def view_transform(from_position: Point, to: Point, up: Vector) -> Matrix:
forward = normalize(to - from_position)
left = cross(forward, normalize(up))
true_up = cross(left, forward)
orientation = Matrix([
[left.x, left.y, left.z, 0],
[true_up.x, true_up.y, true_up.z, 0],
[-forward.x, -forward.y, -forward.z, 0],
[0, 0, 0, 1],
])
return orientation * translation(-from_position.x, -from_position.y,
-from_position.z)
def normal_at(self, world_point: Point) -> Vector:
transformer = inverse(self.transform)
object_point = transformer * world_point
object_normal = object_point - point(0, 0, 0)
world_normal = transpose(transformer) * object_normal
world_normal = vector(world_normal.x, world_normal.y,
world_normal.z) # set w to 0
return normalize(world_normal)
def is_shadowed(world: World, point: Point) -> bool:
if world.light is None:
return False
else:
light_direction = world.light.position - point
distance = magnitude(light_direction)
ray = Ray(point, normalize(light_direction))
intersections = intersect_world(world, ray)
hit = find_hit(intersections)
if hit is None or hit.t > distance:
return False
return True
def lighting(
m: Material,
light: PointLight,
point: Point,
eye: Vector,
normal: Vector,
in_shadow: bool = False,
) -> Color:
"""
Compute color at a point on the surface using the Phong Reflection Model
Composition made up of ambient light, diffused light and specular light
"""
effective_color = m.color * light.intensity
ambient = effective_color * m.ambient
if in_shadow:
return ambient
black = Color(0, 0, 0)
light_direction = normalize(light.position - point)
light_direction_cosine = dot(light_direction, normal)
if light_direction_cosine < 0:
# Light source is on other side of surface => only ambient lighting
diffuse = black
specular = black
else:
diffuse = effective_color * m.diffuse * light_direction_cosine
reflection = reflect(-light_direction, normal)
reflection_eye_cosine = dot(reflection, eye)
if reflection_eye_cosine <= 0:
# Light is reflected away from the eye => no specular lighting
specular = black
else:
factor = reflection_eye_cosine**int(m.shininess)
specular = light.intensity * m.specular * factor
return ambient + diffuse + specular
def run() -> None:
# Eye is at (0,0, 5)
origin = point(0, 0, 5)
shape = Sphere()
# shape.set_transform(scaling(0.5, 1, 1))
shape.material.color = Color(0.9, 0.2, 1)
light = PointLight(point(-10, 10, 10), Color(1, 1, 1))
canvas = Canvas(CANVAS_SIZE, CANVAS_SIZE)
for i in range(CANVAS_SIZE):
for j in range(CANVAS_SIZE):
target = canvas_to_world(point(i, j, 0))
ray = Ray(origin, normalize(target - origin))
hit = find_hit(shape.intersect(ray))
if hit is not None:
hit_point = position(ray, hit.t)
normal = hit.shape.normal_at(hit_point)
pixel_color = lighting(hit.shape.material, light, hit_point,
-ray.direction, normal)
canvas.write_pixel(i, j, pixel_color)
PPM(canvas).save_to_file("sphere.ppm")
def check_normal(context, var_1, var_2):
variable_1 = context.variables[var_1]
variable_2 = context.variables[var_2]
assert variable_1 == normalize(variable_2)
def assign_normalize(context, var, other_var):
other = context.variables[other_var]
context.variables[var] = normalize(other)
def check_approximate_normalize(context, var, x, y, z):
my_variable = context.variables[var]
assert normalize(my_variable).approximately_equals(vector(x, y, z))
def check_normalize(context, var, x, y, z):
my_variable = context.variables[var]
assert normalize(my_variable) == vector(x, y, z)