Browse Source

Added CUBES!

Godzil 4 years ago
parent
commit
81e323fdf4

+ 28 - 0
source/include/cube.h

@@ -0,0 +1,28 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Cube header
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#ifndef DORAYME_CUBE_H
+#define DORAYME_CUBE_H
+
+#include <shape.h>
+#include <ray.h>
+#include <intersect.h>
+
+class Cube : public Shape {
+private:
+    void checkAxis(double axeOrigine, double axeDirection, double *axeMin, double *axeMax);
+
+    Intersect localIntersect(Ray r);
+
+    Tuple localNormalAt(Tuple point);
+
+public:
+    Cube() : Shape(SHAPE_CUBE) {};
+};
+
+#endif /* DORAYME_CUBE_H */

+ 3 - 0
source/include/math_helper.h

@@ -18,4 +18,7 @@ bool double_equal(double a, double b);
 
 double deg_to_rad(double deg);
 
+double min3(double a, double b, double c);
+double max3(double a, double b, double c);
+
 #endif /* DORAYME_MATH_HELPER_H */

+ 2 - 0
source/include/shape.h

@@ -22,6 +22,8 @@ enum ShapeType
     SHAPE_NONE,
     SHAPE_SPHERE,
     SHAPE_PLANE,
+    SHAPE_CUBE,
+    SHAPE_CONE,
 };
 
 /* Base class for all object that can be presented in the world */

+ 38 - 0
source/math_helper.cpp

@@ -31,4 +31,42 @@ bool double_equal(double a, double b)
 double deg_to_rad(double deg)
 {
    return deg * M_PI / 180.;
+}
+
+double min3(double a, double b, double c)
+{
+    if (a <= b)
+    {
+        if (c < a) return c;
+        return a;
+    }
+    if (b <= a)
+    {
+        if (c < b) return c;
+        return b;
+    }
+    if (c <= a)
+    {
+        if (b < c) return b;
+    }
+    return c;
+}
+
+double max3(double a, double b, double c)
+{
+    if (a >= b)
+    {
+        if (c > a) return c;
+        return a;
+    }
+    if (b >= a)
+    {
+        if (c > b) return c;
+        return b;
+    }
+    if (c >= a)
+    {
+        if (b > c) return b;
+    }
+    return c;
 }

+ 76 - 0
source/shapes/cube.cpp

@@ -0,0 +1,76 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Cube implementation
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <tuple.h>
+#include <ray.h>
+#include <shape.h>
+#include <cube.h>
+#include <math_helper.h>
+
+void Cube::checkAxis(double axeOrigin, double axeDirection, double *axeMin, double *axeMax)
+{
+    double tMinNumerator = (-1 - axeOrigin);
+    double tMaxNumerator = (1 - axeOrigin);
+
+    if (fabs(axeDirection) >= getEpsilon())
+    {
+        *axeMin = tMinNumerator / axeDirection;
+        *axeMax = tMaxNumerator / axeDirection;
+    }
+    else
+    {
+        *axeMin = tMinNumerator * INFINITY;
+        *axeMax = tMaxNumerator * INFINITY;
+    }
+
+    if (*axeMin > *axeMax)
+    {
+        double swap = *axeMax;
+        *axeMax = *axeMin;
+        *axeMin = swap;
+    }
+}
+
+Intersect Cube::localIntersect(Ray r)
+{
+    Intersect ret;
+
+    double xtMin, xtMax, ytMin, ytMax, ztMin, ztMax;
+    double tMin, tMax;
+
+    this->checkAxis(r.origin.x, r.direction.x, &xtMin, &xtMax);
+    this->checkAxis(r.origin.y, r.direction.y, &ytMin, &ytMax);
+    this->checkAxis(r.origin.z, r.direction.z, &ztMin, &ztMax);
+
+    tMin = max3(xtMin, ytMin, ztMin);
+    tMax = min3(xtMax, ytMax, ztMax);
+
+    if (tMin <= tMax)
+    {
+        ret.add(Intersection(tMin, this));
+        ret.add(Intersection(tMax, this));
+    }
+
+    return ret;
+}
+
+Tuple Cube::localNormalAt(Tuple point)
+{
+    double maxC = max3(fabs(point.x), fabs(point.y), fabs(point.z));
+
+    if (maxC == fabs(point.x))
+    {
+        return Vector(point.x, 0, 0);
+    }
+    else if (maxC == fabs(point.y))
+    {
+        return Vector(0, point.y, 0);
+    }
+
+    return Vector(0, 0, point.z);
+}

+ 9 - 3
tests/CMakeLists.txt

@@ -3,9 +3,9 @@ project(DoRayTested)
 set(THREADS_PREFER_PTHREAD_FLAG ON)
 find_package(Threads REQUIRED)
 
-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 light_test.cpp material_test.cpp world_test.cpp camera_test.cpp
-        shape_test.cpp plane_test.cpp pattern_test.cpp)
+set(TESTS_SRC math_test.cpp tuple_test.cpp colour_test.cpp canvas_test.cpp matrix_test.cpp transformation_test.cpp
+        ray_test.cpp intersect_test.cpp sphere_test.cpp light_test.cpp material_test.cpp world_test.cpp camera_test.cpp
+        shape_test.cpp plane_test.cpp pattern_test.cpp cube_test.cpp)
 
 add_executable(testMyRays)
 target_include_directories(testMyRays PUBLIC ${gtest_SOURCE_DIR}/include ${gtest_SOURCE_DIR})
@@ -64,6 +64,11 @@ target_include_directories(ch11_test PUBLIC ../source/include)
 target_sources(ch11_test PRIVATE ch11_test.cpp)
 target_link_libraries(ch11_test rayonnement)
 
+add_executable(ch12_test)
+target_include_directories(ch12_test PUBLIC ../source/include)
+target_sources(ch12_test PRIVATE ch12_test.cpp)
+target_link_libraries(ch12_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>)
@@ -72,3 +77,4 @@ 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>)
+add_test(NAME Chapter12_Test COMMAND $<TARGET_FILE:ch12_test>)

+ 1 - 1
tests/ch10_test.cpp

@@ -79,7 +79,7 @@ int main()
     w.addLight(&light);
 
     /* Set the camera */
-    Camera camera = Camera(1920, 1080, M_PI / 3);
+    Camera camera = Camera(100, 50, M_PI / 3);
     camera.setTransform(viewTransform(Point(0, 1.5, -5),
                                       Point(0, 1, 0),
                                       Vector(0, 1, 0)));

+ 213 - 0
tests/ch12_test.cpp

@@ -0,0 +1,213 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Render test for reflection in chapter 12.
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <world.h>
+#include <light.h>
+#include <sphere.h>
+#include <plane.h>
+#include <cube.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();
+
+    /* Add light */
+    Light light = Light(POINT_LIGHT, Point(0, 6.9, -5), Colour(1, 1, 0.9));
+    w.addLight(&light);
+
+    /* ----------------------------- */
+
+    /* The floor / ceiling */
+    Cube floor = Cube();
+    floor.setTransform( scaling(20, 7, 20) * translation(0, 1, 0));
+    floor.material.pattern = new CheckersPattern(Colour(0, 0, 0), Colour(0.25, 0.25, 0.25));
+    floor.material.pattern->setTransform(scaling(0.07, 0.07, 0.07));
+    floor.material.ambient = 0.25;
+    floor.material.diffuse = 0.7;
+    floor.material.specular = 0.9;
+    floor.material.shininess = 300;
+    floor.material.reflective = 0.1;
+    w.addObject(&floor);
+
+    /* Walls */
+    Cube walls = Cube();
+    walls.setTransform(scaling(10, 10, 10));
+    walls.material.pattern = new CheckersPattern(Colour( 0.4863, 0.3765, 0.2941), Colour(0.3725, 0.2902, 0.2275 ));
+    walls.material.pattern->setTransform(scaling(0.05, 20, 0.05));
+    walls.material.ambient = 0.1;
+    walls.material.diffuse = 0.7;
+    walls.material.specular = 0.9;
+    walls.material.shininess = 300;
+    walls.material.reflective = 0.1;
+    w.addObject(&walls);
+
+    /* Table top */
+    Cube tableTop = Cube();
+    tableTop.setTransform(translation(0, 3.1, 0) * scaling(3, 0.1, 2));
+    tableTop.material.pattern = new StripPattern(Colour(0.5529, 0.4235, 0.3255), Colour(0.6588, 0.5098, 0.4000 ));
+    tableTop.material.pattern->setTransform(scaling(0.05, 0.05, 0.05) * rotationY(0.1));
+    tableTop.material.ambient = 0.1;
+    tableTop.material.diffuse = 0.7;
+    tableTop.material.specular = 0.9;
+    tableTop.material.shininess = 300;
+    tableTop.material.reflective = 0.2;
+    w.addObject(&tableTop);
+
+    /* Leg 1 */
+    Cube leg1 = Cube();
+    leg1.setTransform(translation(2.7, 1.5, -1.7) * scaling(0.1, 1.5, 0.1));
+    leg1.material.colour = Colour(0.5529, 0.4235, 0.3255);
+    leg1.material.ambient = 0.2;
+    leg1.material.diffuse = 0.7;
+    w.addObject(&leg1);
+
+    /* Leg 2 */
+    Cube leg2 = Cube();
+    leg2.setTransform(translation(2.7, 1.5, 1.7) * scaling(0.1, 1.5, 0.1));
+    leg2.material.colour = Colour(0.5529, 0.4235, 0.3255);
+    leg2.material.ambient = 0.2;
+    leg2.material.diffuse = 0.7;
+    w.addObject(&leg2);
+
+    /* Leg 3 */
+    Cube leg3 = Cube();
+    leg3.setTransform(translation(-2.7, 1.5, -1.7) * scaling(0.1, 1.5, 0.1));
+    leg3.material.colour = Colour(0.5529, 0.4235, 0.3255);
+    leg3.material.ambient = 0.2;
+    leg3.material.diffuse = 0.7;
+    w.addObject(&leg3);
+
+    /* Leg 4 */
+    Cube leg4 = Cube();
+    leg4.setTransform(translation(-2.7, 1.5, 1.7) * scaling(0.1, 1.5, 0.1));
+    leg4.material.colour = Colour(0.5529, 0.4235, 0.3255);
+    leg4.material.ambient = 0.2;
+    leg4.material.diffuse = 0.7;
+    w.addObject(&leg4);
+
+    /* ----------------------------- */
+
+    /* Glass cube */
+    Cube glassCube = Cube();
+    glassCube.setTransform(translation(0, 3.45001, 0) * rotationY(0.2) * scaling(0.25, 0.25, 0.25));
+    glassCube.dropShadow = false;
+    glassCube.material.colour = Colour(1, 1, 0.8);
+    glassCube.material.ambient = 0;
+    glassCube.material.diffuse = 0.3;
+    glassCube.material.specular = 0.9;
+    glassCube.material.shininess = 300;
+    glassCube.material.reflective = 0.7;
+    glassCube.material.transparency = 0.7;
+    glassCube.material.refractiveIndex = 1.5;
+    w.addObject(&glassCube);
+
+    /* Little cube 1 */
+    Cube lilCube1 = Cube();
+    lilCube1.setTransform(translation(1, 3.25, -0.9) *
+                           rotationY(-0.4) *
+                           scaling(0.15, 0.15, 0.15));
+    lilCube1.material.colour = Colour(1, 0.5, 0.5);
+    lilCube1.material.reflective = 0.6;
+    lilCube1.material.diffuse = 0.4;
+    w.addObject(&lilCube1);
+
+    /* Little cube 2 */
+    Cube lilCube2 = Cube();
+    lilCube2.setTransform(translation(-1.5, 3.27, 0.3) *
+                          rotationY(0.4) *
+                          scaling(0.15, 0.07, 0.15));
+    lilCube2.material.colour = Colour(1, 1, 0.5);
+    w.addObject(&lilCube2);
+
+    /* Little cube 3 */
+    Cube lilCube3 = Cube();
+    lilCube3.setTransform(translation(0, 3.25, 1) *
+                          rotationY(0.4) *
+                          scaling(0.2, 0.05, 0.05));
+    lilCube3.material.colour = Colour(0.5, 1, 0.5);
+    w.addObject(&lilCube3);
+
+    /* Little cube 4 */
+    Cube lilCube4 = Cube();
+    lilCube4.setTransform(translation(-0.6, 3.4, -1) *
+                          rotationY(0.8) *
+                          scaling(0.05, 0.2, 0.05));
+    lilCube4.material.colour = Colour(0.5, 0.5, 1);
+    w.addObject(&lilCube4);
+
+    /* Little cube 5 */
+    Cube lilCube5 = Cube();
+    lilCube5.setTransform(translation(2, 3.4, 1) *
+                          rotationY(0.8) *
+                          scaling(0.05, 0.2, 0.05));
+    lilCube5.material.colour = Colour(0.5, 1, 1);
+    w.addObject(&lilCube5);
+
+    /* ----------------------------- */
+
+    /* Frame 1 */
+    Cube frame1 = Cube();
+    frame1.setTransform(translation(-10, 4, 1) * scaling(0.05, 1, 1));
+    frame1.material.colour = Colour(0.7098, 0.2471, 0.2196);
+    frame1.material.diffuse = 0.6;
+    w.addObject(&frame1);
+
+    /* Frame 2 */
+    Cube frame2 = Cube();
+    frame2.setTransform(translation(-10, 3.4, 2.7) * scaling(0.05, 0.4, 0.4));
+    frame2.material.colour = Colour(0.2667, 0.2706, 0.6902);
+    frame2.material.diffuse = 0.6;
+    w.addObject(&frame2);
+
+    /* Frame 3 */
+    Cube frame3 = Cube();
+    frame3.setTransform(translation(-10, 4.6, 2.7) * scaling(0.05, 0.4, 0.4));
+    frame3.material.colour = Colour(0.3098, 0.5961, 0.3098);
+    frame3.material.diffuse = 0.6;
+    w.addObject(&frame3);
+
+    /* ----------------------------- */
+
+    /* Mirror */
+    Cube mirror = Cube();
+    mirror.setTransform(translation(-2, 3.5, 9.95) * scaling(4.8, 1.4, 0.06));
+    mirror.material.colour = Colour(0, 0, 0);
+    mirror.material.diffuse = 0;
+    mirror.material.ambient = 0;
+    mirror.material.specular = 1;
+    mirror.material.shininess = 300;
+    mirror.material.reflective = 1;
+    w.addObject(&mirror);
+
+    /* ----------------------------- */
+
+    /* Set the camera */
+    Camera camera = Camera(400, 200, 0.785);
+    camera.setTransform(viewTransform(Point(8, 6, -8),
+                                      Point(0, 3, 0),
+                                      Vector(0, 1, 0)));
+
+    /* Now render it */
+    Canvas image = camera.render(w, 4);
+
+    image.SaveAsPNG("ch12_test.png");
+
+    return 0;
+}

+ 117 - 0
tests/cube_test.cpp

@@ -0,0 +1,117 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Cube unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <intersect.h>
+#include <intersection.h>
+#include <cube.h>
+#include <transformation.h>
+#include <gtest/gtest.h>
+
+TEST(CubeTest, A_ray_intersects_a_cube)
+{
+    Cube c = Cube();
+
+    Point Origins[] = {
+            Point(5, 0.5, 0),
+            Point(-5, 0.5, 0),
+            Point(0.5, 5, 0),
+            Point(0.5, -5, 0),
+            Point(0.5, 0, 5),
+            Point(0.5, 0, -5),
+            Point(0, 0.5, 0),
+    };
+
+    Vector Directions[] = {
+            Vector(-1, 0, 0),
+            Vector(1, 0, 0),
+            Vector(0, -1, 0),
+            Vector(0, 1, 0),
+            Vector(0, 0, -1),
+            Vector(0, 0, 1),
+            Vector(0, 0, 1),
+    };
+
+    double t1[] = { 4, 4, 4, 4, 4, 4, -1 };
+    double t2[] = { 6, 6, 6, 6, 6, 6, 1 };
+
+    int i;
+    for(i = 0; i < 7; i++)
+    {
+        Ray r = Ray(Origins[i], Directions[i]);
+        Intersect xs = c.intersect(r);
+
+        ASSERT_EQ(xs.count(), 2);
+        EXPECT_EQ(xs[0].t, t1[i]);
+        EXPECT_EQ(xs[1].t, t2[i]);
+    }
+}
+
+TEST(CubeTest, A_ray_miss_a_cube)
+{
+    Cube c = Cube();
+
+    Point Origins[] = {
+            Point(-2, 0, 0),
+            Point(0, -2, 0),
+            Point(0, 0, -2),
+            Point(2, 0, 2),
+            Point(0, 2, 2),
+            Point(2, 2, 0),
+    };
+
+    Vector Directions[] = {
+            Vector(0.2673, 0.5345, 0.8018),
+            Vector(0.8018, 0.2673, 0.5345),
+            Vector(0.5345, 0.8018, 0.2673),
+            Vector(0, 0, -1),
+            Vector(0, -1, 0),
+            Vector(-1, 0, 0),
+    };
+
+    int i;
+    for(i = 0; i < 6; i++)
+    {
+        Ray r = Ray(Origins[i], Directions[i]);
+        Intersect xs = c.intersect(r);
+
+        ASSERT_EQ(xs.count(), 0);
+    }
+}
+
+TEST(CubeTest, The_normal_on_the_surface_of_a_cube)
+{
+    Cube c = Cube();
+
+    Point HitPoints[] = {
+            Point(1, 0.5, -0.8),
+            Point(-1, -0.2, 0.9),
+            Point(-0.4, 1, -0.1),
+            Point(0.3, -1, -0.7),
+            Point(-0.6, 0.3, 1),
+            Point(0.4, 0.4, -1),
+            Point(1, 1, 1),
+            Point(-1, -1, -1),
+    };
+
+    Vector ExpectedNormals[] = {
+            Vector(1, 0, 0),
+            Vector(-1, 0, 0),
+            Vector(0, 1, 0),
+            Vector(0, -1, 0),
+            Vector(0, 0, 1),
+            Vector(0, 0, -1),
+            Vector(1, 0, 0),
+            Vector(-1, 0, 0),
+    };
+
+    int i;
+    for(i = 0; i < 8; i++)
+    {
+        ASSERT_EQ(c.normalAt(HitPoints[i]), ExpectedNormals[i]);
+    }
+}

+ 97 - 0
tests/math_test.cpp

@@ -0,0 +1,97 @@
+/*
+ *  DoRayMe - a quick and dirty Raytracer
+ *  Math helper unit tests
+ *
+ *  Created by Manoël Trapier
+ *  Copyright (c) 2020 986-Studio.
+ *
+ */
+#include <math_helper.h>
+#include <gtest/gtest.h>
+
+TEST(MathTest, Default_epsilon)
+{
+    ASSERT_EQ(getEpsilon(), FLT_EPSILON);
+}
+
+TEST(MathTest, Check_setting_epsilon)
+{
+    set_equal_precision(0.00001);
+
+    ASSERT_EQ(getEpsilon(), 0.00001);
+
+    set_equal_precision(FLT_EPSILON);
+}
+
+TEST(MathTest, Check_double_equal_is_working)
+{
+    ASSERT_TRUE(double_equal(0 - DBL_EPSILON, 0));
+
+    ASSERT_FALSE(double_equal(0 - FLT_EPSILON, 0));
+    ASSERT_TRUE(double_equal(0 - FLT_EPSILON/2.0, 0));
+
+    ASSERT_FALSE(double_equal(0 - 0.001, 0));
+    ASSERT_FALSE(double_equal(0 - 0.00001, 0));
+    ASSERT_FALSE(double_equal(0 - 0.000001, 0));
+
+    set_equal_precision(0.00001);
+    ASSERT_TRUE(double_equal(0 - FLT_EPSILON*2, 0));
+    ASSERT_FALSE(double_equal(0 - 0.001, 0));
+    ASSERT_FALSE(double_equal(0 - 0.00001, 0));
+    ASSERT_TRUE(double_equal(0 - 0.000001, 0));
+
+    set_equal_precision(FLT_EPSILON);
+}
+
+
+
+TEST(MathTest, Check_that_deg_to_rad_is_working)
+{
+    double angle180 = deg_to_rad(180);
+    double angle90 = deg_to_rad(90);
+    double angle270 = deg_to_rad(270);
+
+    ASSERT_EQ(angle180, M_PI);
+    ASSERT_EQ(angle90, M_PI / 2.);
+    ASSERT_EQ(angle270, M_PI * 1.5);
+}
+
+TEST(MathTest, Min_is_working)
+{
+    ASSERT_EQ(min3(1, 2, 3), 1);
+    ASSERT_EQ(min3(1, 3, 2), 1);
+    ASSERT_EQ(min3(2, 1, 3), 1);
+    ASSERT_EQ(min3(2, 3, 1), 1);
+    ASSERT_EQ(min3(3, 1, 2), 1);
+    ASSERT_EQ(min3(3, 2, 1), 1);
+
+    ASSERT_EQ(min3(1, 2, 2), 1);
+    ASSERT_EQ(min3(2, 1, 2), 1);
+    ASSERT_EQ(min3(2, 2, 1), 1);
+
+    ASSERT_EQ(min3(3, 2, 2), 2);
+    ASSERT_EQ(min3(2, 3, 2), 2);
+    ASSERT_EQ(min3(2, 2, 3), 2);
+
+    ASSERT_EQ(min3(2, 2, 2), 2);
+}
+
+TEST(MathTest, Max_is_working)
+{
+    ASSERT_EQ(max3(1, 2, 3), 3);
+    ASSERT_EQ(max3(1, 3, 2), 3);
+    ASSERT_EQ(max3(2, 1, 3), 3);
+    ASSERT_EQ(max3(2, 3, 1), 3);
+    ASSERT_EQ(max3(3, 1, 2), 3);
+    ASSERT_EQ(max3(3, 2, 1), 3);
+
+    ASSERT_EQ(max3(1, 2, 2), 2);
+    ASSERT_EQ(max3(2, 1, 2), 2);
+    ASSERT_EQ(max3(2, 2, 1), 2);
+
+    ASSERT_EQ(max3(3, 2, 2), 3);
+    ASSERT_EQ(max3(2, 3, 2), 3);
+    ASSERT_EQ(max3(2, 2, 3), 3);
+
+    ASSERT_EQ(max3(2, 2, 2), 2);
+}

+ 0 - 10
tests/transformation_test.cpp

@@ -245,14 +245,4 @@ TEST(TransformationTest, An_arbitrary_view_transformation)
     set_equal_precision(FLT_EPSILON);
 }
 
-TEST(TransformationTest, Check_that_deg_to_rad_is_working)
-{
-    double angle180 = deg_to_rad(180);
-    double angle90 = deg_to_rad(90);
-    double angle270 = deg_to_rad(270);
-
-    ASSERT_EQ(angle180, M_PI);
-    ASSERT_EQ(angle90, M_PI / 2.);
-    ASSERT_EQ(angle270, M_PI * 1.5);
-}