def test_sub(self):
a = Vec3(0.2, 0.3, 0.4)
b = Vec3(0.1, 0.1, 0.1)
c = a - b
self.assertAlmostEqual(c.x, 0.1, 5)
self.assertAlmostEqual(c.y, 0.2, 5)
self.assertAlmostEqual(c.z, 0.3, 5)
def test_add(self):
a = Vec3(0.1, 0.1, 0.2)
b = Vec3(0.2, 0.3, 0.5)
c = a + b
self.assertAlmostEqual(c.x, 0.3, 5)
self.assertAlmostEqual(c.y, 0.4, 5)
self.assertAlmostEqual(c.z, 0.7, 5)
def test_multVector(self):
a = Vec3(0.2, 0.3, 0.4)
b = Vec3(2, 2, 2)
c = a * b
self.assertAlmostEqual(c.x, 0.4, 5)
self.assertAlmostEqual(c.y, 0.6, 5)
self.assertAlmostEqual(c.z, 0.8, 5)
def scatter(self, rIn, rec): # returns (attenuation, scattered) or None reflected = Vec3.reflect(Vec3.unitVector(rIn.direction()), rec.normal) scattered = Ray(rec.p, reflected + Vec3.randomInUnitSphere()*self.fuzz) attenuation = self.albedo if Vec3.dot(scattered.direction(), rec.normal) > 0: return (attenuation, scattered) else: return None
def random_in_unit_sphere():
while True:
p = Vec3(float(random.random()), float(random.random()),
float(random.random())).Scale(2.0).Sub(Vec3(1.0, 1.0, 1.0))
if p.dot(p) >= 1.0:
pass
else:
return p
def __init__(self):
'''
@param {t: hit time, p: hit position, normal: hit point normal, mat_ptr: material}
@return: None
'''
self.t = 0
self.p = Vec3(0.0, 0.0, 0.0)
self.normal = Vec3(0.0, 0.0, 0.0)
self.mat_ptr = None
def render_fast(self):
r = float(self.camera.width) / self.camera.height
S = (-1., 1. / r + .25, 1., -1. / r + .25)
x = jnp.tile(jnp.linspace(S[0], S[2], self.camera.width),
self.camera.height)
y = jnp.repeat(jnp.linspace(S[1], S[3], self.camera.height),
self.camera.width)
origin = Vec3(self.camera.origin[0], self.camera.origin[1],
self.camera.origin[2])
image = self.ray_trace(origin, (Vec3(x, y, 0) - origin).norm())
return image
def dot(self, other):
'''
get product with self and other, self is the left operand.
'''
return Mat3(
Vec3(self.x.dot(other.rx), self.x.dot(other.ry),
self.x.dot(other.rz)),
Vec3(self.y.dot(other.rx), self.y.dot(other.ry),
self.y.dot(other.rz)),
Vec3(self.z.dot(other.rx), self.z.dot(other.ry),
self.z.dot(other.rz)))
def render_pixel_antialias(u,
v,
camera,
light,
asset,
file,
antialias_level=0):
"""
:param u:
:param v:
:param camera:
:param light:
:param asset:
:param file:
:param antialias_level: level of antialiasing n
shoot 2^2n rays per pixel and average the result
:return:
"""
a_n = 2**antialias_level
ray_offset = [2 / a_n * i - (1 - 1 / a_n) for i in range(a_n)]
# ray_offset = [-0.5, 0.5]
# ray_offset = [-0.75, -0.25, 0.25, 0.75]
c_list = []
for du in ray_offset:
for dv in ray_offset:
c = Vec3(0, 0, 0)
ray = camera.shoot_ray(u + du, v + dv)
intersect, i = asset.intersect(ray)
if intersect:
n = asset.normal(i)
l = light.pos - i
r = normalize(2 * n - l)
l_intensity = light.strength(i) * light.color
i_ambient = k_ambient * ambient
i_diffuse = k_diffuse * max(dot(n, normalize(l)),
0) * l_intensity
i_specular = k_specular * pow(
max(dot(r, normalize(-1 * i)), 0),
n_specular) * l_intensity
c = mul(asset.color, i_ambient + i_diffuse + i_specular)
c_list.append(c)
c = Vec3(0, 0, 0)
for ci in c_list:
c += ci
c = c / len(ray_offset)**2
file.write("{} {} {}\n".format(floatto8bit(c.x), floatto8bit(c.y),
floatto8bit(c.z)))
def __init__(self, origin, lookat, vup, vfov, aspectRatio, aperture,
focusDist):
self.origin = origin
self.lensRadius = aperture / 2
self.theta = math.radians(vfov)
self.halfHeight = math.tan(self.theta / 2)
self.halfWidth = aspectRatio * self.halfHeight
self.w = Vec3.unitVector(lookat - origin)
self.u = Vec3.unitVector(Vec3.cross(self.w, vup))
self.v = Vec3.cross(self.u, self.w)
self.lowerLeftCorner = origin - self.u * self.halfWidth * focusDist - self.v * self.halfHeight * focusDist + self.w * focusDist
self.horizontal = self.u * self.halfWidth * focusDist * 2
self.vertical = self.v * self.halfHeight * focusDist * 2
def __init__(self,
camera: Camera,
scene: Scene,
light_position: Vec3 = Vec3(5., 5., -10.)):
self.camera = camera
self.scene = scene
self.light_position = light_position
def scatter(self, ray, rec, wrapper):
'''
@return: bool
'''
self.wrapper = wrapper
outward_normal = None
reflected = self.reflect(ray.direction(), rec.normal)
ni_over_nt = None
self.wrapper.attenuation = Vec3(1.0, 1.0, 1.0)
refracted = None
if (ray.direction().dot(rec.normal) > 0):
# 从密度小的介质到密度大的介质
outward_normal = rec.normal.Scale(-1.0)
ni_over_nt = self.ri
cosine = ray.direction().dot(
rec.normal) / (ray.direction().length() * rec.normal.length())
else:
# 从密度大的介质到密度小的介质
outward_normal = rec.normal
ni_over_nt = 1.0 / self.ri
cosine = -ray.direction().dot(rec.normal) / (
ray.direction().length() * rec.normal.length())
if self.refract(ray.direction(), outward_normal, ni_over_nt,
self.wrapper):
reflect_prob = self.schlick(cosine, self.ri)
else:
reflect_prob = 1.0
if random.random() < reflect_prob:
self.wrapper.scattered = Ray(rec.p, reflected)
else:
self.wrapper.scattered = Ray(rec.p, self.wrapper.refracted)
return True
def __init__(self, t, p, mat, r, outwardNormal): self.t = t self.p = p self.mat = mat self.frontFace = Vec3.dot(r.direction(), outwardNormal) < 0 self.normal = outwardNormal if self.frontFace else outwardNormal*-1
def test_normalize(self):
a = Vec3(0.1, 0.2, 0.3)
b = a.normalize()
# result from here
# https://calculator.academy/normalize-vector-calculator/#f1p1|f2p0
self.assertAlmostEqual(b.x, 0.2672, 3)
self.assertAlmostEqual(b.y, 0.5345, 3)
self.assertAlmostEqual(b.z, 0.8017, 3)
def rayColor(r, world, depth):
# if we've exceeded the ray bounce limit, no more light is gathered.
if depth <= 0:
return Vec3(0,0,0)
rec = world.hit(r, 0.001, float('inf'))
if rec != None:
result = rec.mat.scatter(r, rec)
if result != None:
attenuation = result[0]
scattered = result[1]
return rayColor(scattered, world, depth-1)*attenuation
return Vec3(0,0,0)
# background
unitDirection = Vec3.unitVector(r.direction())
t = (unitDirection.y() + 1.0)*0.5
return Vec3(1.0, 1.0, 1.0)*(1.0-t) + Vec3(0.5, 0.7, 1.0)*t
def __init__(self, look_from, look_at, vup, vfov, aspect):
self.lower_left = Vec3(-2.0, -2.0, -2.0)
self.horizontal = Vec3(4.0, 0.0, 0.0) # width
self.vertical = Vec3(0.0, 4.0, 0.0) # height
self.origin = Vec3(0.0, 0.0, 0.0) # camara position
# Camera cordinate
self.u, self.v, self.w = None, None, None
self.theta = float(vfov * math.pi / 180) # fov theta
self.half_height = float(math.tan(self.theta / 2))
self.half_width = aspect * self.half_height
self.origin = look_from
self.w = look_from.Sub(look_at).normalize()
self.u = vup.cross(self.w).normalize()
self.v = self.w.cross(self.u).normalize()
self.lower_left = self.origin.Sub(self.u.Scale(self.half_width)).Sub(
self.v.Scale(self.half_height)).Sub(self.w)
self.horizontal = self.u.Scale(2 * self.half_width)
self.vertical = self.v.Scale(2 * self.half_height)
def light(self,
origin,
direction,
intersection,
light_position,
eye_position,
scene_objects,
bounce=0,
far=1.0e15):
'''
Basic light model using a only diffuse lighting
'''
rayhit = origin + direction * intersection
normal = ((rayhit - self.center) * (1. / self.radius))
direction_to_light = (light_position - rayhit).norm()
direction_to_eye = (eye_position - rayhit).norm()
nudged = rayhit + normal * 0.001 # To avoid shadow acne
# Create shadow mask
light_distances = [
o.intersect(nudged, direction_to_light, far=far)
for o in scene_objects
]
light_nearest = reduce(jnp.minimum, light_distances)
light_mask = light_distances[scene_objects.index(
self)] == light_nearest
# Ambient light
color = Vec3(0.05, 0.05, 0.05)
# Lambert shading (diffuse)
light_hit = jnp.maximum(normal.dot(direction_to_light), 0)
color += self.diffusecolor(rayhit) * light_hit * light_mask
# Phong light
phong = normal.dot((direction_to_light + direction_to_eye).norm())
color += Vec3(1., 1., 1.) * jnp.power(jnp.clip(phong, 0, 1),
50) * light_mask
return color
def scatter(self, rIn, rec): # returns (attenuation, scattered ray)
attenuation = Vec3(1.0, 1.0, 1.0) # Color
# Check if the enter the material
etaiOverEtat = (1.0 / self.refIdx) if rec.frontFace else self.refIdx
unitDirection = Vec3.unitVector(rIn.direction())
cosTheta = min(Vec3.dot(unitDirection * -1, rec.normal), 1.0)
sinTheta = math.sqrt(1.0 - cosTheta * cosTheta)
# TIR
if etaiOverEtat * sinTheta > 1.0:
reflected = Vec3.reflect(unitDirection, rec.normal)
scattered = Ray(rec.p, reflected)
return (attenuation, scattered)
# Reflection / Refraction ratio
reflectProb = Dielectric.__schlick(cosTheta, etaiOverEtat)
# Reflection
if random.random() < reflectProb:
reflected = Vec3.reflect(unitDirection, rec.normal)
scattered = Ray(rec.p, reflected)
return (attenuation, scattered)
# Refraction
refracted = Vec3.refract(unitDirection, rec.normal, etaiOverEtat)
scattered = Ray(rec.p, refracted)
return (attenuation, scattered)
def ray_trace(self, origin, normalized_direction):
far = 1.0e15 # A large number, which we can never hit
distances = [
o.intersect(origin, normalized_direction, far)
for o in self.scene.objects
]
nearest = reduce(jnp.minimum, distances)
color = Vec3(0, 0, 0)
for (o, d) in zip(self.scene.objects, distances):
color += o.light(
origin, normalized_direction, d, self.light_position, origin,
self.scene.objects) * (nearest != far) * (d == nearest)
return color
def color(r, world, depth):
'''
@param {ray, hitable_list, recursion_depth}
@return:
'''
rec = HitRecord()
if world.hit(r, 0, float('inf'), rec):
# ray reflect target
wrapper = Wrapper()
# target = rec.p.Add(rec.normal).Add(random_in_unit_sphere())
# paint according to normal value
# decay 50% every reflect
if depth < 50 and rec.mat_ptr.scatter(r, rec, wrapper):
return wrapper.attenuation.Mul(
color(wrapper.scattered, world, depth + 1))
#return color(Ray(rec.p, target.Sub(rec.p)), world, depth+1).Scale(0.5)
else:
return Vec3(0.0, 0.0, 0.0)
else:
unit_dir = r.direction().normalize()
t = 0.5 * (unit_dir.y() + 1.0)
return Vec3(1.0, 1.0,
1.0).Scale(1.0 - t).Add(Vec3(0.5, 0.7, 1.0).Scale(t))
def create_scene():
obj_list = []
obj_list.append(
Sphere(Vec3(0.0, 0.0, -1.0), 0.5, Lambertian(Vec3(0.1, 0.2, 0.5))))
obj_list.append(Sphere(Vec3(-1.0, 0.0, -1.0), 0.5, Deilectric(1.5)))
obj_list.append(
Sphere(Vec3(1.0, 0.0, -1.0), 0.5, Metal(Vec3(0.8, 0.6, 0.2), 0.2)))
# Ground
obj_list.append(
Sphere(Vec3(0.0, -100.5, -1.0), 100.0, Lambertian(Vec3(0.5, 0.5,
0.5))))
world = Hitable_list(obj_list)
return world
def writePPM():
width = 400
height = 200
ns = 100 # smaple nums
lower_left = Vec3(-2.0, -2.0, -2.0)
horizontal = Vec3(4.0, 0.0, 0.0)
vertical = Vec3(0.0, 4.0, 0.0)
origin = Vec3(0.0, 0.0, 0.0)
with open('result.ppm', 'w') as f:
f.write("P3\n" + str(width) + " " + str(height) + "\n255\n")
index = 0
world = create_scene()
camera = Camera(Vec3(-2.0, 2.0, 1.0), Vec3(0.0, 0.0, -1.0),
Vec3(0.0, 1.0, 0.0), 40.0,
float(width) / float(height))
with tqdm(total=height) as pbar:
for j in range(height - 1, -1, -1):
for i in range(0, width):
col = Vec3(0, 0, 0)
for s in range(0, ns):
u = float(i + random.random()) / float(
width) # antialiasing
v = float(j + random.random()) / float(height)
ray = camera.GetRay(u, v)
col = col.Add(color(ray, world, 0))
col = col.Scale(1.0 / float(ns)) # average color
# gamma
col = Vec3(float(math.sqrt(col.x())),
float(math.sqrt(col.y())),
float(math.sqrt(col.z())))
index += 1
ir = int(255.59 * col.x())
ig = int(255.59 * col.y())
ib = int(255.59 * col.z())
f.write(str(ir) + " " + str(ig) + " " + str(ib) + "\n")
pbar.update(1)
def render_pixel(u, v, camera, light, asset, file):
c = Vec3(0, 0, 0)
ray = camera.shoot_ray(u, v)
intersect, i = asset.intersect(ray)
if intersect:
n = asset.normal(i)
l = light.pos - i
r = normalize(2 * n - l)
l_intensity = light.strength(i) * light.color
i_ambient = k_ambient * ambient
i_diffuse = k_diffuse * max(dot(n, normalize(l)), 0) * l_intensity
i_specular = k_specular * pow(max(dot(r, normalize(-1 * i)), 0),
n_specular) * l_intensity
c = mul(asset.color, i_ambient + i_diffuse + i_specular)
file.write("{} {} {}\n".format(floatto8bit(c.x), floatto8bit(c.y),
floatto8bit(c.z)))
def hit(self, r, tMin, tMax):
a = r.direction().lengthSquared()
oc = r.origin() - self.center
halfB = Vec3.dot(oc, r.direction())
c = oc.lengthSquared() - self.radius * self.radius
discriminant = halfB * halfB - a * c
if discriminant > 0:
root = sqrt(discriminant)
t = (-halfB - root) / a
if t < tMax and t > tMin:
p = r.pointAtParameter(t)
outwardNormal = (p - self.center) / self.radius
return HitRecord(t, p, self.mat, r, outwardNormal)
t = (-halfB + root) / a
if t < tMax and t > tMin:
p = r.pointAtParameter(t)
outwardNormal = (p - self.center) / self.radius
return HitRecord(t, p, self.mat, r, outwardNormal)
return None
def main():
res = 100 # rendered image resolution
camera = Camera((res, res))
sphere = Sphere(pos=Vec3(0, 2, 0), radius=0.5, color=Vec3(1, 0.2, 0.2))
light = Light(pos=Vec3(1, 0.5, 1),
color=Vec3(1, 1, 0.5),
strength=1,
radius=1)
triangle = Triangle([Vec3(0, 0, 1), Vec3(1, 0, 1), Vec3(0, 1, 1)])
asset = sphere
#asset = triangle
out_file = open("out.ppm", "w")
out_file.write("P3\n{} {} {}\n".format(camera.res_width, camera.res_height,
255))
for u in range(camera.res_width):
for v in range(camera.res_height):
render_pixel_antialias(u, v, camera, light, asset, out_file,
antialias_level)
if __name__ == '__main__':
cam = Camera(width=400, origin=jnp.array([0, 0.05, -1.]))
num_spheres = 50
scene_objects = []
min_x = -7.5
min_y = .5
min_z = 2.5
size_deviation = 0.5
max_deviation_x = 15.
max_deviation_y = 10.
max_deviation_z = 20.
import random
colorful_factor = 0.35
for i in range(1, num_spheres + 1):
color = Vec3(random.random(), random.random(), random.random())
color_to_add = random.randint(0, 2)
if color_to_add == 0:
color.x += colorful_factor
color.y -= colorful_factor
color.z -= colorful_factor
elif color_to_add == 1:
color.x -= colorful_factor
color.y += colorful_factor
color.x -= colorful_factor
else:
color.x -= colorful_factor
color.y -= colorful_factor
color.x += colorful_factor
x_coord = random.random() * max_deviation_x + min_x
def trans(self, v):
'''
in-place transform the vector.
'''
return Vec3(self.x.dot(v), self.y.dot(v), self.z.dot(v))
def randomSphereScene(): world = HitableList() # Bottom "plane" world.add(Sphere(Vec3(0,-1000,0), 1000, Lambertian(Vec3(0.5, 0.5, 0.5)))) # three large spheres world.add(Sphere(Vec3(0, 1, 0), 1.0, Dielectric(1.5))) world.add(Sphere(Vec3(-4, 1, 0), 1.0, Lambertian(Vec3(0.4, 0.2, 0.1)))) world.add(Sphere(Vec3(4, 1, 0), 1.0, Metal(Vec3(0.7, 0.6, 0.5), 0.0))) # numerous small spheres i = 1 for a in range(-11, 11): for b in range(-11, 11): chooseMat = random.random() center = Vec3(a + 0.9*random.random(), 0.2, b + 0.9*random.uniform(0,1)) if (center - Vec3(4, 0.2, 0)).length() > 0.9: if chooseMat < 0.8: # diffuse albedo = Vec3.random() * Vec3.random() world.add(Sphere(center, 0.2, Lambertian(albedo))) elif chooseMat < 0.95: # metal albedo = random.uniform(.5, 1) fuzz = random.uniform(0, .5) world.add(Sphere(center, 0.2, Metal(albedo, fuzz))) else: # glass world.add(Sphere(center, 0.2, Dielectric(1.5))) return world
def scatter(self, rIn, rec): # returns (attenuation, scattered) scatterDirection = rec.normal + Vec3.randomInUnitSphere() scattered = Ray(rec.p, scatterDirection) attenuation = self.albedo return (attenuation, scattered)
# return the translated [0,255] value of each color component. return [int(256 * clamp(r, 0.0, 0.999)), int(256 * clamp(g, 0.0, 0.999)), int(256 * clamp(b, 0.0, 0.999))] if __name__ == "__main__": aspectRatio = 16.0 / 9.0 imageWidth = 500 imageHeight = int(imageWidth / aspectRatio) samplesPerPixel = 1 maxDepth = 10 world = randomSphereScene() lookFrom = Vec3(13,2,3) lookAt = Vec3(0,0,0) vUp = Vec3(0,1,0) distToFocus = 10.0 aperture = 0.1 cam = Camera(lookFrom, lookAt, vUp, 20, aspectRatio, aperture, distToFocus) stopwatch = Stopwatch() image = imageHeight*imageWidth*[[0,0,0]] index = 0 for j in range(imageHeight): showProgress(stopwatch, j, imageHeight) for i in range(imageWidth): pixelColor = Vec3(0,0,0) for s in range(samplesPerPixel):
