Now we can transform!

source/CMakeLists.txt

@@ -3,8 +3,8 @@
 # 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 include/matrix.h)
+set(RAY_HEADERS include/tuples.h include/math_helper.h include/colour.h include/canvas.h include/matrix.h include/transformation.h)
-set(RAY_SOURCES tuples.cpp math_helper.cpp colour.cpp canvas.cpp matrix.cpp)
+set(RAY_SOURCES tuples.cpp math_helper.cpp colour.cpp canvas.cpp matrix.cpp transformation.cpp)
 
 target_include_directories(rayonnement PUBLIC include)
 target_sources(rayonnement PRIVATE ${RAY_HEADERS} ${RAY_SOURCES})

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/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;
+}

tests/CMakeLists.txt

@@ -3,7 +3,7 @@ project(DoRayTested)
 set(THREADS_PREFER_PTHREAD_FLAG ON)
 find_package(Threads REQUIRED)
 
-set(TESTS_SRC tuples_test.cpp colour_test.cpp canvas_test.cpp matrix_test.cpp)
+set(TESTS_SRC tuples_test.cpp colour_test.cpp canvas_test.cpp matrix_test.cpp transformation_test.cpp)
 
 add_executable(testMyRays)
 target_include_directories(testMyRays PUBLIC ${gtest_SOURCE_DIR}/include ${gtest_SOURCE_DIR})

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 <tuples.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));
+}