
+            if (j == column)
+            {
+                /* skip that column */
+                continue;
+            }
+            ret.set(x, y, this->get(i, j));
+            y++;
+        }
+        x++;
+    }
+    return ret;
+}
+
+double Matrix::determinant()
+{
+    double det = 0;
+    if (this->size == 2)
+    {
+        det = this->data[0] * this->data[3] - this->data[1] * this->data[2];
+    }
+    else
+    {
+        int col;
+        for(col = 0; col < this->size; col++)
+        {
+            det = det + this->get(0, col) * this->cofactor(0, col);
+        }
+    }
+    return det;
+}
+
+Matrix Matrix::inverse()
+{
+    Matrix ret = Matrix(this->size);
+
+    if (this->isInvertible())
+    {
+        int row, col;
+        double c;
+        for (row = 0; row < this->size; row++)
+        {
+            for (col = 0; col < this->size; col++)
+            {
+                c = this->cofactor(row, col);
+                ret.set(col, row, c / this->determinant());
+            }
+        }
+    }
+
+    return ret;
+}

source/objects/object.cpp

@@ -0,0 +1,31 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Object implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+
+#include <ray.h>
+#include <object.h>
+#include <matrix.h>
+#include <tuple.h>
+#include <intersect.h>
+
+Object::Object()
+{
+    this->transformMatrix = Matrix4().identity();
+    this->inverseTransform = this->transformMatrix.inverse();
+}
+
+Intersect Object::intersect(Ray r)
+{
+    return Intersect();
+};
+
+void Object::setTransform(Matrix transform)
+{
+    this->transformMatrix = transform;
+    this->inverseTransform = transform.inverse();
+}

source/objects/ray.cpp

@@ -0,0 +1,8 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Ray implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */

source/objects/sphere.cpp

@@ -0,0 +1,38 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Sphere implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <math.h>
+
+#include <sphere.h>
+#include <ray.h>
+#include <tuple.h>
+#include <intersect.h>
+
+Intersect Sphere::intersect(Ray r)
+{
+    Intersect ret;
+    double a, b, c, discriminant;
+
+    Ray transRay = this->invTransform(r);
+
+    Tuple sphere_to_ray = transRay.origin - Point(0, 0, 0);
+
+    a = transRay.direction.dot(transRay.direction);
+    b = 2 * transRay.direction.dot(sphere_to_ray);
+    c = sphere_to_ray.dot(sphere_to_ray) - 1;
+
+    discriminant = b * b - 4 * a * c;
+
+    if (discriminant >= 0)
+    {
+        ret.add(Intersection((-b - sqrt(discriminant)) / (2 * a), this));
+        ret.add(Intersection((-b + sqrt(discriminant)) / (2 * a), this));
+    }
+
+    return ret;
+}

source/transformation.cpp

@@ -0,0 +1,84 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Transformation implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <math.h>
+
+#include <transformation.h>
+
+Matrix translation(double x, double y, double z)
+{
+   Matrix ret = Matrix4().identity();
+   
+   ret.set(0, 3, x);
+   ret.set(1, 3, y);
+   ret.set(2, 3, z);
+   
+   return ret;
+}
+
+Matrix scaling(double x, double y, double z)
+{
+   Matrix ret = Matrix4();
+   
+   ret.set(0, 0, x);
+   ret.set(1, 1, y);
+   ret.set(2, 2, z);
+   ret.set(3, 3, 1);
+   
+   return ret;
+}
+
+Matrix rotation_x(double angle)
+{
+   Matrix ret = Matrix4().identity();
+   
+   ret.set(1, 1, cos(angle));
+   ret.set(1, 2, -sin(angle));
+   ret.set(2, 1, sin(angle));
+   ret.set(2, 2, cos(angle));
+   
+   return ret;
+}
+
+Matrix rotation_y(double angle)
+{
+   Matrix ret = Matrix4().identity();
+   
+   ret.set(0, 0, cos(angle));
+   ret.set(0, 2, sin(angle));
+   ret.set(2, 0, -sin(angle));
+   ret.set(2, 2, cos(angle));
+   
+   return ret;
+}
+
+Matrix rotation_z(double angle)
+{
+   Matrix ret = Matrix4().identity();
+   
+   ret.set(0, 0, cos(angle));
+   ret.set(0, 1, -sin(angle));
+   ret.set(1, 0, sin(angle));
+   ret.set(1, 1, cos(angle));
+   
+   return ret;
+}
+
+Matrix shearing(double Xy, double Xz, double Yx, double Yz, double Zx, double Zy)
+{
+    Matrix ret = Matrix4().identity();
+
+    ret.set(0, 1, Xy);
+    ret.set(0, 2, Xz);
+    ret.set(1, 0, Yx);
+    ret.set(1, 2, Yz);
+    ret.set(2, 0, Zx);
+    ret.set(2, 1, Zy);
+
+    return ret;
+}

source/tuple.cpp

@@ -6,7 +6,7 @@
  *  Copyright (c) 2020 986-Studio.
  *
  */
-#include <tuples.h>
+#include <tuple.h>
 
 #include <math.h>
 
@@ -27,9 +27,10 @@ double Tuple::dot(const Tuple &b)
     return this->x * b.x + this->y * b.y + this->z * b.z + this->w * b.w;
 }
 
-Vector Vector::cross(const Vector &b) const
+Tuple Tuple::cross(const Tuple &b) const
 {
-    return Vector(this->y * b.z - this->z * b.y,
-                  this->z * b.x - this->x * b.z,
-                  this->x * b.y - this->y * b.x);
+    return Tuple(this->y * b.z - this->z * b.y,
+                 this->z * b.x - this->x * b.z,
+                 this->x * b.y - this->y * b.x,
+                 0);
 }

tests/CMakeLists.txt

@@ -3,10 +3,22 @@ project(DoRayTested)
 set(THREADS_PREFER_PTHREAD_FLAG ON)
 find_package(Threads REQUIRED)
 
-set(TESTS_SRC tuples_test.cpp colour_test.cpp canvas_test.cpp)
+set(TESTS_SRC tuple_test.cpp colour_test.cpp canvas_test.cpp matrix_test.cpp transformation_test.cpp ray_test.cpp
+        intersect_test.cpp sphere_test.cpp)
 
 add_executable(testMyRays)
 target_include_directories(testMyRays PUBLIC ${gtest_SOURCE_DIR}/include ${gtest_SOURCE_DIR})
 target_include_directories(testMyRays PUBLIC ../source/include)
 target_sources(testMyRays PRIVATE ${TESTS_SRC})
-target_link_libraries(testMyRays gtest gtest_main rayonnement Threads::Threads)
+target_link_libraries(testMyRays gtest gtest_main rayonnement Threads::Threads)
+
+gtest_discover_tests(testMyRays
+   WORKING_DIRECTORY ${PROJECT_DIR}
+   PROPERTIES VS_DEBUGGER_WORKING_DIRECTORY "${PROJECT_DIR}"
+   )
+
+
+add_executable(ch5_test)
+target_include_directories(ch5_test PUBLIC ../source/include)
+target_sources(ch5_test PRIVATE ch5_test.cpp)
+target_link_libraries(ch5_test rayonnement)

tests/ch5_test.cpp

@@ -0,0 +1,46 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Render test for chapter 5 "Put it together".
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <ray.h>
+#include <sphere.h>
+#include <colour.h>
+#include <canvas.h>
+#include <transformation.h>
+
+int main()
+{
+    int x, y;
+    Canvas c = Canvas(100, 100);
+
+    Sphere s = Sphere();
+    Colour red = Colour(1, 0, 0);
+
+    Point cameraOrigin = Point(0, 0, -5);
+    double wallDistance = 10;
+    double wallSize = 7;
+    double pixelSize = wallSize / c.width;
+    for(y = 0; y < c.height; y++)
+    {
+        double worldY = (wallSize / 2) - pixelSize * y;
+        for(x = 0; x < c.width; x++)
+        {
+            double worldX = (wallSize / 2) - pixelSize * x;
+            Point position = Point(worldX, worldY, wallDistance);
+            Ray r = Ray(cameraOrigin, (position - cameraOrigin).normalise());
+            Intersect xs = s.intersect(r);
+
+            if (!xs.hit().nothing())
+            {
+                c.put_pixel(x, y, red);
+            }
+        }
+    }
+
+    c.SaveAsPNG("ch5_test.png");
+    return 0;
+}

tests/intersect_test.cpp

@@ -0,0 +1,132 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Intersect unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <intersect.h>
+#include <sphere.h>
+#include <gtest/gtest.h>
+
+
+TEST(IntersectTest, Creating_an_intersect_and_do_some_check)
+{
+    Intersect i;
+
+    ASSERT_EQ(i.count(), 0);
+
+    i.add(Intersection(1.0, nullptr));
+    i.add(Intersection(4.2, nullptr));
+
+    ASSERT_EQ(i.count(), 2);
+
+    ASSERT_EQ(i[0].t, 1.0);
+    ASSERT_EQ(i[1].t, 4.2);
+}
+
+TEST(IntersectTest, An_intersection_encapsulate_t_and_object)
+{
+    Sphere s = Sphere();
+    Intersection i = Intersection(3.5, &s);
+
+    ASSERT_EQ(i.t, 3.5);
+    ASSERT_EQ(i.object, (Object *)&s);
+}
+
+TEST(IntersectTest, Aggregating_intersections)
+{
+    Sphere s = Sphere();
+    Intersection i1 = Intersection(1, &s);
+    Intersection i2 = Intersection(2, &s);
+
+    Intersect xs = Intersect();
+    xs.add(i1);
+    xs.add(i2);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].t, 1);
+    ASSERT_EQ(xs[1].t, 2);
+}
+
+TEST(IntersectTest, Intersect_sets_the_object_on_the_intersection)
+{
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].object, (Object *)&s);
+    ASSERT_EQ(xs[1].object, (Object *)&s);
+}
+
+TEST(IntersectTest, The_hit_when_all_intersection_have_positive_t)
+{
+    Sphere s = Sphere();
+    Intersect xs = Intersect();
+
+    Intersection i1 = Intersection(1, &s);
+    Intersection i2 = Intersection(2, &s);
+
+    xs.add(i1);
+    xs.add(i2);
+
+    Intersection i = xs.hit();
+
+    ASSERT_EQ(i, i1);
+}
+
+TEST(IntersectTest, The_hit_when_some_intersection_have_negative_t)
+{
+    Sphere s = Sphere();
+    Intersect xs = Intersect();
+
+    Intersection i1 = Intersection(-1, &s);
+    Intersection i2 = Intersection(2, &s);
+    Intersection i3 = Intersection(12, &s);
+
+    xs.add(i1);
+    xs.add(i2);
+    xs.add(i3);
+
+    Intersection i = xs.hit();
+
+    ASSERT_EQ(i, i2);
+}
+
+TEST(IntersectTest, The_hit_when_all_intersection_have_negative_t)
+{
+    Sphere s = Sphere();
+    Intersect xs = Intersect();
+
+    Intersection i1 = Intersection(-2, &s);
+    Intersection i2 = Intersection(-1, &s);
+
+    xs.add(i1);
+    xs.add(i2);
+
+    Intersection i = xs.hit();
+
+    ASSERT_TRUE(i.nothing());
+}
+
+TEST(IntersectTest, The_hit_is_always_the_lowest_nonnegative_intersection)
+{
+    Sphere s = Sphere();
+    Intersect xs = Intersect();
+
+    Intersection i1 = Intersection(5, &s);
+    Intersection i2 = Intersection(7, &s);
+    Intersection i3 = Intersection(-3, &s);
+    Intersection i4 = Intersection(2, &s);
+
+    xs.add(i1);
+    xs.add(i2);
+    xs.add(i3);
+    xs.add(i4);
+
+    Intersection i = xs.hit();
+
+    ASSERT_EQ(i, i4);
+}

tests/matrix_test.cpp

@@ -0,0 +1,390 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Matric unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <matrix.h>
+#include <tuple.h>
+#include <math.h>
+#include <gtest/gtest.h>
+
+
+TEST(MatrixTest, Constructing_and_inspecting_a_4x4_Matrix)
+{
+    double values[] = {1,    2,    3,    4,
+                       5.5,  6.5,  7.5,  8.5,
+                       9,    10,   11,   12,
+                       13.5, 14.5, 15.5, 16.5};
+
+    Matrix4 m = Matrix4(values);
+
+    ASSERT_EQ(m.get(0, 0), 1);
+    ASSERT_EQ(m.get(0, 3), 4);
+    ASSERT_EQ(m.get(1, 0), 5.5);
+    ASSERT_EQ(m.get(1, 2), 7.5);
+    ASSERT_EQ(m.get(2, 2), 11);
+    ASSERT_EQ(m.get(3, 0), 13.5);
+    ASSERT_EQ(m.get(3, 2), 15.5);
+}
+
+TEST(MatrixTest, A_2x2_matric_ought_to_be_representable)
+{
+    double values[] = {-3, 5,
+                        1, -2};
+
+    Matrix2 m = Matrix2(values);
+
+    ASSERT_EQ(m.get(0, 0), -3);
+    ASSERT_EQ(m.get(0, 1), 5);
+    ASSERT_EQ(m.get(1, 0), 1);
+    ASSERT_EQ(m.get(1, 1), -2);
+}
+
+TEST(MatrixTest, A_3x3_matric_ought_to_be_representable)
+{
+    double values[] = {-3, 5, 0,
+                       1,  -2, -7,
+                       0,  1,  1};
+
+    Matrix3 m = Matrix3(values);
+
+    ASSERT_EQ(m.get(0, 0), -3);
+    ASSERT_EQ(m.get(1, 1), -2);
+    ASSERT_EQ(m.get(2, 2), 1);
+}
+
+TEST(MatrixTest, Matrix_equality_with_identical_matrix)
+{
+    double values1[] = {1, 2, 3, 4,
+                        5, 6, 7, 8,
+                        9, 8, 7, 6,
+                        5, 4, 3, 2};
+
+    double values2[] = {1, 2, 3, 4,
+                        5, 6, 7, 8,
+                        9, 8, 7, 6,
+                        5, 4, 3, 2};
+    Matrix4 A = Matrix4(values1);
+    Matrix4 B = Matrix4(values2);
+
+    ASSERT_EQ(A, B);
+}
+
+TEST(MatrixTest, Matrix_equality_with_different_matrix)
+{
+    double values1[] = {1, 2, 3, 4,
+                        5, 6, 7, 8,
+                        9, 8, 7, 6,
+                        5, 4, 3, 2};
+
+    double values2[] = {2, 3, 4, 5,
+                        6, 7, 8, 9,
+                        8, 7, 6, 5,
+                        4, 3, 2, 1};
+    Matrix4 A = Matrix4(values1);
+    Matrix4 B = Matrix4(values2);
+
+    ASSERT_NE(A, B);
+}
+
+TEST(MatrixTest, Multiplying_two_matrices)
+{
+    double values1[] = {1, 2, 3, 4,
+                        5, 6, 7, 8,
+                        9, 8, 7, 6,
+                        5, 4, 3, 2};
+
+    double values2[] = {-2, 1, 2, 3,
+                        3, 2, 1, -1,
+                        4, 3, 6, 5,
+                        1, 2, 7, 8};
+
+    double results[] = {20, 22, 50, 48,
+                        44, 54, 114, 108,
+                        40, 58, 110, 102,
+                        16, 26, 46, 42};
+
+    Matrix4 A = Matrix4(values1);
+    Matrix4 B = Matrix4(values2);
+
+
+    ASSERT_EQ(A * B, Matrix4(results));
+}
+
+TEST(MatrixTest, A_matrix_multiplyed_by_a_tuple)
+{
+    double valuesA[] = {1, 2, 3, 4,
+                        2, 4, 4, 2,
+                        8, 6, 4, 1,
+                        0, 0, 0, 1};
+
+    Matrix4 A = Matrix4(valuesA);
+    Tuple b = Tuple(1, 2, 3, 1);
+
+    ASSERT_EQ(A * b, Tuple(18, 24, 33, 1));
+}
+
+TEST(MatrixTest, Multiplying_a_matrix_by_the_identity_matrix)
+{
+    double valuesA[] = {0, 1, 2, 4,
+                        1, 2, 4, 8,
+                        2, 4, 8, 16,
+                        4, 8, 16, 32};
+
+    Matrix4 A = Matrix4(valuesA);
+    Matrix ident = Matrix4().identity();
+
+    ASSERT_EQ(A * ident, A);
+}
+
+TEST(MatrixTest, Multiplying_the_identity_matrix_by_a_tuple)
+{
+    Tuple a = Tuple(1, 2, 3, 4);
+    Matrix ident = Matrix4().identity();
+
+    ASSERT_EQ(ident * a, a);
+}
+
+TEST(MatrixTest, Transposing_a_matrix)
+{
+    double valuesA[] = {0, 9, 3, 0,
+                        9, 8, 0, 8,
+                        1, 8, 5, 3,
+                        0, 0, 5, 8};
+
+    double results[] = {0, 9, 1, 0,
+                        9, 8, 8, 0,
+                        3, 0, 5, 5,
+                        0, 8, 3, 8};
+
+    Matrix A = Matrix4(valuesA);
+
+    ASSERT_EQ(A.transpose(), Matrix4(results));
+}
+
+TEST(MatrixTest, Transposing_this_identity_matrix)
+{
+    Matrix ident = Matrix4().identity();
+
+    ASSERT_EQ(ident.transpose(), ident);
+}
+
+TEST(MatrixTest, Calculating_the_determinant_of_a_2x2_matrix)
+{
+    double valuesA[] = { 1, 5,
+                         -3, 2 };
+    Matrix2 A = Matrix2(valuesA);
+
+    ASSERT_EQ(A.determinant(), 17);
+}
+
+TEST(MatrixTest, A_submatrix_of_a_3x3_matrix_is_a_2x2_matrix)
+{
+    double valuesA[] = { 1, 5, 0,
+                         -3, 2, 7,
+                         0, 6, -3 };
+    double results[] = { -3, 2,
+                         0, 6 };
+    Matrix3 A = Matrix3(valuesA);
+
+    ASSERT_EQ(A.submatrix(0, 2), Matrix2(results));
+}
+
+TEST(MatrixTest, A_submatrix_of_a_4x4_matrix_is_a_3x3_matrix)
+{
+    double valuesA[] = { -6, 1, 1, 6,
+                         -8, 5, 8, 6,
+                         -1, 0, 8, 2,
+                         -7, 1, -1, 1 };
+    double results[] = { -6, 1, 6,
+                         -8, 8, 6,
+                         -7,-1, 1 };
+    Matrix4 A = Matrix4(valuesA);
+
+    ASSERT_EQ(A.submatrix(2, 1), Matrix3(results));
+}
+
+TEST(MatrixTest, Calculate_a_minor_of_a_3x3_matrix)
+{
+    double valuesA[] = { 3, 5, 0,
+                         2, -1, -7,
+                         6, -1, 5 };
+
+    Matrix3 A = Matrix3(valuesA);
+
+    Matrix B = A.submatrix(1, 0);
+
+    ASSERT_EQ(B.determinant(), 25);
+    ASSERT_EQ(A.minor(1, 0), 25);
+}
+
+TEST(MatrixTest, Calculating_a_cofactor_of_a_3x3_matrix)
+{
+    double valuesA[] = { 3, 5, 0,
+                         2, -1, -7,
+                         6, -1, 5 };
+
+    Matrix3 A = Matrix3(valuesA);
+
+    ASSERT_EQ(A.minor(0, 0), -12);
+    ASSERT_EQ(A.cofactor(0, 0), -12);
+    ASSERT_EQ(A.minor(1, 0), 25);
+    ASSERT_EQ(A.cofactor(1, 0), -25);
+}
+
+TEST(MatrixTest, Calculating_the_determinant_of_a_3x3_matrix)
+{
+    double valuesA[] = { 1, 2, 6,
+                         -5, 8, -4,
+                         2, 6, 4 };
+
+    Matrix A = Matrix3(valuesA);
+
+    ASSERT_EQ(A.cofactor(0, 0), 56);
+    ASSERT_EQ(A.cofactor(0, 1), 12);
+    ASSERT_EQ(A.minor(0, 2), -46);
+    ASSERT_EQ(A.determinant(), -196);
+}
+
+TEST(MatrixTest, Calculating_the_determinant_of_a_4x4_matrix)
+{
+    double valuesA[] = { -2, -8, 3, 5,
+                         -3, 1, 7, 3,
+                         1, 2, -9, 6,
+                         -6, 7, 7, -9 };
+
+    Matrix A = Matrix4(valuesA);
+
+    ASSERT_EQ(A.cofactor(0, 0), 690);
+    ASSERT_EQ(A.cofactor(0, 1), 447);
+    ASSERT_EQ(A.cofactor(0, 2),  210);
+    ASSERT_EQ(A.minor(0, 3), -51);
+    ASSERT_EQ(A.determinant(), -4071);
+}
+
+TEST(MatrixTest, Testing_an_invertible_matrix_for_invertibility)
+{
+    double valuesA[] = { 6, 4, 4, 4,
+                         5, 5, 7, 6,
+                         4, -9, 3, -7,
+                         9, 1, 7, -6 };
+    Matrix A = Matrix4(valuesA);
+
+    ASSERT_EQ(A.determinant(), -2120);
+    ASSERT_TRUE(A.isInvertible());
+}
+
+TEST(MatrixTest, Testing_an_noninvertible_matrix_for_invertibility)
+{
+    double valuesA[] = { -4, 2, -2, -3,
+                         9, 6, 2, 6,
+                         0, -5, 1, -5,
+                         0, 0, 0, 0 };
+    Matrix A = Matrix4(valuesA);
+
+    ASSERT_EQ(A.determinant(), 0);
+    ASSERT_FALSE(A.isInvertible());
+}
+
+TEST(MatrixTest, Calculating_the_inverse_of_a_matrix)
+{
+    double valuesA[] = { -5, 2, 6, -8,
+                         1, -5, 1, 8,
+                         7, 7, -6, -7,
+                         1, -3, 7, 4 };
+
+    double results[] = {  0.21805, 0.45113, 0.24060, -0.04511,
+                         -0.80827, -1.45677, -0.44361, 0.52068,
+                         -0.07895, -0.22368, -0.05263, 0.19737,
+                         -0.52256, -0.81391, -0.30075, 0.30639 };
+
+    Matrix A = Matrix4(valuesA);
+    Matrix B = A.inverse();
+
+    ASSERT_EQ(A.determinant(), 532);
+    ASSERT_EQ(A.cofactor(2, 3), -160);
+    ASSERT_NEAR(B.get(3, 2), -160./532., DBL_EPSILON);
+    ASSERT_EQ(A.cofactor(3, 2), 105);
+    ASSERT_NEAR(B.get(2, 3), 105./532., DBL_EPSILON);
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00001);
+
+    ASSERT_EQ(B, Matrix4(results));
+
+    /* Revert to default */
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(MatrixTest, Calculating_the_inverse_of_another_matrix)
+{
+    double valuesA[] = {  8, -5,  9,  2,
+                          7,  5,  6,  1,
+                         -6,  0,  9,  6,
+                         -3,  0, -9, -4 };
+
+    double results[] = {  -0.15385, -0.15385, -0.28205, -0.53846,
+                          -0.07692,  0.12308,  0.02564,  0.03077,
+                           0.35897,  0.35897,  0.43590,  0.92308,
+                          -0.69231, -0.69231, -0.76923, -1.92308 };
+
+    Matrix A = Matrix4(valuesA);
+    Matrix B = A.inverse();
+
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00001);
+
+    ASSERT_EQ(B, Matrix4(results));
+
+    /* Revert to default */
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(MatrixTest, Calculating_the_inverse_of_third_matrix)
+{
+    double valuesA[] = {  9,  3,  0,  9,
+                         -5, -2, -6, -3,
+                         -4,  9,  6,  4,
+                         -7,  6,  6,  2 };
+
+    double results[] = { -0.04074, -0.07778,  0.14444, -0.22222,
+                         -0.07778,  0.03333,  0.36667, -0.33333,
+                         -0.02901, -0.14630, -0.10926,  0.12963,
+                          0.17778,  0.06667, -0.26667,  0.33333 };
+
+    Matrix A = Matrix4(valuesA);
+    Matrix B = A.inverse();
+
+
+    /* Temporary lower the precision */
+    set_equal_precision(0.00001);
+
+    ASSERT_EQ(B, Matrix4(results));
+
+    /* Revert to default */
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(MatrixTest, Multiplying_a_product_by_its_inverse)
+{
+    double valuesA[] = {  3, -9, 7, 3,
+                          3, -8, 2, -9,
+                          -4, 4, 4, 1,
+                          -6, 5, -1, 1 };
+
+    double valuesB[] = { 8, 2, 2, 2,
+                        3, -1, 7, 0,
+                        7, 0, 5, 4,
+                        6, -2, 0, 5 };
+
+    Matrix A = Matrix4(valuesA);
+    Matrix B = Matrix4(valuesB);
+
+    Matrix C = A * B;
+
+    ASSERT_EQ(C * B.inverse(), A);
+}

tests/ray_test.cpp

@@ -0,0 +1,64 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Ray unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <ray.h>
+#include <transformation.h>
+#include <object.h>
+#include <gtest/gtest.h>
+
+
+TEST(RayTest, Creating_a_ray_and_querying_it)
+{
+    Point origin = Point(1, 2, 3);
+    Vector direction = Vector(4, 5, 6);
+
+    Ray r = Ray(origin, direction);
+
+    ASSERT_EQ(r.origin, origin);
+    ASSERT_EQ(r.direction, direction);
+}
+
+TEST(RayTest, Computing_a_point_from_a_distance)
+{
+    Ray r = Ray(Point(2, 3, 4), Vector(1, 0, 0));
+
+    ASSERT_EQ(r.position(0), Point(2, 3, 4));
+    ASSERT_EQ(r.position(1), Point(3, 3, 4));
+    ASSERT_EQ(r.position(-1), Point(1, 3, 4));
+    ASSERT_EQ(r.position(2.5), Point(4.5, 3, 4));
+}
+
+TEST(RayTest, Translating_a_ray)
+{
+    Ray r = Ray(Point(1, 2, 3), Vector(0, 1, 0));
+
+    Matrix m = translation(3, 4, 5);
+    Object o = Object();
+
+    o.setTransform(m);
+
+    Ray r2 = o.transform(r);
+
+    ASSERT_EQ(r2.origin, Point(4, 6, 8));
+    ASSERT_EQ(r2.direction, Vector(0, 1, 0));
+}
+
+TEST(RayTest, Scaling_a_ray)
+{
+    Ray r = Ray(Point(1, 2, 3), Vector(0, 1, 0));
+
+    Matrix m = scaling(2, 3, 4);
+    Object o = Object();
+
+    o.setTransform(m);
+
+    Ray r2 = o.transform(r);
+
+    ASSERT_EQ(r2.origin, Point(2, 6, 12));
+    ASSERT_EQ(r2.direction, Vector(0, 3, 0));
+}

tests/sphere_test.cpp

@@ -0,0 +1,108 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Sphere unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <ray.h>
+#include <sphere.h>
+#include <transformation.h>
+#include <gtest/gtest.h>
+
+
+TEST(SphereTest, A_ray_intersect_a_sphere_at_two_points)
+{
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].t, 4.0);
+    ASSERT_EQ(xs[1].t, 6.0);
+}
+
+TEST(SphereTest, A_ray_intersect_a_sphere_at_a_tangent)
+{
+    Ray r = Ray(Point(0, 1, -5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].t, 5.0);
+    ASSERT_EQ(xs[1].t, 5.0);
+}
+
+TEST(SphereTest, A_ray_miss_a_sphere)
+{
+    Ray r = Ray(Point(0, 2, -5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 0);
+}
+
+TEST(SphereTest, A_ray_originate_inside_a_sphere)
+{
+    Ray r = Ray(Point(0, 0, 0), Vector(0, 0, 1));
+    Sphere s = Sphere();
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].t, -1.0);
+    ASSERT_EQ(xs[1].t, 1.0);
+}
+
+TEST(SphereTest, A_sphere_is_behind_a_ray)
+{
+    Ray r = Ray(Point(0, 0, 5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].t, -6.0);
+    ASSERT_EQ(xs[1].t, -4.0);
+}
+
+TEST(SphereTest, A_sphere_default_transformation)
+{
+    Sphere s = Sphere();
+    ASSERT_EQ(s.transformMatrix, Matrix4().identity());
+}
+
+TEST(SphereTest, Changing_a_sphere_transformation)
+{
+    Sphere s = Sphere();
+    Matrix t = translation(2, 3, 4);
+
+    s.setTransform(t);
+
+    ASSERT_EQ(s.transformMatrix, t);
+}
+
+TEST(SphereTest, Intersecting_a_scaled_sphere_with_a_ray)
+{
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+
+    s.setTransform(scaling(2, 2, 2));
+
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 2);
+    ASSERT_EQ(xs[0].t, 3.0);
+    ASSERT_EQ(xs[1].t, 7.0);
+}
+
+TEST(SphereTest, Intersecting_a_translated_sphere_with_a_ray)
+{
+    Ray r = Ray(Point(0, 0, -5), Vector(0, 0, 1));
+    Sphere s = Sphere();
+
+    s.setTransform(translation(5, 0, 0));
+
+    Intersect xs = s.intersect(r);
+
+    ASSERT_EQ(xs.count(), 0);
+}

tests/transformation_test.cpp

@@ -0,0 +1,191 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Transformations unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <transformation.h>
+#include <tuple.h>
+#include <math.h>
+#include <gtest/gtest.h>
+
+TEST(TransformationTest, Multiplying_by_a_translation_matrix)
+{
+   Matrix transform = translation(5, -3, 2);
+   Point p = Point(-3, 4, 5);
+   
+   ASSERT_EQ(transform * p, Point(2, 1, 7));
+}
+
+TEST(TransformationTest, Multiplying_by_the_inverse_of_a_translation_matrix)
+{
+   Matrix transform = translation(5, -3, 2);
+   Matrix inv = transform.inverse();
+   
+   Point p = Point(-3, 4, 5);
+   
+   ASSERT_EQ(inv * p, Point(-8, 7, 3));
+}
+
+TEST(TransformationTest, Translation_does_not_affect_vectors)
+{
+   Matrix transform = translation(5, -3, 2);
+   
+   Vector v = Vector(-3, 4, 5);
+   
+   ASSERT_EQ(transform * v, Vector(-3, 4, 5));
+}
+
+TEST(TransformationTest, A_scaling_matrix_applied_to_a_point)
+{
+   Matrix transform = scaling(2, 3, 4);
+   
+   Point p = Point(-4, 6, 8);
+   
+   ASSERT_EQ(transform * p, Point(-8, 18, 32));
+}
+
+TEST(TransformationTest, A_scaling_matrix_applied_to_a_vector)
+{
+   Matrix transform = scaling(2, 3, 4);
+   
+   Vector v = Vector(-4, 6, 8);
+   
+   ASSERT_EQ(transform * v, Vector(-8, 18, 32));
+}
+
+TEST(TransformationTest, Multiplaying_by_the_inverse_of_a_scaling_matrix)
+{
+   Matrix transform = scaling(2, 3, 4);
+   Matrix inv = transform.inverse();
+   
+   Vector v = Vector(-4, 6, 8);
+   
+   ASSERT_EQ(inv * v, Vector(-2, 2, 2));
+}
+
+TEST(TransformationTest, Reflexion_is_scaling_by_a_negative_value)
+{
+   Matrix transform = scaling(-1, 1, 1);
+   
+   Point p = Point(2, 3, 4);
+   
+   ASSERT_EQ(transform * p, Point(-2, 3, 4));
+}
+
+TEST(TransformationTest, Rotating_a_point_around_the_X_axis)
+{
+   Point p = Point(0, 1, 0);
+   Matrix half_quarter = rotation_x(M_PI / 4.);
+   Matrix full_quarter = rotation_x(M_PI / 2.);
+   
+   ASSERT_EQ(half_quarter * p, Point(0, sqrt(2)/2, sqrt(2)/2));
+   ASSERT_EQ(full_quarter * p, Point(0, 0, 1));
+}
+
+TEST(TransformationTest, The_inverse_of_an_x_rotation_rotates_in_the_opposite_direction)
+{
+   Point p = Point(0, 1, 0);
+   Matrix half_quarter = rotation_x(M_PI / 4.);
+   Matrix inv = half_quarter.inverse();
+   
+   ASSERT_EQ(inv * p, Point(0, sqrt(2)/2, -sqrt(2)/2));
+}
+
+TEST(TransformationTest, Rotating_a_point_around_the_Y_axis)
+{
+   Point p = Point(0, 0, 1);
+   Matrix half_quarter = rotation_y(M_PI / 4.);
+   Matrix full_quarter = rotation_y(M_PI / 2.);
+   
+   ASSERT_EQ(half_quarter * p, Point(sqrt(2)/2, 0, sqrt(2)/2));
+   ASSERT_EQ(full_quarter * p, Point(1, 0, 0));
+}
+
+TEST(TransformationTest, Rotating_a_point_around_the_Z_axis)
+{
+   Point p = Point(0, 1, 0);
+   Matrix half_quarter = rotation_z(M_PI / 4.);
+   Matrix full_quarter = rotation_z(M_PI / 2.);
+   
+   ASSERT_EQ(half_quarter * p, Point(-sqrt(2)/2, sqrt(2)/2, 0));
+   ASSERT_EQ(full_quarter * p, Point(-1, 0, 0));
+}
+
+TEST(TransformationTest, A_shearing_transformation_moves_x_in_proportion_to_y)
+{
+    Matrix transform = shearing(1, 0, 0, 0, 0, 0);
+    Point p = Point(2, 3, 4);
+
+    ASSERT_EQ(transform * p, Point(5, 3, 4));
+}
+
+TEST(TransformationTest, A_shearing_transformation_moves_x_in_proportion_to_z)
+{
+    Matrix transform = shearing(0, 1, 0, 0, 0, 0);
+    Point p = Point(2, 3, 4);
+
+    ASSERT_EQ(transform * p, Point(6, 3, 4));
+}
+
+TEST(TransformationTest, A_shearing_transformation_moves_y_in_proportion_to_x)
+{
+    Matrix transform = shearing(0, 0, 1, 0, 0, 0);
+    Point p = Point(2, 3, 4);
+
+    ASSERT_EQ(transform * p, Point(2, 5, 4));
+}
+
+TEST(TransformationTest, A_shearing_transformation_moves_y_in_proportion_to_z)
+{
+    Matrix transform = shearing(0,  0, 0, 1, 0, 0);
+    Point p = Point(2, 3, 4);
+
+    ASSERT_EQ(transform * p, Point(2, 7, 4));
+}
+
+TEST(TransformationTest, A_shearing_transformation_moves_z_in_proportion_to_x)
+{
+    Matrix transform = shearing(0, 0, 0, 0, 1, 0);
+    Point p = Point(2, 3, 4);
+
+    ASSERT_EQ(transform * p, Point(2, 3, 6));
+}
+
+TEST(TransformationTest, A_shearing_transformation_moves_z_in_proportion_to_y)
+{
+    Matrix transform = shearing(0, 0, 0, 0, 0, 1);
+    Point p = Point(2, 3, 4);
+
+    ASSERT_EQ(transform * p, Point(2, 3, 7));
+}
+
+TEST(TransformationTest, Individual_trnasformations_are_applied_in_sequence)
+{
+    Point p = Point(1, 0, 1);
+    Matrix A = rotation_x(M_PI / 2.);
+    Matrix B = scaling(5, 5, 5);
+    Matrix C = translation(10, 5, 7);
+
+    Tuple p2 = A * p;
+    ASSERT_EQ(p2, Point(1, -1, 0));
+
+    Tuple p3 = B * p2;
+    ASSERT_EQ(p3, Point(5, -5, 0));
+
+    Tuple p4 = C * p3;
+    ASSERT_EQ(p4, Point(15, 0, 7));
+}
+
+TEST(TransformationTest, Chained_transformation_must_be_applied_in_reverse_order)
+{
+    Point p = Point(1, 0, 1);
+    Matrix A = rotation_x(M_PI / 2.);
+    Matrix B = scaling(5, 5, 5);
+    Matrix C = translation(10, 5, 7);
+
+    Matrix T = C * B * A;
+    ASSERT_EQ(T * p, Point(15, 0, 7));
+}

tests/tuple_test.cpp

@@ -6,7 +6,7 @@
  *  Copyright (c) 2020 986-Studio.
  *
  */
-#include <tuples.h>
+#include <tuple.h>
 #include <math.h>
 #include <gtest/gtest.h>