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import numpy as np
import time
class vec3():
def __init__(self, x, y, z):
(self.x, self.y, self.z) = (x, y, z)
def __mul__(self, other):
return vec3(self.x * other, self.y * other, self.z * other)
def __add__(self, other):
return vec3(self.x + other.x, self.y + other.y, self.z + other.z)
def __sub__(self, other):
return vec3(self.x - other.x, self.y - other.y, self.z - other.z)
def dot(self, other):
return (self.x * other.x) + (self.y * other.y) + (self.z * other.z)
def __abs__(self):
return self.dot(self)
def norm(self):
mag = np.sqrt(abs(self))
return self * (1.0 / np.where(mag == 0, 1, mag))
def components(self):
return (self.x, self.y, self.z)
rgb = vec3
(w, h) = (400, 300) # Screen size
L = vec3(5, 5., -10) # Point light position
E = vec3(0., 0.35, -1.) # Eye position
FARAWAY = 1.0e39 # an implausibly huge distance
def raytrace(O, D, scene, bounce = 0):
# O is the ray origin, D is the normalized ray direction
# scene is a list of Sphere objects (see below)
# bounce is the number of the bounce, starting at zero for camera rays
distances = [s.intersect(O, D) for s in scene]
nearest = reduce(np.minimum, distances)
color = rgb(0, 0, 0)
for (s, d) in zip(scene, distances):
color += s.light(O, D, d, scene, bounce) * (nearest != FARAWAY) * (d == nearest)
return color
class Sphere:
def __init__(self, center, r, diffuse, mirror = 0.5):
self.c = center
self.r = r
self.diffuse = diffuse
self.mirror = mirror
def intersect(self, O, D):
b = 2 * D.dot(O - self.c)
c = abs(self.c) + abs(O) - 2 * self.c.dot(O) - (self.r * self.r)
disc = (b ** 2) - (4 * c)
sq = np.sqrt(np.maximum(0, disc))
h0 = (-b - sq) / 2
h1 = (-b + sq) / 2
h = np.where((h0 > 0) & (h0 < h1), h0, h1)
pred = (disc > 0) & (h > 0)
return np.where(pred, h, FARAWAY)
def diffusecolor(self, M):
return self.diffuse
def light(self, O, D, d, scene, bounce):
M = (O + D * d) # intersection point
N = (M - self.c) * (1. / self.r) # normal
toL = (L - M).norm() # direction to light
toO = (E - M).norm() # direction to ray origin
nudged = M + N * .0001 # M nudged to avoid itself
# Shadow: find if the point is shadowed or not.
light_distances = [s.intersect(nudged, toL) for s in scene]
light_nearest = reduce(np.minimum, light_distances)
seelight = light_distances[scene.index(self)] == light_nearest
# Ambient
color = rgb(0.05, 0.05, 0.05)
# Lambert shading (diffuse)
lv = np.maximum(N.dot(toL), 0)
color += self.diffusecolor(M) * lv * seelight
# Reflection
if bounce < 2:
rayD = (D - N * 2 * D.dot(N)).norm()
color += raytrace(nudged, rayD, scene, bounce + 1) * self.mirror
# Blinn-Phong shading (specular)
phong = N.dot((toL + toO).norm())
color += rgb(1, 1, 1) * np.power(np.clip(phong, 0, 1), 50) * seelight
return color
class CheckeredSphere(Sphere):
def diffusecolor(self, M):
checker = ((M.x * 2).astype(int) % 2) == ((M.z * 2).astype(int) % 2)
return self.diffuse * checker
scene = [
Sphere(vec3(.75, .1, 1.), .6, rgb(0, 0, 1)),
Sphere(vec3(-.75, .1, 2.25), .6, rgb(.5, .223, .5)),
Sphere(vec3(-2.75, .1, 3.5), .6, rgb(1., .572, .184)),
CheckeredSphere(vec3(0,-99999.5, 0), 99999, rgb(.75, .75, .75), 0.25),
]
r = float(w) / h
# Screen coordinates: x0, y0, x1, y1.
S = (-1., 1. / r + .25, 1., -1. / r + .25)
x = np.tile(np.linspace(S[0], S[2], w), h)
y = np.repeat(np.linspace(S[1], S[3], h), w)
t0 = time.time()
Q = vec3(x, y, 0)
color = raytrace(E, (Q - E).norm(), scene)
print "Took", time.time() - t0
import Image
rgb = [Image.fromarray((255 * np.clip(c, 0, 1).reshape((h, w))).astype(np.uint8), "L") for c in color.components()]
Image.merge("RGB", rgb).save("fig.png")