def hit(self, ray: Ray):
c = self.origin
e = ray.origin
d = ray.dir
r = self.radius
# check discriminant
disc = (d.dot(e - c))**2 - (d.dot(d)) * ((e - c).dot(e - c) - r**2)
if disc < 0:
return (False, None)
elif disc > 0:
# two solutions
t1 = ((d.scale(-1)).dot(e - c) - math.sqrt(disc))/d.dot(d)
t2 = ((d.scale(-1)).dot(e - c) + math.sqrt(disc))/d.dot(d)
n1 = self.normal(ray.getPoint(t1))
n2 = self.normal(ray.getPoint(t2))
# print(str(t1) + ', ' + str(t2))
if t2 < 10**(-8):
return (False, None)
elif t1 < 10**(-8) and t2 >= 10**(-8):
return (True, HitRec([t2], [n2]))
elif t1 >= 10**(-8):
return (True, HitRec([t1, t2], [n1, n2]))
else:
# one solution
t1 = ((d.scale(-1)).dot(e - c))/d.dot(d)
n1 = self.normal(ray.getPoint(t1))
return (True, HitRec([t1], [n1]))
def rayColor(ray: Ray, objects: list, depth: int, obj_ignore: Surface):
if depth == 5:
return (0, 0, 0)
obj_hit, t, n = hit(ray, objects, obj_ignore)
if (obj_hit):
lightsource = Vec3(-50, 20, 50)
lightsource_dir = (lightsource - ray.getPoint(t)).normalize()
shadow_ray = Ray(ray.getPoint(t), lightsource_dir)
SHADOWED = False
# hex_fill = None
for o in objects:
res = o.hit(shadow_ray)
if (res[0]):
SHADOWED = True
break
if (not SHADOWED):
h = ((ray.dir.scale(-1)) + lightsource_dir).normalize()
reflection_dir = ray.dir - n.scale(2*ray.dir.dot(n))
reflection = Ray(ray.getPoint(t), reflection_dir)
rec_ref = rayColor(reflection, objects, depth+1, obj_hit)
Lr = min(int((0.1 * 4.5 * max(0, n.dot(lightsource_dir)) + 0.5 * 4.5 * max(0, n.dot(h)**8) + 2*rec_ref[0]/255) * 255), 255)
Lg = min(int((0.3 * 3 * max(0, n.dot(lightsource_dir)) + 0.5 * 3 * max(0, n.dot(h)**8) + 2*rec_ref[1]/255) * 255), 255)
Lb = min(int((0.6 * 0.3 * max(0, n.dot(lightsource_dir)) + 0.5 * 0.3 * max(0, n.dot(h)**8) + 2*rec_ref[2]/255) * 255), 255)
return (Lr, Lg, Lb)
else:
h = ((ray.dir.scale(-1)) + lightsource_dir).normalize()
# print(ray.getPoint(t))
Lr = min(int(0.1 * 4.5 * max(0, n.dot(lightsource_dir)) * 255), 255)
Lg = min(int(0.3 * 3 * max(0, n.dot(lightsource_dir)) * 255) , 255)
Lb = min(int(0.3 * 0.3 * max(0, n.dot(lightsource_dir)) * 255) , 255)
return (Lr, Lg, Lb)
return (0 , 0, 0)
def hit(self, ray: Ray):
xa = self.a.x
ya = self.a.y
za = self.a.z
xb = self.b.x
yb = self.b.y
zb = self.b.z
xc = self.c.x
yc = self.c.y
zc = self.c.z
xd = ray.dir.x
yd = ray.dir.y
zd = ray.dir.z
xe = ray.origin.x
ye = ray.origin.y
ze = ray.origin.z
a = xa - xb
b = ya - yb
c = za - zb
d = xa - xc
e = ya - yc
f = za - zc
g = xd
h = yd
i = zd
j = xa - xe
k = ya - ye
l = za - ze
M = a*(e*i - h*f) + b*(g*f - d*i) + c*(d*h - e*g)
if (-10**(-8) <= M <= 10**(-8)):
return (False, None)
t = -1* (f*(a*k - j*b) + e*(j*c - a*l) + d*(b*l - k*c))/M
if (t <= 10**(-8)):
return (False, None)
gamma = (i*(a*k - j*b) + h*(j*c - a*l) + g*(b*l - k*c))/M
if (gamma < 0 or gamma > 1):
return (False, None)
beta = (j*(e*i - h*f) + k*(g*f - d*i) + l*(d*h - e*g))/M
if (beta < 0 or (beta + gamma) > 1 ):
return (False, None)
n = self.normal(ray.getPoint(t))
return (True, HitRec([t], [n]))