def refracted_color(self, comps: Precomputed, remaining: int = 5) -> Color:
if remaining <= 0:
return Color(0, 0, 0)
if comps.object.material.transparency == 0:
return Color(0, 0, 0)
# Find the ratio of the first index of refraction to the second.
# (Yup, this is inverted from the definition of Snell's Law.)
n_ratio = comps.n1 / comps.n2
# cos(theta_i) is the same as the dot product of the two vectors
cos_i = Vec3.dot(comps.eyev, comps.normalv)
# Find sin(theta_t)^2 via trigonometric identity
sin2_t = n_ratio**2 * (1 - cos_i**2)
if sin2_t > 1:
return Color(0, 0, 0)
# Find cos(theta_t) via trigonometric identity
cos_t = math.sqrt(1.0 - sin2_t)
# Compute the direction of the refracted ray
direction = comps.normalv * (n_ratio * cos_i -
cos_t) - comps.eyev * n_ratio
# Create the refracted ray
refract_ray = Ray(comps.under_point, direction)
# Find the color of the refracted ray, making sure to multiply
# by the transparency value to account for any opacity
result = self.color_at(refract_ray, remaining - 1) *\
comps.object.material.transparency
return result
def ch7():
# Step 1
floor = Sphere()
floor.transform = Matrix.scaling(10, 0.01, 10)
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
floor.material.specular = 0
# Step 2
left_wall = Sphere()
left_wall.transform = Matrix.translation(0, 0, 5) * Matrix.rotation_y(-45) * \
Matrix.rotation_x(90) * Matrix.scaling(10, 0.01, 10)
left_wall.material = floor.material
# Step 3
right_wall = Sphere()
right_wall.transform = Matrix.translation(0, 0, 5) * Matrix.rotation_y(45) * \
Matrix.rotation_x(90) * Matrix.scaling(10, 0.01, 10)
right_wall.material = floor.material
# Step 4
middle = Sphere()
middle.transform = Matrix.translation(-0.5, 1, 0.5)
middle.material = Material()
middle.material.color = Color(0.1, 1, 0.5)
middle.material.diffuse = 0.7
middle.material.specular = 0.3
# Step 5
right = Sphere()
right.transform = Matrix.translation(1.5, 0.5, -0.5) * Matrix.scaling(
0.5, 0.5, 0.5)
right.material = Material()
right.material.color = Color(0.5, 1, 0.1)
right.material.diffuse = 0.7
right.material.specular = 0.3
# Step 6
left = Sphere()
left.transform = Matrix.translation(-1.5, 0.33, -0.75) * Matrix.scaling(
0.33, 0.33, 0.33)
left.material = Material()
left.material.color = Color(1, 0.8, 0.1)
left.material.diffuse = 0.7
left.material.specular = 0.3
world = World()
world.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
world.objects.extend([floor, left_wall, right_wall, middle, right, left])
camera = Camera(100, 50, 60)
# camera = Camera(500, 250, 60)
camera.transform = view_transform(point(0, 1.5, -5), point(0, 1, 0),
vector(0, 1, 0))
canvas = camera.render(world)
with open('ch8.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def reflected_color(self, comps: Precomputed, remaining: int = 5) -> Color:
if remaining <= 0:
return Color(0, 0, 0)
if comps.object.material.reflective == 0.0:
return Color(0, 0, 0)
reflect_ray = Ray(comps.over_point, comps.reflectv)
color = self.color_at(reflect_ray, remaining - 1)
return color * comps.object.material.reflective
def lighting(self, obj, light: PointLight, point: Point, eyev: Vector,
normalv: Vector, in_shadow: bool) -> Color:
"""Calculates the color shaded on the surface of the object using various
properties from the material.
:param obj: The Shape object that will be used if a pattern is set.
:param light: A light source that potentially intersects with the surface.
:param point: A point in the space.
:param eyev: A vector representing the direction from the point on the surface to the eye of the view
:param normalv: The normal of the surface.
:param in_shadow: Boolean indicating if the point is in shadow between an object and the light source.
:return:
"""
color = self.pattern.pattern_at_shape(
obj, point) if self.pattern is not None else self.color
# combine the surface color with the light's color/intensity
effective_color = color * light.intensity
# find the direction to the light source
lightv = (light.position - point).normalize()
# compute the ambient contribution
ambient = effective_color * self.ambient
# if the point is in shadow, ambient should be the only color factored into
if in_shadow:
return ambient
# light_dot_normal represent the cosine of the angle between the
# light vector and the normal vector. A negative number means the
# light is on the other side of the surface.
light_dot_normal = Vec3.dot(lightv, normalv)
if light_dot_normal < 0:
diffuse = Color(0, 0, 0)
specular = Color(0, 0, 0)
else:
# compute the diffuse contribution
diffuse = effective_color * self.diffuse * light_dot_normal
# reflect_dot_eye represents the cosine of the angle between the
# reflection vector and the eye vector. A negative number means the
# light reflects away from the eye.
reflectv = reflect(-lightv, normalv)
reflect_dot_eye = Vec3.dot(reflectv, eyev)
if reflect_dot_eye <= 0:
specular = Color(0, 0, 0)
else:
# compute the specular contribution
factor = reflect_dot_eye**self.shininess
specular = light.intensity * self.specular * factor
return ambient + diffuse + specular
def default_world():
world = World()
world.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
s1 = Sphere()
s1.material.color = Color(0.8, 1.0, 0.6)
s1.material.diffuse = 0.7
s1.material.specular = 0.2
world.objects.append(s1)
s2 = Sphere()
s2.transform = Matrix.scaling(0.5, 0.5, 0.5)
world.objects.append(s2)
return world
def color_at(self, ray: Ray, remaining: int = 5) -> Color:
intersections = self.intersect_world(ray)
intersect = intersections.hit()
if intersect is None:
return Color(0, 0, 0)
precomputed = intersect.prepare_computations(ray)
return self.shade_hit(precomputed, remaining)
def ch9():
# Step 1
floor = Plane()
floor.transform = Matrix.scaling(10, 0.01, 10)
floor.material = Material()
floor.material.color = Color(1, 0.9, 0.9)
floor.material.specular = 0
floor.material.pattern = StripePattern(Color(1, 0, 0), Color(0, 0, 1))
# Middle biggest sphere
middle = Sphere()
middle.transform = Matrix.translation(-0.5, 1, 0.5)
middle.material = Material()
middle.material.color = Color(0.1, 1, 0.5)
middle.material.diffuse = 0.7
middle.material.specular = 0.3
middle.material.pattern = RingPattern(Color(1, 0, 1), Color(1, 1, 1))
middle.material.pattern.transform = Matrix.scaling(0.25, 0.5, 0.25)
# Smaller right sphere
right = Sphere()
right.transform = Matrix.translation(1.5, 0.5, -0.5) * Matrix.scaling(0.5, 0.5, 0.5)
right.material = Material()
right.material.color = Color(0.5, 1, 0.1)
right.material.diffuse = 0.7
right.material.specular = 0.3
right.material.reflective = 1.0
# Left yellow sphere
left = Sphere()
left.transform = Matrix.translation(-1.5, 0.33, -0.75) * Matrix.scaling(0.33, 0.33, 0.33)
left.material = Material()
left.material.color = Color(1, 0.8, 0.1)
left.material.diffuse = 0.7
left.material.specular = 0.3
world = World()
world.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
world.objects.extend([floor, middle, right, left])
camera = Camera(100, 50, 60)
# camera = Camera(500, 250, 60)
camera.transform = view_transform(point(0, 1.5, -5),
point(0, 1, 0),
vector(0, 1, 0))
canvas = camera.render(world)
with open('ch9.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def __init__(self, width, height):
self.width = width
self.height = height
self.pixels = []
# Set each pixel to be black by default
for row in range(self.height):
pixel_rows = []
for column in range(self.width):
pixel_rows.append(Color(0, 0, 0))
self.pixels.append(pixel_rows)
def ch14():
world = World()
world.light = PointLight(point(-10, 10, -10), Color(1, 1, 1))
hex = hexagon()
world.objects.append(hex)
camera = Camera(100, 50, 60)
camera.transform = view_transform(point(0, 2, -1), point(0, 0, 0),
vector(0, 1, 0))
canvas = camera.render(world)
with open('ch14.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def __init__(self,
color=None,
ambient=0.1,
diffuse=0.9,
specular=0.9,
shininess=200.0):
self.color = Color(1, 1, 1) if color is None else color
self.ambient = ambient
self.diffuse = diffuse
self.specular = specular
self.shininess = shininess
self.pattern = None
self.reflective = 0.0
self.transparency = 0.0
self.refractive_index = 1.0
def clean(self, filter_func):
new_img_data = []
color_black = (0, 0, 0)
color_white = (255, 255, 255)
for i, colordata in enumerate(self.im.convert("HSV").getdata()):
color = Color(colordata)
if filter_func(color):
new_img_data.append(color_black)
continue
new_img_data.append(color_white)
self.im = Image.new(self.im.mode, self.im.size)
self.im.putdata(new_img_data)
return
# Can probably have this done internally in the Canvas class, but left
# it here for simplicity and it doesn't hide how the conversion is done.
def convert_position_to_canvas(canvas: Canvas, world_position: Vec3):
"""Converts the position from world to canvas. This is done by subtracting
the z world position from the canvas height, the other positions are left alone."""
return point(
round(world_position.x + (canvas.width / 2)), round(world_position.y),
round((canvas.height - (canvas.height / 2) - world_position.z)))
if __name__ == '__main__':
width = 400
height = 400
canvas = Canvas(width, height)
hour_rotation = 360 / 12
hour_rotation_matrix = Matrix.rotation_y(hour_rotation)
radius = (3 / 8) * canvas.width
print(f'Radius: {radius}')
position = point(0, 0, 1) * radius
for i in range(12):
canvas_point = convert_position_to_canvas(canvas, position)
print(f'Position:{position}\nCanvas:{canvas_point}')
canvas.write_pixel(canvas_point.x, canvas_point.z, Color(1, 1, 1))
position = hour_rotation_matrix * position
with open('clock2.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def step_impl(context, attribute, r, g, b):
expected = Color(r, g, b)
result = context
for prop in attribute.split('.'):
result = getattr(result, prop)
assert expected == result, f'{result} != {expected}'
def step_impl(context, attribute, r, g, b):
setattr(context, attribute, Color(r, g, b))
0) # The starting position can be set anywhere different
velocity = vector(1, 1.8, 0).normalize(
) * 11.25 # This can be changed to any value to change the trajectory
p = Projectile(start, velocity)
gravity = vector(
0, -0.1,
0) # This can be changed to force the projectile down faster/slower
wind = vector(
-0.01, 0,
0) # This can changed to force the projectile forward less or more
e = Environment(gravity, wind)
screen_width = 900 # You can play around with the width of the canvas
screen_height = 550 # You can play around with the height of the canvas
c = Canvas(screen_width, screen_height)
# It's ok if the y position is above the canvas as it can come down into it still.
# But with the x-axis, it's not worth it since, once it's off screen, the wind is
# is too strong in the beginning or the it will not return on-screen on the right end
while p.position.y > 0 and 0 <= p.position.x < c.width:
canvas_position = convert_position_to_canvas(c, p.position)
c.write_pixel(canvas_position.x, canvas_position.y, Color(1, 0, 0))
p = tick(e, p)
# The final process of storing the canvas to a .ppm file.
# You can change the name of the file to whatever you like
with open('ch1and2.ppm', 'w') as fp:
fp.write(c.to_ppm())
def ch5and6():
# start the ray at z = -5
ray_origin = point(0, 0, -5)
# put the wall at z = 10
wall_z = 10
wall_size = 7
canvas_pixels = 100
pixel_size = wall_size / canvas_pixels
half = wall_size / 2
canvas = Canvas(canvas_pixels, canvas_pixels)
shape = Sphere()
# Optional sphere transformations - uncomment to see the sphere changes
# shape.transform = Matrix.rotation_z(45) * Matrix.scaling(0.5, 1, 1)
# shape.transform = Matrix.scaling(1, 0.5, 1)
# shape.transform = Matrix.shearing(1, 0, 0, 0, 0, 0) * Matrix.scaling(0.5, 1, 1)
# CH 6
# CH 6.1
shape.material.color = Color(1, 0.2, 1)
# CH 6.2
light_position = point(-10, 10, -10)
light_color = Color(1, 1, 1)
light = PointLight(light_position, light_color)
# for each row of pixels in the canvas
for y in range(canvas_pixels):
# compute the world y coordinate (top = +half, bottom = -half)
# canvas -> world coordinate conversion
# (0, 0) -> (-3.5, 3.5)
# (99, 99) -> (3.43, -3.43)
world_y = half - pixel_size * y
# for each pixel in the row
for x in range(canvas_pixels):
# compute the world x coordinate (left = -half, right = half)
world_x = -half + pixel_size * x
# describe the point on the wall that the ray will target
position = point(world_x, world_y, wall_z)
r = Ray(ray_origin, (position - ray_origin).normalize())
xs = shape.intersect(r)
intersection = xs.hit()
if intersection is not None:
# World position of the intersection
intersect_point = r.position(intersection.t)
# World position of the normal at the point
intersect_normal = intersection.obj.normal_at(intersect_point)
# Reverse ray direction to get vector from intersection to eye
eye = -r.direction
# Color is calculate by the material of the sphere, ambient, diffuse, specular, and the light sources
color = intersection.obj.material.lighting(
light, intersect_point, eye, intersect_normal)
canvas.write_pixel(x, y, color)
with open('ch6.ppm', 'w') as fp:
fp.write(canvas.to_ppm())
def step_impl(context, x, y, r, g, b):
expected = Color(r, g, b)
result = context.image.pixel_at(x, y)
assert expected == result, f'{result} != {expected}'
def pattern_at(self, point: Vec3) -> Color:
return Color(point.x, point.y, point.z)
def step_impl(context, x, y, z, r, g, b):
context.w.light = PointLight(point(x, y, z), Color(r, g, b))
def step_impl(context, r1, g1, b1, r2, g2, b2):
context.m.pattern = StripePattern(Color(r1, g1, b1), Color(r2, g2, b2))
def step_impl(context, x, y, z):
expected = Color(0, 0, 0)
result = context.pattern.pattern_at(point(x, y, z))
assert expected == result, f'{result} != {expected}'
def step_impl(context, r, g, b):
expected = Color(r, g, b)
result = context.result
assert expected == result, f'{result} != {expected}'
# Copyright(c) Eric Steinberger 2018
from src.Color import Color
from src.config import RobotConfig
BLACK = Color(name="black",
rgb=[25, 25, 25],
position=RobotConfig.POS_COLOR_BLACK,
color_id=0,
code=[1, 1, 1, 0])
GREEN = Color(name="green",
rgb=[0, 148, 84],
position=RobotConfig.POS_COLOR_GREEN,
color_id=1,
code=[1, 0, 0, 0])
BLUE = Color(name="blue",
rgb=[1, 51, 236],
position=RobotConfig.POS_COLOR_BLUE,
color_id=2,
code=[1, 0, 1, 0])
YELLOW = Color(name="yellow",
rgb=[255, 219, 0],
position=RobotConfig.POS_COLOR_YELLOW,
color_id=3,
code=[0, 1, 0, 0])
RED = Color(name="red",
rgb=[240, 14, 17],
position=RobotConfig.POS_COLOR_RED,
color_id=4,
code=[0, 1, 1, 0])
WHITE = Color(name="white",
def step_impl(context, r, g, b):
context.intensity = Color(r, g, b)