2019年5月22日水曜日

開発環境

The Ray Tracer Challenge: A Test-Driven Guide to Your First 3D Renderer (Jamis Buck(著)、Pragmatic Bookshelf)、Chapter 11(Reflection and Refraction)のReflectionを取り組んでみる。

コード

Python 3

materials_test.py

#!/usr/bin/env python3
from unittest import TestCase, main
from materials import Material
from tuples import Point, Vector, Color
from lights import Light
from patterns import Solid, Stripe
from spheres import Sphere
import math


class MaterialTest(TestCase):
    def setUp(self):
        self.m = Material()
        self.position = Point(0, 0, 0)
        self.obj = Sphere()

    def tearDown(self):
        pass

    def test_marial(self):
        m = Material()
        tests = [(m.color, Color(1, 1, 1)),
                 (m.ambient, 0.1),
                 (m.diffuse, 0.9),
                 (m.specular, 0.9),
                 (m.shininess, 200)]
        for a, b in tests:
            self.assertEqual(a, b)

    def test_lighting_with_eye_between_light_surface(self):
        eye_vecotr = Vector(0, 0, -1)
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 0, -10), Color(1, 1, 1))
        result = self.m.lighting(
            self.obj, light, self.position, eye_vecotr, normal_vector)
        self.assertEqual(result, Color(1.9, 1.9, 1.9))

    def test_lighting_with_eye_between_light_surface_eye45(self):
        eye_vector = Vector(0, 1 / math.sqrt(2), -1 / math.sqrt(2))
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 0, -10), Color(1, 1, 1))
        self.assertEqual(
            self.m.lighting(self.obj, light, self.position,
                            eye_vector, normal_vector),
            Color(1.0, 1.0, 1.0))

    def test_lighting_with_eye_opposite_surface_light45(self):
        eye_vector = Vector(0, 0, -1)
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 10, -10), Color(1, 1, 1))
        self.assertEqual(
            self.m.lighting(self.obj, light, self.position,
                            eye_vector, normal_vector),
            Color(0.7364, 0.7364, 0.7364))

    def test_lighting_eye_reflection(self):
        eye_vector = Vector(0, -1 / math.sqrt(2), -1 / math.sqrt(2))
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 10, -10), Color(1, 1, 1))
        self.assertEqual(
            self.m.lighting(self.obj, light, self.position,
                            eye_vector, normal_vector),
            Color(1.6364, 1.6364, 1.6364))

    def test_lighting_behind_surface(self):
        eye_vector = Vector(0, 0, -1)
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 0, 10), Color(1, 1, 1))
        self.assertEqual(
            self.m.lighting(self.obj, light, self.position,
                            eye_vector, normal_vector),
            Color(0.1, 0.1, 0.1))

    def test_lighting_with_surface_in_shadow(self):
        eye_vercotr = Vector(0, 0, -1)
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 0, -10), Color(1, 1, 1))
        in_shadow = True
        result = self.m.lighting(self.obj, light, self.position, eye_vercotr,
                                 normal_vector, in_shadow)
        self.assertEqual(result, Color(0.1, 0.1, 0.1))

    def test_lighting_with_stripe_aplied(self):
        self.m.pattern = Stripe(Solid(Color(1, 1, 1)), Solid(Color(0, 0, 0)))
        self.m.ambient = 1
        self.m.diffuse = 0
        self.m.specular = 0
        eye_vector = Vector(0, 0, -1)
        normal_vector = Vector(0, 0, -1)
        light = Light(Point(0, 0, -10), Color(1, 1, 1))
        for xyz, color in [((0.9, 0, 0), Color(1, 1, 1)),
                           ((1.1, 0, 0), Color(0, 0, 0))]:
            self.assertEqual(
                self.m.lighting(self.obj, light, Point(
                    *xyz), eye_vector, normal_vector),
                color)

    def test_reflectivity(self):
        self.assertEqual(self.m.reflective, 0.0)


if __name__ == '__main__':
    main()

materials.py

from tuples import Color, is_equal


class Material:
    def __init__(self, color=Color(1, 1, 1), ambient=0.1, diffuse=0.9,
                 specular=0.9, shininess=200, pattern=None, reflective=0):
        self.color = color
        self.ambient = ambient
        self.diffuse = diffuse
        self.specular = specular
        self.shininess = shininess
        self.pattern = pattern
        self.reflective = reflective

    def __repr__(self):
        return f'Material({self.color},{self.ambient},{self.diffuse},' +\
            f'{self.specular},{self.shininess})'

    def __eq__(self, other):
        if self.color != other.color:
            return False
        tests = [(self.ambient, other.ambient),
                 (self.diffuse, other.diffuse),
                 (self.specular, other.specular),
                 (self.shininess, other.shininess)]
        for a, b in tests:
            if not is_equal(a, b):
                return False
        return True

    def lighting(self, obj, light, point, eye_vector, normal_vector,
                 in_shadow=False) -> Color:
        if self.pattern is None:
            color = self.color
        else:
            color = self.pattern.at_shape(obj, point)
        effective_color = color * light.intensity
        light_vector = (light.position - point).normalize()
        ambient = effective_color * self.ambient
        if in_shadow:
            return ambient
        light_dot_normal = light_vector.dot(normal_vector)
        if light_dot_normal < 0:
            diffuse = Color(0, 0, 0)
            specular = Color(0, 0, 0)
        else:
            diffuse = effective_color * self.diffuse * light_dot_normal
            reflect_vector = -light_vector.reflect(normal_vector)
            reflect_dot_eye = reflect_vector.dot(eye_vector)
            if reflect_dot_eye <= 0:
                specular = Color(0, 0, 0)
            else:
                factor = reflect_dot_eye ** self.shininess
                specular = light.intensity * self.specular * factor
        return ambient + diffuse + specular

intersections_test.py

#!/usr/bin/env python3
from unittest import TestCase, main
import math
from intersections import Intersection, Intersections
from tuples import Point, Vector, EPSILON
from spheres import Sphere
from planes import Plane
from rays import Ray
from transformations import translation


class IntersectionTest(TestCase):
    def setUp(self):
        pass

    def tearDown(self):
        pass

    def test_intersection(self):
        s = Sphere()
        i = Intersection(3.5, s)
        self.assertEqual(i.t, 3.5)
        self.assertEqual(i.obj, s)

    def test_prepare_computations(self):
        r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
        shape = Sphere()
        i = Intersection(4, shape)
        comps = i.prepare_computations(r)
        for a, b in [(comps.t, i.t),
                     (comps.obj, i.obj),
                     (comps.point, Point(0, 0, -1)),
                     (comps.eye_vector, Vector(0, 0, -1)),
                     (comps.normal_vector, Vector(0, 0, -1))]:
            self.assertEqual(a, b)

    def test_hit_intersection_outside(self):
        r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
        shape = Sphere()
        i = Intersection(4, shape)
        comps = i.prepare_computations(r)
        self.assertFalse(comps.inside)

    def test_hit_intersection_inside(self):
        r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
        shape = Sphere()
        i = Intersection(1, shape)
        comps = i.prepare_computations(r)
        for a, b in [(comps.point, Point(0, 0, 1)),
                     (comps.eye_vector, Vector(0, 0, -1)),
                     (comps.normal_vector, Vector(0, 0, -1))]:
            self.assertEqual(a, b)
        self.assertTrue(comps.inside)

    def test_hit_shoud_offset_point(self):
        ray = Ray(Point(0, 0, -5), Vector(0, 0, 1))
        shape = Sphere(transform=translation(0, 0, 1))
        i = Intersection(5, shape)
        comps = i.prepare_computations(ray)
        self.assertLess(comps.over_point.z, -EPSILON / 2)
        self.assertGreater(comps.point.z, comps.over_point.z)

    def test_precomputing_reflection_vvector(self):
        shape = Plane()
        ray = Ray(Point(0, 1, -1),
                  Vector(0, -1 / math.sqrt(2), 1 / math.sqrt(2)))
        intersection = Intersection(math.sqrt(2), shape)
        comps = intersection.prepare_computations(ray)
        self.assertEqual(comps.reflect_vector,
                         Vector(0, 1 / math.sqrt(2), 1 / math.sqrt(2)))


class IntersectionsTest(TestCase):
    def setUp(self):
        pass

    def tearDown(self):
        pass

    def test_intersection(self):
        s = Sphere()
        i1 = Intersection(1, s)
        i2 = Intersection(2, s)
        xs = Intersections(i1, i2)
        for a, b in [(len(xs), 2), (xs[0].t, 1), (xs[1].t, 2)]:
            self.assertEqual(a, b)

    def test_hit(self):
        s = Sphere()
        i1 = Intersection(1, s)
        i2 = Intersection(2, s)
        xs = Intersections(i2, i1)
        self.assertEqual(xs.hit(), i1)

    def test_hit_positive_and_negative(self):
        s = Sphere()
        i1 = Intersection(-1, s)
        i2 = Intersection(1, s)
        xs = Intersections(i2, i1)
        self.assertEqual(xs.hit(), i2)

    def test_hit_none(self):
        s = Sphere()
        i1 = Intersection(-2, s)
        i2 = Intersection(-1, s)
        xs = Intersections(i2, i1)
        self.assertIsNone(xs.hit())

    def test_hit_nonnegative(self):
        s = Sphere()
        intersections = [Intersection(t, s) for t in [5, 7, -3, 2]]
        xs = Intersections(*intersections)
        self.assertEqual(xs.hit(), intersections[-1])


if __name__ == '__main__':
    main()

intersections.py

from tuples import Point, EPSILON


class Intersection:
    def __init__(self, t: float, obj):
        self.t = t
        self.obj = obj

    def __repr__(self):
        return f'Intersection({self.t},{self.obj})'

    def prepare_computations(self, ray):
        point = ray.position(self.t)
        eye_vector = -ray.direction
        normal_vector = self.obj.normal_at(point)
        return Computations(t=self.t,
                            obj=self.obj,
                            point=point,
                            eye_vector=eye_vector,
                            normal_vector=normal_vector,
                            ray=ray)


class Intersections:
    def __init__(self, *args):
        self.xs = list(args)
        self.xs.sort(key=lambda o: o.t)

    def __getitem__(self, i: int):
        return self.xs[i]

    def __len__(self):
        return len(self.xs)

    def __repr__(self):
        return f'Inersections({self.xs})'

    def hit(self):
        for i in self.xs:
            if i.t > 0:
                return i
        return None


class Computations:
    def __init__(self, t, obj, point, eye_vector, normal_vector, ray):
        self.t = t
        self.obj = obj
        self.point = point
        self.eye_vector = eye_vector
        self.normal_vector = normal_vector
        if normal_vector.dot(eye_vector) < 0:
            self.inside = True
            self.normal_vector = -self.normal_vector
        else:
            self.inside = False
        self.over_point = point + self.normal_vector * EPSILON
        self.reflect_vector = ray.direction.reflect(self.normal_vector)

    def __repr__(self):
        return f'Computations({self.t},{self.obj},{self.point},' +\
            f'{self.eye_vector},{self.normal_vector},{self.inside})'

world_test.py

#!/usr/bin/env python3
from unittest import TestCase, main
import math
from tuples import Point, Vector, Color
from lights import Light
from spheres import Sphere
from planes import Plane
from materials import Material
from transformations import scaling, translation
from rays import Ray
from intersections import Intersection
from world import World


class WorldTest(TestCase):
    def setUp(self):
        self.light = Light(Point(-10, 10, -10), Color(1, 1, 1))
        self.sphere1 = Sphere(material=Material(color=Color(0.8, 1.0, 0.6),
                                                diffuse=0.7,
                                                specular=0.2))
        self.sphere2 = Sphere(transform=scaling(0.5, 0.5, 0.5))
        self.world = World(objs=[self.sphere1, self.sphere2], light=self.light)

    def tearDown(self):
        pass

    def test_world(self):
        w = World()
        self.assertEqual(len(w), 0)
        self.assertIsNone(w.light)

    def test_default_world(self):
        self.assertEqual(self.world.light, self.light)
        for s in [self.sphere1, self.sphere2]:
            self.assertIn(s, self.world)

    def test_intersect_ray(self):
        r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
        xs = self.world.intersect(r)
        self.assertEqual(len(xs), 4)
        for i, t in enumerate([4, 4.5, 5.5, 6]):
            self.assertEqual(xs[i].t, t)

    def test_shade_hit(self):
        r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
        shape = self.world[0]
        i = Intersection(4, shape)
        comps = i.prepare_computations(r)
        c = self.world.shade_hit(comps)
        self.assertEqual(c, Color(0.38066, 0.47583, 0.2855))

    def test_shade_hit_from_inside(self):
        self.world.light = Light(Point(0, 0.25, 0), Color(1, 1, 1))
        r = Ray(Point(0, 0, 0), Vector(0, 0, 1))
        shape = self.world[1]
        i = Intersection(0.5, shape)
        comps = i.prepare_computations(r)
        c = self.world.shade_hit(comps)
        self.assertEqual(c, Color(0.90498, 0.90498, 0.90498))

    def test_color_ray_misses(self):
        r = Ray(Point(0, 0, -5), Vector(0, 1, 0))
        c = self.world.color_at(r)
        self.assertEqual(c, Color(0, 0, 0))

    def test_color_ray_hits(self):
        r = Ray(Point(0, 0, -5), Vector(0, 0, 1))
        c = self.world.color_at(r)
        self.assertEqual(c, Color(0.38066, 0.47583, 0.2855))

    def test_color_intersection_behind_the_ray(self):
        outer = self.world[0]
        inner = self.world[1]
        outer.material.ambient = 1
        inner.material.ambient = 1
        r = Ray(Point(0, 0, 0.75), Vector(0, 0, -1))
        c = self.world.color_at(r)
        self.assertNotEqual(c, outer.material.color)
        self.assertEqual(c, inner.material.color)

    def test_no_shadow_nothing_is_collinear_with_point_and_light(self):
        p = Point(0, 10, 0)
        self.assertFalse(self.world.is_shadowed(p))

    def test_shadow_obj_between_point_and_light(self):
        p = Point(10, -10, 10)
        self.assertTrue(self.world.is_shadowed(p))

    def test_no_shadow_obj_behind_light(self):
        p = Point(-20, 20, -20)
        self.assertFalse(self.world.is_shadowed(p))

    def test_no_shadow_obj_behind_point(self):
        p = Point(-2, 2, -2)
        self.assertFalse(self.world.is_shadowed(p))

    def test_shade_hit_given_intersection_in_shadow(self):
        light = Light(Point(0, 0, -10), Color(1, 1, 1))
        s1 = Sphere()
        s2 = Sphere(translation(0, 0, 10))
        w = World([s1, s2], light)
        ray = Ray(Point(0, 0, 5), Vector(0, 0, 1))
        i = Intersection(4, s2)
        comps = i.prepare_computations(ray)
        c = w.shade_hit(comps)
        self.assertEqual(c, Color(0.1, 0.1, 0.1))

    def test_reflected_color_for_nonreflecive_material(self):
        ray = Ray(Point(0, 0, 0), Vector(0, 0, 1))
        shape = self.sphere2
        shape.material.ambient = 1
        intersection = Intersection(1, shape)
        comps = intersection.prepare_computations(ray)
        color = self.world.reflected_color(comps)
        self.assertEqual(color, Color(0, 0, 0))

    def test_reflected_color_for_reflective_material(self):
        shape = Plane(material=Material(reflective=0.5),
                      transform=translation(0, -1, 0))
        self.world.objs.append(shape)
        ray = Ray(Point(0, 0, -3),
                  Vector(0, -1 / math.sqrt(2), 1 / math.sqrt(2)))
        intersection = Intersection(math.sqrt(2), shape)
        comps = intersection.prepare_computations(ray)
        color = self.world.reflected_color(comps)
        self.assertEqual(color, Color(0.19033, 0.23791, 0.14274))

    def test_shade_hit_with_reflective_material(self):
        shape = Plane(material=Material(reflective=0.5),
                      transform=translation(0, -1, 0))
        self.world.objs.append(shape)
        ray = Ray(Point(0, 0, -3),
                  Vector(0, -1 / math.sqrt(2), 1 / math.sqrt(2)))
        intersection = Intersection(math.sqrt(2), shape)
        comps = intersection.prepare_computations(ray)
        color = self.world.shade_hit(comps)
        self.assertEqual(color, Color(0.87675, 0.92434, 0.82917))

    def test_reflected_color_at_maximum_recursive_depth(self):
        shape = Plane(material=Material(reflective=0.5),
                      transform=translation(0, -1, 0))
        self.world.objs.append(shape)
        ray = Ray(Point(0, 0, -3),
                  Vector(0, -1 / math.sqrt(2), 1 / math.sqrt(2)))
        intersection = Intersection(math.sqrt(2), shape)
        comps = intersection.prepare_computations(ray)
        color = self.world.reflected_color(comps, 0)
        self.assertEqual(color, Color(0, 0, 0))


if __name__ == '__main__':
    main()

world.py

#!/usr/bin/env python3
from intersections import Intersections
from tuples import Color
from rays import Ray


class World:
    def __init__(self, objs=None, light=None):
        if objs is None:
            self.objs = []
        else:
            self.objs = objs
        self.light = light

    def __getitem__(self, y):
        return self.objs[y]

    def __cointains__(self, key):
        return key in self.objs

    def __len__(self):
        return len(self.objs)

    def __repr__(self):
        return f'World({self.objs}, {self.light})'

    def intersect(self, ray):
        intersections = []
        for obj in self.objs:
            intersections += obj.intersect(ray)
        return Intersections(*intersections)

    def shade_hit(self, comps, remaining=1):
        surface = comps.obj.material.lighting(
            comps.obj, self.light, comps.point, comps.eye_vector,
            comps.normal_vector, self.is_shadowed(comps.over_point))
        reflected = self.reflected_color(comps, remaining)
        return surface + reflected

    def color_at(self, ray, remaining=1):
        intersections = self.intersect(ray)
        hit = intersections.hit()
        if hit is None:
            return Color(0, 0, 0)
        comps = hit.prepare_computations(ray)
        return self.shade_hit(comps, remaining)

    def is_shadowed(self, point) -> bool:
        vector = self.light.position - point
        distance = vector.magnitude()
        direction = vector.normalize()
        ray = Ray(point, direction)
        intersections = self.intersect(ray)
        hit = intersections.hit()
        return (hit is not None) and hit.t < distance

    def reflected_color(self, comps, remaining=5):
        if remaining <= 0:
            return Color(0, 0, 0)
        if comps.obj.material.reflective == 0:
            return Color(0, 0, 0)
        reflect_ray = Ray(comps.over_point, comps.reflect_vector)
        color = self.color_at(reflect_ray, remaining)
        return color * comps.obj.material.reflective

sample1.py

#!/usr/bin/env python3
import math
import time
from tuples import Point, Vector, Color
from planes import Plane
from spheres import Sphere
from materials import Material
from patterns import Solid, Stripe, Checkers
from camera import Camera
from lights import Light
from world import World
from transformations import translation, scaling, view_transform
print('ファイル名, rendering time(秒)')

width = 250
height = 125

checkers = Checkers(Solid(Color(0, 1, 0)), Solid(Color(1, 1, 1)))
planes = [Plane(material=Material(pattern=checkers, reflective=1)),
          Plane(material=Material(pattern=checkers))]

stripe = Stripe(Solid(Color(1, 0, 0)), Solid(Color(0, 0, 1)),
                transform=scaling(0.5, 0.5, 0.5))
spheres = [Sphere(material=Material(pattern=stripe),
                  transform=translation(0, 1, 0)),
           Sphere(material=Material(pattern=stripe, reflective=1),
                  transform=translation(0, 1, 0))]

camera = Camera(width, height, math.pi / 2,
                transform=view_transform(Point(0, 1.5, -5), Point(0, 1, 0),
                                         Vector(0, 1, 0)))
world = World([], Light(Point(-10, 10, -10), Color(1, 1, 1)))

for i, objs in enumerate(zip(planes, spheres), 1):
    world.objs = objs
    start = time.time()
    canvas = camera.render(world)
    s = time.time() - start
    with open(f'sample{i}.ppm', 'w') as f:
        canvas.to_ppm(f)
    print(f'sample{i}.ppm,{s}')

入出力結果(Bash、cmd(コマンドプロンプト)、Terminal、Jupyter(IPython))

C:\Users\...>py materials_test.py
........
----------------------------------------------------------------------
Ran 8 tests in 0.003s

OK

C:\Users\...>py patterns_test.py
................
----------------------------------------------------------------------
Ran 16 tests in 0.007s

OK

C:\Users\...>py sample4.py
ファイル名, rendering time(秒)
sample6.ppm,132.31091618537903
sample7.ppm,143.2693841457367

C:\Users\...>

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