def fromnormals_faster(n1, n2): axis = vec3.normalize(vec3.cross(n1, n2)) half_n = vec3.normalize(vec3.add(n1, n2)) cos_half_angle = vec3.dot(n1, half_n) sin_half_angle = 1.0 - cos_half_angle ** 2 return vec3.mulN(axis, sin_half_angle) + (cos_half_angle,)
def fromnormals_faster(n1,n2): axis= vec3.normalize(vec3.cross(n1, n2)) half_n= vec3.normalize(vec3.add(n1, n2)) cos_half_angle= vec3.dot(n1, half_n) sin_half_angle= 1.0 - cos_half_angle**2 return vec3.mulN(axis, sin_half_angle) + (cos_half_angle,)
def __init__(self, origin, lookat, up, fov, aspect):
theta = fov * math.pi / 180
half_height = math.tan(theta / 2)
half_width = aspect * half_height
self.origin = origin
w = vec3.normalize(vec3.subtract(origin, lookat))
u = vec3.normalize(vec3.cross(up, w))
v = vec3.cross(w, u)
self.horizontal = vec3.scale(u, 2 * half_width)
self.vertical = vec3.scale(v, 2 * half_height)
center = vec3.subtract(origin, w)
shift = vec3.scale(vec3.add(self.horizontal, self.vertical), 0.5)
self.llc = vec3.subtract(center, shift)
def scatter(self, ray, record):
reflected = vec3.reflect(vec3.normalize(ray.direction), record.normal)
outward_normal = (0, 0, 0)
idx_ratio = 0
if vec3.dot(ray.direction, record.normal) > 0:
outward_normal = vec3.scale(record.normal, -1)
idx_ratio = self.ri
cos = self.ri * vec3.dot(vec3.normalize(ray.direction),
record.normal)
else:
outward_normal = record.normal
idx_ratio = 1.0 / self.ri
cos = -vec3.dot(vec3.normalize(ray.direction), record.normal)
refracted = vec3.refract(ray.direction, outward_normal, idx_ratio)
if refracted:
reflect_prob = self.schlick(cos, self.ri)
if random.random() < reflect_prob:
return Ray(record.p, reflected)
return Ray(record.p, refracted)
else:
return Ray(record.p, reflected)
def color(ray, world, depth):
record = world.hit(ray, eps, float('inf'))
if record:
# camera receives color from a ray scattered randomly off surface
if (depth < 10):
scattered = record.material.scatter(ray, record)
if scattered:
return vec3.mult(color(scattered, world, depth + 1),
record.material.attenuation)
unit = vec3.normalize(ray.direction)
t = 0.5 * (unit[1] + 1.0)
c1 = vec3.scale((1.0, 1.0, 1.0), 1.0 - t)
c2 = vec3.scale((0.5, 0.7, 1.0), t)
return vec3.add(c1, c2)
def hit(self, ray, t_min, t_max):
record = HitRecord()
oc = vec3.subtract(ray.origin, self.center)
a = vec3.squared_length(ray.direction)
b = vec3.dot(oc, ray.direction)
c = vec3.squared_length(oc) - self.radius**2
discriminant = b**2 - a * c
if discriminant > 0:
t = (-b - math.sqrt(discriminant)) / a
if (t < t_max and t > t_min):
record.t = t
record.p = ray.point_at_time(t)
record.normal = vec3.normalize(
vec3.subtract(record.p, self.center))
record.material = self.material
return record
return None
def fromvectors(v1, v2): return fromnormals(vec3.normalize(v1), vec3.normalize(v2))
def fromnormals(n1, n2): axis, angle = vec3.normalize(vec3.cross(n1, n2)), math.acos(vec3.dot(n1, n2)) return fromaxisangle((axis, angle))
def fromvectors(v1,v2): return fromnormals(vec3.normalize(v1), vec3.normalize(v2))
def fromnormals(n1,n2): axis,angle= vec3.normalize(vec3.cross(n1, n2)), math.acos(vec3.dot(n1, n2)) return fromaxisangle((axis,angle))
def scatter(self, ray, record):
reflected = vec3.reflect(vec3.normalize(ray.direction), record.normal)
scattered = Ray(record.p, reflected)
return scattered if vec3.dot(scattered.direction,
record.normal) > 0 else None