[WIP] Test 7 of refraction is in wip

raytracing/src/core/intersection-data.cpp

@@ -49,7 +49,6 @@ IntersectionData::IntersectionData(void) :
 
 IntersectionData::~IntersectionData(void)
 {
-    printf("destructor\n");
     m_shape = nullptr;
 }
 
@@ -111,6 +110,20 @@ void IntersectionData::set_over_point(const Tuple &a_point)
 
 /* ------------------------------------------------------------------------- */
 
+const Tuple &IntersectionData::under_point(void) const
+{
+    return m_under_point;
+}
+
+/* ------------------------------------------------------------------------- */
+
+void IntersectionData::set_under_point(const Tuple &a_point)
+{
+    m_under_point = a_point;
+}
+
+/* ------------------------------------------------------------------------- */
+
 const Tuple &IntersectionData::eyev(void) const
 {
     return m_eyev;

raytracing/src/core/intersection-data.h

@@ -54,6 +54,9 @@ namespace Raytracer
         const Tuple &over_point(void) const;
         void set_over_point(const Tuple &a_point);
 
+        const Tuple &under_point(void) const;
+        void set_under_point(const Tuple &a_point);
+
         const Tuple &eyev(void) const;
         void set_eyev(const Tuple &an_eyev);
 
@@ -78,6 +81,7 @@ namespace Raytracer
         Shape *m_shape;
         Tuple m_point;
         Tuple m_over_point;
+        Tuple m_under_point;
         Tuple m_eyev;
         Tuple m_normalv;
         Tuple m_reflectv;

raytracing/src/core/intersection.cpp

@@ -190,6 +190,7 @@ IntersectionData Intersection::prepare_computations(const Ray &a_ray, Intersecti
     the_data.set_eyev(-a_ray.direction());
     the_data.set_normalv(m_shape->normal_at(the_data.point()));
     the_data.set_over_point(the_data.point() + the_data.normalv() * kEpsilon);
+    the_data.set_under_point(the_data.point() - the_data.normalv() * kEpsilon);
     the_data.set_inside();
     the_data.set_reflectv(a_ray.direction().reflect(the_data.normalv()));
 

raytracing/src/renderer/world.cpp

@@ -28,6 +28,8 @@
 
 /* ------------------------------------------------------------------------- */
 
+#include <cmath>
+
 #include "core/common.h"
 #include "core/matrix.h"
 
@@ -159,21 +161,21 @@ Intersections World::intersect_world(const Ray &a_ray) const
 
 /* ------------------------------------------------------------------------- */
 
-Color World::shade_hit(const IntersectionData &an_intersection_data, uint32_t a_remainging) const
+Color World::shade_hit(const IntersectionData &an_intersection_data, uint32_t a_remaining) const
 {
     bool the_shadowed = is_shadowed(an_intersection_data.over_point());
     Shape *the_object = an_intersection_data.object();
     Color the_surface = the_object->material().lighting(the_object, m_light, an_intersection_data.over_point(),
                                                         an_intersection_data.eyev(), an_intersection_data.normalv(), the_shadowed);
-    Color the_reflected = reflected_color(an_intersection_data, a_remainging);
+    Color the_reflected = reflected_color(an_intersection_data, a_remaining);
     return the_surface + the_reflected;
 }
 
 /* ------------------------------------------------------------------------- */
 
-Color World::reflected_color(const IntersectionData &a_data, uint32_t a_remainging) const
+Color World::reflected_color(const IntersectionData &a_data, uint32_t a_remaining) const
 {
-    if (a_remainging <= 0)
+    if (a_remaining <= 0)
     {
         return Color(0, 0, 0);
     }
@@ -183,14 +185,63 @@ Color World::reflected_color(const IntersectionData &a_data, uint32_t a_remaingi
         return Color(0, 0, 0);
     }
     Ray the_reflected_ray(a_data.over_point(), a_data.reflectv());
-    Color the_color = color_at(the_reflected_ray, a_remainging - 1);
+    Color the_color = color_at(the_reflected_ray, a_remaining - 1);
 
     return the_color * a_data.object()->material().reflective();
 }
 
 /* ------------------------------------------------------------------------- */
 
-Color World::color_at(const Ray &a_ray, uint32_t a_remainging) const
+Color World::refracted_color(const IntersectionData &an_intersection_data, uint32_t a_remaining) const
+{
+    double the_n_ratio, the_cos_i, the_cos_t, the_sin_t;
+    Tuple the_direction;
+    Color the_color;
+    double the_transparency;
+
+    if (a_remaining <= 0)
+    {
+        return Color(0, 0, 0);
+    }
+
+    the_transparency = an_intersection_data.object()->material().transparency();
+    if (double_equal(the_transparency, 0))
+    {
+        return Color(0, 0, 0);
+    }
+
+    // Find the ratio of first index of refraction to the second.
+    // Yup, this inverted for the definition of the snell's Law
+    the_n_ratio = an_intersection_data.n1() / an_intersection_data.n2();
+
+    // Cos(theta_i) is the same as the dot product of the two vectors.
+    the_cos_i = an_intersection_data.eyev().dot(an_intersection_data.normalv());
+
+    // Find sin(theta_t)^2 via trigonometric identity
+    the_sin_t = the_n_ratio * the_n_ratio * (1.0 - the_cos_i * the_cos_i);
+    if (the_sin_t > 1)
+    {
+        return Color(0, 0, 0);
+    }
+
+    // Find cos(theta_t) via trigonometric identity
+    the_cos_t = std::sqrt(1.0 - the_sin_t);
+
+    // Compute the direction of the refracted ray
+    the_direction = an_intersection_data.normalv() * (the_n_ratio * the_cos_i - the_cos_t) -
+                    an_intersection_data.eyev() * the_n_ratio;
+    Ray the_refracted_ray(an_intersection_data.under_point(), the_direction);
+
+    // Find the color of the refracted ray, making sure to multiply by the transparency value
+    // to account for any opacity
+    the_color = color_at(the_refracted_ray, a_remaining - 1) * an_intersection_data.object()->material().transparency();
+
+    return the_color;
+}
+
+/* ------------------------------------------------------------------------- */
+
+Color World::color_at(const Ray &a_ray, uint32_t a_remaining) const
 {
     Color the_color = Color::Black();
 
@@ -208,7 +259,7 @@ Color World::color_at(const Ray &a_ray, uint32_t a_remainging) const
 
     IntersectionData the_comps = the_intersec.prepare_computations(a_ray);
 
-    the_color = shade_hit(the_comps, a_remainging);
+    the_color = shade_hit(the_comps, a_remaining);
 
     return the_color;
 }

raytracing/src/renderer/world.h

@@ -67,6 +67,8 @@ namespace Raytracer
         Intersections intersect_world(const Ray &a_ray) const;
         Color shade_hit(const IntersectionData &an_intersection_data, uint32_t a_remainging = kRemainingDefaultDepth) const;
         Color reflected_color(const IntersectionData &an_intersection_data, uint32_t a_remainging = kRemainingDefaultDepth) const;
+        Color refracted_color(const IntersectionData &an_intersection_data, uint32_t a_remainging = kRemainingDefaultDepth) const;
+
         Color color_at(const Ray &a_ray, uint32_t a_remainging = kRemainingDefaultDepth) const;
 
         bool is_shadowed(const Tuple &a_point) const;

tests/05_rays.cpp

@@ -232,7 +232,7 @@ SCENARIO("An intersection encapsulates t and object", "[features/intersections.f
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        WHEN("intersection(3.5,s)")
+        WHEN("intersection(3.5, s)")
         {
             Intersection i(3.5, &s);
 
@@ -284,7 +284,7 @@ SCENARIO("Intersection could be compared", "[features/intersections.feature]")
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        AND_GIVEN("i1 <- intersection(3,s) and i2 <- intersection(4,s)")
+        AND_GIVEN("i1 <- intersection(3, s) and i2 <- intersection(4, s)")
         {
             Intersection i1(3.0, &s);
             Intersection i2(4.0, &s);
@@ -324,13 +324,13 @@ SCENARIO("Aggregating intersections", "[features/intersections.feature]")
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        AND_GIVEN("i1 <- intersection(1,s)")
+        AND_GIVEN("i1 <- intersection(1, s)")
         {
             Intersection i1(1, &s);
-            AND_GIVEN("i2 <- intersection(2,s)")
+            AND_GIVEN("i2 <- intersection(2, s)")
             {
                 Intersection i2(2, &s);
-                WHEN("xs <- intersections(i1,i2)")
+                WHEN("xs <- intersections(i1, i2)")
                 {
                     Intersections xs = Intersections({i1, i2});
                     THEN("xs.count = 2")
@@ -394,7 +394,7 @@ SCENARIO("Intersect sets the object on the intersection", "[features/spheres.fea
         AND_GIVEN("s <- sphere()")
         {
             Sphere s;
-            WHEN("xs <- intersect(s,r)")
+            WHEN("xs <- intersect(s, r)")
             {
                 Intersections xs = s.intersect(r);
                 THEN("xs.count = 2")
@@ -421,13 +421,13 @@ SCENARIO("The hit, when all intersections have positive t", "[features/intersect
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        AND_GIVEN("i1 <- intersection(1,s)")
+        AND_GIVEN("i1 <- intersection(1, s)")
         {
             Intersection i1(1, &s);
-            AND_GIVEN("i2 <- intersection(2,s)")
+            AND_GIVEN("i2 <- intersection(2, s)")
             {
                 Intersection i2(2, &s);
-                AND_GIVEN("xs <- intersections(i1,i2)")
+                AND_GIVEN("xs <- intersections(i1, i2)")
                 {
                     Intersections xs = Intersections({i2, i1});
                     WHEN("i <- hit(xs)")
@@ -451,13 +451,13 @@ SCENARIO("The hit, when some intersections have negative t", "[features/intersec
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        AND_GIVEN("i1 <- intersection(-1,s)")
+        AND_GIVEN("i1 <- intersection(-1, s)")
         {
             Intersection i1(-1, &s);
-            AND_GIVEN("i2 <- intersection(2,s)")
+            AND_GIVEN("i2 <- intersection(2, s)")
             {
                 Intersection i2(1, &s);
-                AND_GIVEN("xs <- intersections(i1,i2)")
+                AND_GIVEN("xs <- intersections(i1, i2)")
                 {
                     Intersections xs = Intersections({i2, i1});
                     WHEN("i <- hit(xs)")
@@ -481,13 +481,13 @@ SCENARIO("The hit, when all intersections have negative t", "[features/intersect
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        AND_GIVEN("i1 <- intersection(-2,s)")
+        AND_GIVEN("i1 <- intersection(-2, s)")
         {
             Intersection i1(-2, &s);
-            AND_GIVEN("i2 <- intersection(-1,s)")
+            AND_GIVEN("i2 <- intersection(-1, s)")
             {
                 Intersection i2(-1, &s);
-                AND_GIVEN("xs <- intersections(i1,i2)")
+                AND_GIVEN("xs <- intersections(i1, i2)")
                 {
                     Intersections xs = Intersections({i1, i2});
                     WHEN("i <- hit(xs)")
@@ -512,16 +512,16 @@ SCENARIO("The hit is always the lowest nonnegative intersection", "[features/int
     GIVEN("s <- sphere()")
     {
         Sphere s;
-        AND_GIVEN("i1 <- intersection(5,s)")
+        AND_GIVEN("i1 <- intersection(5, s)")
         {
             Intersection i1(5, &s);
-            AND_GIVEN("i2 <- intersection(7,s)")
+            AND_GIVEN("i2 <- intersection(7, s)")
             {
                 Intersection i2(7, &s);
-                AND_GIVEN("i3 <- intersection(-3,s)")
+                AND_GIVEN("i3 <- intersection(-3, s)")
                 {
                     Intersection i3(-3, &s);
-                    AND_GIVEN("i4 <- intersection(2,s)")
+                    AND_GIVEN("i4 <- intersection(2, s)")
                     {
                         Intersection i4(2, &s);
                         AND_GIVEN("xs <- intersections(i1, i2, i3, i4)")
@@ -645,7 +645,7 @@ SCENARIO("Intersecting a scaled sphere with a ray", "[features/spheres.feature]"
         AND_GIVEN("s <- Sphere()")
         {
             Sphere s;
-            WHEN("set_transform(s,scaling(2,2,2))")
+            WHEN("set_transform(s,scaling(2, 2, 2))")
             {
                 s.set_transform(Matrix::scaling(2, 2, 2));
                 AND_WHEN("xs <- intersect(s,r)")

tests/11_reflection_refraction.cpp

@@ -33,6 +33,19 @@ using namespace Raytracer;
 
 /* ------------------------------------------------------------------------- */
 
+class TestPattern : public Pattern
+{
+public:
+    TestPattern(void) = default;
+
+    const Color pattern_at(const Tuple &a_point) const override
+    {
+        return Color(a_point.x(), a_point.y(), a_point.z());
+    }
+};
+
+/* ------------------------------------------------------------------------- */
+
 SCENARIO("Reflectivity for the default material", "[features/materials.feature]")
 {
     GIVEN("m <- material()")
@@ -349,7 +362,7 @@ SCENARIO("Finding n1 and n2 at various intersections", "[features/intersections.
             B.material().set_refractive_index(2.0);
             GIVEN("C <- glass_sphere() with:")
             // | transform                 | translation(0, 0, 0.25) |
-            // | material.refractive_index | 2.5                      |
+            // | material.refractive_index | 2.5                     |
             {
                 Sphere C = Sphere::Glass();
                 C.set_transform(Matrix::translation(0, 0, 0.25));
@@ -405,3 +418,218 @@ SCENARIO("Finding n1 and n2 at various intersections", "[features/intersections.
         }
     }
 }
+
+/* ------------------------------------------------------------------------- */
+
+SCENARIO("The under point is offset below the surface", "[features/intersections.feature]")
+{
+    GIVEN("r <- ray(point(0, 0, -5), vector(0, 0, 1)")
+    {
+        Ray r(Tuple::Point(0, 0, -5), Tuple::Vector(0, 0, 1));
+        AND_GIVEN("shape <- glass_sphere() with:")
+        // | transform                 | translation(0, 0, 1)  |
+        {
+            Sphere shape = Sphere::Glass();
+            shape.set_transform(Matrix::translation(0, 0, 1));
+            AND_GIVEN("i <- intersection(5, shape)")
+            {
+                Intersection i(5, &shape);
+                AND_GIVEN("xs <- intersections(i)")
+                {
+                    Intersections xs = Intersections({i});
+                    WHEN("comps <- prepare_computations(i, r, xs)")
+                    {
+                        IntersectionData comps = i.prepare_computations(r, &xs);
+                        THEN("comps.under_point.z > EPSILON / 2")
+                        {
+                            REQUIRE(comps.under_point().z() > kEpsilon / 2);
+                        }
+                        AND_THEN("comps.point.z < comps.under_point.z")
+                        {
+                            REQUIRE(comps.point().z() < comps.under_point().z());
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+/* ------------------------------------------------------------------------- */
+
+SCENARIO("The refracted color with a, opaque surface", "[features/world.feature]")
+{
+    GIVEN("w <- default_world()")
+    {
+        World w = World::default_world();
+        AND_GIVEN("shape <- first object of w")
+        {
+            Shape *shape = w.objects(0);
+            AND_GIVEN("r <- ray(point(0, 0, -5), vector(0, 0, 1))")
+            {
+                Ray r(Tuple::Point(0, 0, -5), Tuple::Vector(0, 0, 1));
+                AND_GIVEN("xs <- intersections(4:shape, 6:shape)")
+                {
+                    Intersections xs = Intersections({Intersection(4.0, shape),
+                                                      Intersection(6.0, shape)});
+                    WHEN("comps <- prepare_computations(xs[0], r, xs)")
+                    {
+                        IntersectionData comps = xs[0].prepare_computations(r, &xs);
+                        AND_WHEN("c <- refracted_color(w, comps, 5)")
+                        {
+                            Color c = w.refracted_color(comps, 5);
+                            THEN("c = color(0, 0, 0)")
+                            {
+                                REQUIRE(c == Color(0, 0, 0));
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+/* ------------------------------------------------------------------------- */
+
+SCENARIO("The refracted color at the maximum recursive depth", "[features/world.feature]")
+{
+    GIVEN("w <- default_world()")
+    {
+        World w = World::default_world();
+        AND_GIVEN("shape <- first object of w")
+        {
+            Shape *shape = w.objects(0);
+            AND_GIVEN("shape has:")
+            {
+                // | material.transparency     | 1.0       |
+                // | material.refractive_index | 1.5       |
+                shape->material().set_transparency(1.0);
+                shape->material().set_refractive_index(1.5);
+                AND_GIVEN("r <- ray(point(0, 0, -5), vector(0, 0, 1))")
+                {
+                    Ray r(Tuple::Point(0, 0, -5), Tuple::Vector(0, 0, 1));
+                    AND_GIVEN("xs <- intersections(4:shape, 6:shape)")
+                    {
+                        Intersections xs = Intersections({Intersection(4.0, shape),
+                                                          Intersection(6.0, shape)});
+                        WHEN("comps <- prepare_computations(xs[0], r, xs)")
+                        {
+                            IntersectionData comps = xs[0].prepare_computations(r, &xs);
+                            AND_WHEN("c <- refracted_color(w, comps, 0)")
+                            {
+                                Color c = w.refracted_color(comps, 0);
+                                THEN("c = color(0, 0, 0)")
+                                {
+                                    REQUIRE(c == Color(0, 0, 0));
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+/* ------------------------------------------------------------------------- */
+
+SCENARIO("The refracted color under total internal reflection", "[features/world.feature]")
+{
+    GIVEN("w <- default_world()")
+    {
+        World w = World::default_world();
+        AND_GIVEN("shape <- first object of w")
+        {
+            Shape *shape = w.objects(0);
+            AND_GIVEN("shape has:")
+            {
+                // | material.transparency     | 1.0       |
+                // | material.refractive_index | 1.5       |
+                shape->material().set_transparency(1.0);
+                shape->material().set_refractive_index(1.5);
+                AND_GIVEN("r <- ray(point(0, 0, sqrt(2) / 2), vector(0, 1, 0))")
+                {
+                    Ray r(Tuple::Point(0, 0, sqrt(2) / 2), Tuple::Vector(0, 1, 0));
+                    AND_GIVEN("xs <- intersections(-(sqrt(2) / 2):shape, sqrt(2) / 2:shape)")
+                    {
+                        Intersections xs = Intersections({Intersection(-(sqrt(2) / 2), shape),
+                                                          Intersection(sqrt(2) / 2, shape)});
+                        // NOTE: this time you're inside the sphere, so you need to look at the
+                        // second intersection, xs[1] and not xs[0]
+                        WHEN("comps <- prepare_computations(xs[1], r, xs)")
+                        {
+                            IntersectionData comps = xs[1].prepare_computations(r, &xs);
+                            AND_WHEN("c <- refracted_color(w, comps, 5)")
+                            {
+                                Color c = w.refracted_color(comps, 5);
+                                THEN("c = color(0, 0, 0)")
+                                {
+                                    REQUIRE(c == Color(0, 0, 0));
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}
+
+/* ------------------------------------------------------------------------- */
+
+SCENARIO("The refracted color with a refracted ray", "[features/world.feature]")
+{
+    GIVEN("w <- default_world()")
+    {
+        World w = World::default_world();
+        AND_GIVEN("A <- first object of w")
+        {
+            Shape *A = w.objects(0);
+            AND_GIVEN("A has:")
+            {
+                // | material.ambient  | 1.0            |
+                // | material.pattern  | test_pattern() |
+                A->material().set_ambient(1.0);
+                TestPattern the_pattern;
+                A->material().set_pattern(&the_pattern);
+                AND_GIVEN("B <- second object of w")
+                {
+                    Shape *B = w.objects(1);
+                    AND_GIVEN("shape has:")
+                    {
+                        // | material.transparency     | 1.0       |
+                        // | material.refractive_index | 1.5       |
+                        B->material().set_transparency(1.0);
+                        B->material().set_refractive_index(1.5);
+                        AND_GIVEN("r <- ray(point(0, 0, 0.1, vector(0, 1, 0))")
+                        {
+                            Ray r(Tuple::Point(0, 0, 0.1), Tuple::Vector(0, 1, 0));
+                            AND_GIVEN("xs <- intersections(-0.9899:A, -0.4899:B, 0.4899:B, 0.9899:A)")
+                            {
+                                Intersections xs = Intersections({
+                                    Intersection(-0.9899, A),
+                                    Intersection(-0.4899, B),
+                                    Intersection(0.4899, B),
+                                    Intersection(0.9899, A),
+                                });
+                                WHEN("comps <- prepare_computations(xs[2], r, xs)")
+                                {
+                                    IntersectionData comps = xs[2].prepare_computations(r, &xs);
+                                    AND_WHEN("c <- refracted_color(w, comps, 5)")
+                                    {
+                                        Color c = w.refracted_color(comps, 5);
+                                        THEN("c = color(0, 0.99888, 0.04725)")
+                                        {
+                                            REQUIRE(c == Color(0, 0.99888, 0.04725));
+                                        }
+                                    }
+                                }
+                            }
+                        }
+                    }
+                }
+            }
+        }
+    }
+}