def intersect(self, raypos, raydir):
tr = self.transform
raydir = tr.inv_transform_vector(raydir)
scale = 1.0 / length(raydir)
raydir = mul(raydir, scale) # normalize
raypos = tr.inv_transform_point(raypos)
s = dot(neg(raypos), raydir)
lsq = dot(raypos, raypos)
if s < 0.0 and lsq > 1.0:
return []
msq = lsq - s * s
if msq > 1.0:
return []
q = math.sqrt(1.0 - msq)
t1 = s + q
t2 = s - q
if t1 > t2:
t1, t2 = t2, t1
ts = []
if t1 > 0.0:
ts.append(
Intersection(scale, t1, raypos, raydir, self,
Intersection.ENTRY, 0))
if t2 > 0.0:
ts.append(
Intersection(scale, t2, raypos, raydir, self,
Intersection.EXIT, 0))
return ts
def get_intensity(self, pos):
q = sub(self.pos, pos)
dsq = dot(q, q)
invlend = 1 / math.sqrt(dsq)
cosangle = -dot(q, self.d) * invlend
if cosangle < self.coscutoff:
return (0.0, 0.0, 0.0)
i = pow(dot(self.d, mul(d, -invlend)), self.exp)
return mul(self.color, i * 100.0 / (99.0 + dsq))
def trace(amb, lights, scene, depth, raypos, raydir):
i = scene.intersect(raypos, raydir)
if i:
#for ic in i:
# print ic
#print
isect = i[0]
if isect.t == Intersection.EXIT:
return (0.0, 0.0, 0.0)
sc, kd, ks, n = isect.primitive.get_surface(isect)
c = get_ambient(sc, amb, kd)
diffuse = (0.0, 0.0, 0.0)
specular = (0.0, 0.0, 0.0)
pos = isect.wpos
normal = isect.normal
for light in lights:
lightdir, lightdistance = light.get_direction(pos)
df = dot(normal, lightdir)
if df > 0.0:
poseps = add(pos, mul(lightdir, 1e-7))
i = scene.intersect(poseps, lightdir)
if not i or (lightdistance and
(lightdistance < i[0].distance)):
ic = cmul(sc, light.get_intensity(pos))
if kd > 0.0:
diffuse = add(diffuse, mul(ic, df))
if ks > 0.0:
specular = add(
specular,
get_specular(ic, lightdir, normal, pos, raypos, n))
c = add(c, add(mul(diffuse, kd), mul(specular, ks)))
if ks > 0.0 and depth > 0:
refl_raydir = normalize(
sub(raydir, mul(normal, 2 * dot(raydir, normal))))
poseps = add(pos, mul(refl_raydir, 1e-7))
rc = trace(amb, lights, scene, depth - 1, poseps, refl_raydir)
return add(c, mul(cmul(rc, sc), ks))
else:
return c
else:
return (0.0, 0.0, 0.0)
def intersect(self, raypos, raydir):
tr = self.transform
raydir = tr.inv_transform_vector(raydir)
scale = 1.0 / length(raydir)
raydir = mul(raydir, scale) # normalize
raypos = tr.inv_transform_point(raypos)
np = self.np
denom = dot(np, raydir)
if abs(denom) < 1e-7:
return []
t = -dot(np, raypos) / denom
if t < 0.0:
return []
if denom > 0.0:
return [
Intersection(scale, t, raypos, raydir, self, Intersection.EXIT,
0)
]
else:
return [
Intersection(scale, t, raypos, raydir, self,
Intersection.ENTRY, 0)
]
def get_specular(ic, lightdir, sn, pos, raypos, n):
halfway = normalize(add(lightdir, normalize(sub(raypos, pos))))
sp = dot(sn, halfway)
if sp > 0.0:
return mul(ic, pow(sp, n))
return (0.0, 0.0, 0.0)
def get_intensity(self, pos):
d = sub(self.pos, pos)
dsq = dot(d, d)
return mul(self.color, 100.0 / (99.0 + dsq))
def covariance(x, y):
n = len(x)
return vecmat.dot(de_mean(x), de_mean(y)) / (n - 1)
def test1(self):
self.assertEqual(vecmat.dot(v, w), 32)