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rays.py
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rays.py
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from PIL import Image
import math
import numpy as np
import rt4
import time
rgb = rt4.rgb
vec3 = rt4.vec3
########################################################################
# Based on "JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN."
# http://mrl.nyu.edu/~perlin/noise/
p0 = [ 151,160,137,91,90,15,
131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23,
190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33,
88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166,
77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244,
102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196,
135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123,
5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42,
223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9,
129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228,
251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107,
49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254,
138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180] * 2
perm = np.array(p0).astype(np.uint8)
perm15 = perm & 15
def frac(x):
return x - np.floor(x)
def lerp(t, a, b):
return a + t * (b - a)
def mod256(x):
q = x * (1.0 / 256.0)
f = frac(q)
return (f * 256).astype(int)
def fade(t):
return t * t * t * (t * (t * 6 - 15) + 10)
# u v
# 0 x y
# 4 x z
# 8 y z
# 12 y x
# 14 y x
def grad(prehash, x, y, z):
h = np.take(perm15, prehash)
u = np.where(h < 8, x, y)
v = np.where(h < 4, y, np.where((h == 12) | (h == 14), x, z))
return np.where((h & 1) == 0, u, -u) + np.where((h & 2) == 0, v, -v)
def noise(p):
X = np.floor(p.x)
Y = np.floor(p.y)
Z = np.floor(p.z)
X = X.astype(np.uint8) & 0xff
Y = Y.astype(np.uint8) & 0xff
Z = Z.astype(np.uint8) & 0xff
x = frac(p.x)
y = frac(p.y)
z = frac(p.z)
u = fade(x)
v = fade(y)
w = fade(z)
A = np.take(perm, X) + Y
AA = np.take(perm, A) + Z
AB = np.take(perm, A + 1) + Z
B = np.take(perm, X+1) + Y
BA = np.take(perm, B) + Z
BB = np.take(perm, B + 1) + Z
return lerp(w, lerp(v, lerp(u, grad(AA , x , y , z ), # AND ADD
grad(BA , x-1, y , z )), # BLENDED
lerp(u, grad(AB , x , y-1, z ), # RESULTS
grad(BB , x-1, y-1, z ))),# FROM 8
lerp(v, lerp(u, grad(AA+1, x , y , z-1 ), # CORNERS
grad(BA+1, x-1, y , z-1 )), # OF CUBE
lerp(u, grad(AB+1, x , y-1, z-1 ),
grad(BB+1, x-1, y-1, z-1 ))));
def fBm(point, H, lacunarity = 2.0, octaves = 8):
value = 0.0
for i in range(octaves):
exponent = math.pow(lacunarity, -i*H)
value += noise(point) * exponent
point *= lacunarity
return value
def moonFunc(p):
# range of H is 0.4 - 0.9
#H = lerp(0.4, 0.9, 0.5 + 0.5 * noise(p + vec3(9,0,8)))
if 1:
t = fBm(p + vec3(1,3,2), 0.6, 2, 7)
return 1.0 + t
def moonHeight(p):
f = moonFunc(p)
return np.minimum(lerp(f - 1, 0.4, 0.405), 0.4)
def computeNormal(p, n, o, r, func):
u = n.cross(r).norm()
v = u.cross(n)
epsilon = 1.e-4
u *= epsilon
v *= epsilon
a = func(p)
au = func(p + u)
av = func(p + v)
du = (u + n * (au - a))
dv = (v + n * (av - a))
n = dv.cross(du).norm()
return n
class CheckeredSphere(rt4.Sphere):
diffuse = rgb(1,1,1)
def normal(self, p):
n = (p - self.c) * (1. / self.r) # normal
r = vec3(-1, 0, 0)
u = n.cross(r).norm()
v = u.cross(n)
epsilon = 1.e-4
u *= epsilon
v *= epsilon
func = moonHeight
a = func(p)
au = func(p + u)
av = func(p + v)
du = (u + n * (au - a))
dv = (v + n * (av - a))
n = dv.cross(du).norm()
return n
def diffusecolor(self, M):
f = moonFunc(M)
mare = (f < 1)
l = np.where(mare, lerp(f, 0.5, 0.6), lerp(f - 1, 0.8, 1.0))
return rgb(255 * l, 248 * l, 220 * l) * (1. / 255)
def saw(x, y, t):
n = noise(vec3(x, y, frac(t)))
return n * (1 - (2 * abs(0.5 - frac(t))))
def smoothstep(t):
return t * t * (3.0 - 2.0 * t)
if __name__ == '__main__':
D = 637
w = 4 * D
h = 4 * D
x = np.tile(np.linspace(0, 1, w), h)
y = np.repeat(np.linspace(0, 1, h), w)
vel = -0.9
for f in range(1):
# polar
r = np.sqrt(x ** 2 + y ** 2)
th = np.arctan2(y, x)
th1 = np.fmod(3 * th / (0.5 * math.pi), 1)
# a is alpha mask
a = np.where((0.16 < th1) * (th1 < 0.66), 1.0, 0.0)
# d is distance to edge
d = np.minimum(abs(th1 - 0.16), abs(th1 - 0.66))
# b is brightness
b = np.clip((1 - 4 * d) ** 6, .5, 1)
# falloff towards (0,0)
falloff = smoothstep(np.clip(5 * (r - .2), 0, 1))
l = falloff * (b * a)
color = rgb(1, 1, 1) * l
crgb = [Image.fromarray((255 * np.clip(c, 0, 1).reshape((h, w))).astype(np.uint8), "L") for c in color.components()]
Image.merge("RGB", crgb).resize((D, D), Image.BICUBIC).save("%04d.png" % (f + 1))