def sphere_intersection_point(theRay, theSphere):
dotvector_of_raydir_sqr = vector_math.dot_vector(theRay.dir, theRay.dir)
diffpoint_of_raypt_sphcen = vector_math.difference_point(
theRay.pt, theSphere.center)
dotvector_of_raydir_diffpoint = vector_math.dot_vector(
diffpoint_of_raypt_sphcen, theRay.dir)
dotvector_of_diffpoint_sqr = vector_math.dot_vector(
diffpoint_of_raypt_sphcen, diffpoint_of_raypt_sphcen)
A = dotvector_of_raydir_sqr #(theRay.dir * theRay.dir)
B = dotvector_of_raydir_diffpoint * 2 #(2 * (theRay.pt - theSphere.center) * theRay.dir)
C = dotvector_of_diffpoint_sqr - theSphere.radius**2 #(((theRay.pt - theSphere.center) * (theRay.pt - theSphere.center)) - theSphere.radius ** 2)
D = B**2 - 4 * A * C #discriminant
if D < 0: #D < 0 means no real roots, thus sphere does not intersect with ray
return 'None'
elif D == 0:
t = (-B + math.sqrt(D)) / (2 * A)
if t < 0:
return 'None'
else:
pointt = vector_math.translate_point(
theRay.pt, vector_math.scale_vector(theRay.dir, t))
return pointt
else:
t1 = (-B + math.sqrt(D)) / (2 * A)
t2 = (-B - math.sqrt(D)) / (2 * A)
if t1 >= 0 and t2 >= 0:
pointt = vector_math.translate_point(
theRay.pt, vector_math.scale_vector(theRay.dir, min(t1, t2)))
return pointt
elif t1 < 0 and t2 < 0:
return 'None'
elif t1 < 0 or t2 < 0:
pointt = vector_math.translate_point(
theRay.pt, vector_math.scale_vector(theRay.dir, max(t1, t2)))
return pointt
def sphere_intersection_point(ray,sphere):
def point_t(t):
return vector_math.translate_point(ray.pt,
vector_math.scale_vector(ray.dir,t))
diff_pt = vector_math.difference_point(ray.pt,sphere.center)
a = vector_math.dot_vector(ray.dir, ray.dir)
b = vector_math.dot_vector(vector_math.scale_vector(diff_pt,2),
ray.dir)
c = vector_math.dot_vector(diff_pt,diff_pt) - sphere.radius ** 2
disc = b ** 2 - 4 * a * c
if disc < 0:
return None
elif disc == 0:
t3 = (-b / (2 * a))
if t3 >= 0:
return point_t(t3)
else:
return None
else:
disc_root = math.sqrt(disc)
t1 = (-b + disc_root) / (2 * a)
t2 = (-b - disc_root) / (2 * a)
if t1 >= 0 and t2 >= 0:
return point_t(min(t1,t2))
elif t1 < 0 and t2 < 0:
return None
else:
if t1 >= 0:
return point_t(t1)
elif t2 >= 0:
return point_t(t2)
def sphere_intersection_point(ray,sphere):
a = vector_math.dot_vector(ray.dir, ray.dir)
b = (2 * (vector_math.dot_vector(vector_math.difference_point(ray.pt, sphere.center), ray.dir)))
c = vector_math.dot_vector(vector_math.difference_point(ray.pt, sphere.center), (vector_math.difference_point(ray.pt, sphere.center))) - sphere.radius**2
d = b**2 - 4*a*c
if d < 0:
return None
if d == 0:
t1 = (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)
if t1 > 0:
x = (t1 * ray.dir.x) + ray.pt.x
y = (t1 * ray.dir.y) + ray.pt.y
z = (t1 * ray.dir.z) + ray.pt.z
return data.Point(x,y,z)
else:
return None
if d > 0:
t1 = (-b + math.sqrt(b**2 - 4*a*c)) / (2*a)
t2 = (-b - math.sqrt(b**2 - 4*a*c)) / (2*a)
if t2 < 0 and t1 < 0:
return None
elif t2 < 0:
x = (t1 * ray.dir.x) + ray.pt.x
y = (t1 * ray.dir.y) + ray.pt.y
z = (t1 * ray.dir.z) + ray.pt.z
return data.Point(x,y,z)
else:
x = (t2 * ray.dir.x) + ray.pt.x
y = (t2 * ray.dir.y) + ray.pt.y
z = (t2 * ray.dir.z) + ray.pt.z
return data.Point(x,y,z)
def sphere_intersection_point(ray, sphere):
def point_t(t):
return vector_math.translate_point(
ray.pt, vector_math.scale_vector(ray.dir, t))
diff_pt = vector_math.difference_point(ray.pt, sphere.center)
a = vector_math.dot_vector(ray.dir, ray.dir)
b = vector_math.dot_vector(vector_math.scale_vector(diff_pt, 2), ray.dir)
c = vector_math.dot_vector(diff_pt, diff_pt) - sphere.radius**2
disc = b**2 - 4 * a * c
if disc < 0:
return None
elif disc == 0:
t3 = (-b / (2 * a))
if t3 >= 0:
return point_t(t3)
else:
return None
else:
disc_root = math.sqrt(disc)
t1 = (-b + disc_root) / (2 * a)
t2 = (-b - disc_root) / (2 * a)
if t1 >= 0 and t2 >= 0:
return point_t(min(t1, t2))
elif t1 < 0 and t2 < 0:
return None
else:
if t1 >= 0:
return point_t(t1)
elif t2 >= 0:
return point_t(t2)
def getSpecular(ray, intersection_list, light, point):
closest = findClosestSphere(ray, intersection_list)
csphere = closest[0]
cpoint = closest[1]
n_vector = collisions.sphere_normal_at_point(csphere, cpoint)
scaled_vector = vector_math.scale_vector(n_vector, 0.01)
p_e = vector_math.translate_point(cpoint, scaled_vector)
light_vector = vector_math.vector_from_to(p_e, light.pt)
L_dir = vector_math.normalize_vector(light_vector)
light_dot_product = vector_math.dot_vector(n_vector, L_dir)
#gets spec values
n_scale = vector_math.scale_vector(n_vector, (2 * light_dot_product))
reflection = vector_math.difference_vector(L_dir, n_scale)
pe_eyevec = vector_math.normalize_vector(
vector_math.difference_point(p_e, point))
specularIntensity = vector_math.dot_vector(pe_eyevec, reflection)
if specularIntensity > 0:
sphere_spec = csphere.finish.specular
sphere_rough = csphere.finish.roughness
specCont_r = (light.color.r * sphere_spec) * (specularIntensity**(
1 / float(sphere_rough)))
specCont_g = (light.color.g * sphere_spec) * (specularIntensity**(
1 / float(sphere_rough)))
specCont_b = (light.color.b * sphere_spec) * (specularIntensity**(
1 / float(sphere_rough)))
else:
specCont_r = 0
specCont_g = 0
specCont_b = 0
return (specCont_r, specCont_g, specCont_b)
def sphere_intersection_point(ray, sphere):
a = vector_math.dot_vector(ray.dir, ray.dir)
b = 2 * vector_math.dot_vector(
ray.dir, vector_math.difference_point(ray.pt, sphere.center))
c = vector_math.dot_vector(
vector_math.difference_point(ray.pt, sphere.center),
vector_math.difference_point(ray.pt, sphere.center)) - (sphere.radius**
2)
d = discriminant(a, b, c)
if d < 0:
return None
elif d == 0:
t = solve_quadratic(a, b, c)
if t > 0:
return point_along_ray(ray, t)
else:
return None
elif d > 0:
t1 = solve_quadratic(a, b, c)
t2 = solve_quadratic_2(a, b, c)
if t1 > 0 and t2 > 0:
return point_along_ray(ray, min(t1, t2))
elif xor(t1 > 0, t2 > 0):
return point_along_ray(ray, max(t1, t2))
elif t1 == 0 and t2 == 0:
return ray.pt
else:
return None
else:
return "something went wrong"
def cast_ray(ray, sphere_list, color, light):
"""Find the rendered color at the nearest intersection point along ray"""
nearest = closest_intersect(ray, sphere_list)
if not nearest:
# No intersection, return white
return Color(1.0, 1.0, 1.0)
point, sphere = nearest
# Compute initial ambient colors
r = sphere.color.r * sphere.finish.ambient * color.r
g = sphere.color.g * sphere.finish.ambient * color.g
b = sphere.color.b * sphere.finish.ambient * color.b
# Calculate diffuse value
normal = sphere_normal_at_point(sphere, point)
to_light = normalize_vector(vector_from_to(point, light.pt))
l_dot = dot_vector(normal, to_light)
diffuse = sphere.finish.diffuse * l_dot
if diffuse < 0:
diffuse = 0
else:
# Check for shadows
new_point = translate_point(point, scale_vector(normal, 0.01))
light_ray = Ray(new_point, to_light)
shadow_intersect = closest_intersect(light_ray, sphere_list)
if (shadow_intersect and
length_vector_sq(vector_from_to(new_point, shadow_intersect[0]))
< length_vector_sq(vector_from_to(new_point, light.pt))):
diffuse = 0
# Add diffuse to existing colors
r += sphere.color.r * diffuse * light.color.r
g += sphere.color.g * diffuse * light.color.g
b += sphere.color.b * diffuse * light.color.b
# Compute specular intensity
if diffuse > 0:
reflection = difference_vector(to_light, scale_vector(normal, 2 * l_dot))
intensity = dot_vector(reflection, normalize_vector(ray.dir))
power = 1. / sphere.finish.roughness
if intensity > 0:
r += light.color.r * sphere.finish.specular * intensity ** power
g += light.color.g * sphere.finish.specular * intensity ** power
b += light.color.b * sphere.finish.specular * intensity ** power
# Max out colors at 1.0
if r > 1:
r = 1
if g > 1:
g = 1
if b > 1:
b = 1
return Color(r, g, b)
def test_get_diffuse_contribution(self):
sphere = data.Sphere(data.Point(0, 0, 0), 1, data.Color(0.5, 0.7, 0.8), data.Finish(0.5, 0.5, 0.5, 0.05))
light = data.Light(data.Point(0, 0, 100), data.Color(1.5, 1.2, 1.3))
inter_point = data.Point(0, 0, 1)
normal = collisions.sphere_normal_at_point(sphere, inter_point)
inter_list = []
off_pt = cast.find_pt_off_sphere(inter_point, normal)
dir_vect = vector_math.normalize_vector(vector_math.vector_from_to(off_pt, light.pt))
ray = data.Ray(off_pt, dir_vect)
result = cast.get_diffuse_contribution(sphere, light, ray, inter_list, normal, dir_vect, off_pt)
self.assertEqual(result[0], (vector_math.dot_vector(normal, dir_vect) * 1.5 * 0.5 * 0.5))
self.assertEqual(result[1], (vector_math.dot_vector(normal, dir_vect) * 1.2 * 0.7 * 0.5))
self.assertEqual(result[2], (vector_math.dot_vector(normal, dir_vect) * 1.3 * 0.8 * 0.5))
def cast_ray(ray, sphere_list, amb, light, eye_point):
result_color = data.Color(1.0, 1.0, 1.0)
# test for closest sphere to the eye
collision_tuple = find_closest_collision(ray, sphere_list)
if collision_tuple:
# some useful variables
sphere_hit = collision_tuple[0]
sphere_hit_point = collision_tuple[1]
# basic color before manipulation
result_r = sphere_hit.color.r * sphere_hit.finish.amb * amb.r
result_g = sphere_hit.color.g * sphere_hit.finish.amb * amb.g
result_b = sphere_hit.color.b * sphere_hit.finish.amb * amb.b
# computing light intensity
sphere_vector = vector_math.vector_from_to(sphere_hit.center, sphere_hit_point)
sphere_normal = vector_math.normalize_vector(sphere_vector)
scaled_normal = vector_math.scale_vector(sphere_normal, 0.01)
hit_point = vector_math.translate_point(sphere_hit_point, scaled_normal)
light_vector = vector_math.vector_from_to(hit_point, light.pt)
light_normal = vector_math.normalize_vector(light_vector)
light_scale = vector_math.dot_vector(sphere_normal, light_normal)
if light_scale > 0:
sphere_normal_ray = data.Ray(hit_point, light_normal)
possible_obstruction = find_closest_collision(sphere_normal_ray, sphere_list)
if possible_obstruction == None or distance(hit_point, possible_obstruction[1]) > distance(
hit_point, light.pt
):
result_r += sphere_hit.color.r * light_scale * light.color.r * sphere_hit.finish.diff
result_g += sphere_hit.color.g * light_scale * light.color.g * sphere_hit.finish.diff
result_b += sphere_hit.color.b * light_scale * light.color.b * sphere_hit.finish.diff
# computing specular intensity
tmp_vector = vector_math.scale_vector(sphere_normal, 2 * light_scale)
reflection_vector = vector_math.difference_vector(light_normal, tmp_vector)
eye_vector = vector_math.vector_from_to(eye_point, hit_point)
eye_normal = vector_math.normalize_vector(eye_vector)
spec_scale = vector_math.dot_vector(reflection_vector, eye_normal)
if spec_scale > 0:
result_r += light.color.r * sphere_hit.finish.spec * spec_scale ** (1 / float(sphere_hit.finish.rough))
result_g += light.color.g * sphere_hit.finish.spec * spec_scale ** (1 / float(sphere_hit.finish.rough))
result_b += light.color.b * sphere_hit.finish.spec * spec_scale ** (1 / float(sphere_hit.finish.rough))
result_color = data.Color(result_r, result_g, result_b)
return result_color
def test_dot_1(self):
v1 = data.Vector(1,2,3)
v2 = data.Vector(4,5,6)
dot = vector_math.dot_vector(v1, v2)
self.assertAlmostEqual(dot, 32)
pass
def test_cast_ray_1(self):
ray = data.Ray(data.Point(0, 10, 6), data.Vector(0, 0, -2))
sphere_list = [
data.Sphere(data.Point(0, 10, -2), 3, data.Color(0, 0.5, 1.0), data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(0, 10, -20), 0.5, data.Color(0, 0.3, 0.2), data.Finish(0.5, 0.4, 0.5, 0.05)),
]
ambient_color = data.Color(0.25, 0.5, 0.75)
light = data.Light(data.Point(-100.0, 100.0, -100.0), data.Color(1.5, 1.5, 1.5))
eye_position = data.Point(0, 0, -14)
cr = cast.cast_ray(ray, sphere_list, ambient_color, light, eye_position)
inter_point = collisions.sphere_intersection_point(ray, sphere_list[0])
normal = collisions.sphere_normal_at_point(sphere_list[0], inter_point)
off_pt = cast.find_pt_off_sphere(inter_point, normal)
l_dir = vector_math.normalize_vector(vector_math.vector_from_to(off_pt, light.pt))
l_dot_n = vector_math.dot_vector(normal, l_dir)
diffuse_list = cast.determine_diffuse_contribution(
sphere_list[0], off_pt, light, normal, sphere_list, l_dir, l_dot_n
)
spec_list = cast.determine_specular_contribution(
l_dir, l_dot_n, normal, eye_position, off_pt, light.color, sphere_list[0].finish
)
self.assertEqual(
cr,
data.Color(
0 + diffuse_list[0] + spec_list[0],
0.125 + diffuse_list[1] + spec_list[1],
0.375 + diffuse_list[2] + spec_list[2],
),
)
def test_determine_diffuse_contribution(self):
sphere = data.Sphere(data.Point(0, 0, 0), 1, data.Color(0.5, 0.7, 0.8), data.Finish(0.5, 0.5, 0.5, 0.05))
light = data.Light(data.Point(0, 0, 100), data.Color(1.5, 1.2, 1.3))
inter_point = data.Point(0, 0, 1)
inter_list = [
(
data.Sphere(data.Point(0, 0, 102), 1, data.Color(0.5, 0.7, 0.8), data.Finish(0.5, 0.5, 0.5, 0.05)),
data.Point(0, 0, 101),
)
]
normal = collisions.sphere_normal_at_point(sphere, inter_point)
off_pt = cast.find_pt_off_sphere(inter_point, normal)
dir_vect = vector_math.normalize_vector(vector_math.vector_from_to(off_pt, light.pt))
ray = data.Ray(off_pt, dir_vect)
sphere_list = []
l_dir = vector_math.normalize_vector(vector_math.vector_from_to(off_pt, light.pt))
l_dot_n = vector_math.dot_vector(normal, l_dir)
result = cast.determine_diffuse_contribution(sphere, off_pt, light, normal, sphere_list, l_dir, l_dot_n)
self.assertEqual(
result[0], cast.get_diffuse_contribution(sphere, light, ray, inter_list, normal, dir_vect, off_pt)[0]
)
self.assertEqual(
result[1], cast.get_diffuse_contribution(sphere, light, ray, inter_list, normal, dir_vect, off_pt)[1]
)
self.assertEqual(
result[2], cast.get_diffuse_contribution(sphere, light, ray, inter_list, normal, dir_vect, off_pt)[2]
)
def determine_specular_contribution(l_dir,l_dot_n,normal,eye_position,
off_pt,light,sphere_finish,ray,
inter_list):
reflection_vect = vector_math.difference_vector(l_dir,
vector_math.scale_vector(normal,
2 * l_dot_n))
v_dir = vector_math.normalize_vector(
vector_math.vector_from_to(eye_position,off_pt))
spec_intensity = vector_math.dot_vector(reflection_vect,v_dir)
def compute_spec(color_comp):
return (color_comp * sphere_finish.specular *
(spec_intensity ** (1 / sphere_finish.roughness)))
if spec_intensity > 0:
r_comp = compute_spec(light.color.r)
g_comp = compute_spec(light.color.g)
b_comp = compute_spec(light.color.b)
if inter_list == []:
return [r_comp,g_comp,b_comp]
else:
dist_pt_to_light = distance(off_pt,light.pt)
nearest_point = find_nearest(inter_list,ray)
if distance(off_pt,nearest_point) < dist_pt_to_light:
return [0,0,0]
else:
return [r_comp,g_comp,b_comp]
else:
return [0,0,0]
def determine_specular_contribution(l_dir, l_dot_n, normal, eye_position,
off_pt, light, sphere_finish, ray,
inter_list):
reflection_vect = vector_math.difference_vector(
l_dir, vector_math.scale_vector(normal, 2 * l_dot_n))
v_dir = vector_math.normalize_vector(
vector_math.vector_from_to(eye_position, off_pt))
spec_intensity = vector_math.dot_vector(reflection_vect, v_dir)
def compute_spec(color_comp):
return (color_comp * sphere_finish.specular *
(spec_intensity**(1 / sphere_finish.roughness)))
if spec_intensity > 0:
r_comp = compute_spec(light.color.r)
g_comp = compute_spec(light.color.g)
b_comp = compute_spec(light.color.b)
if inter_list == []:
return [r_comp, g_comp, b_comp]
else:
dist_pt_to_light = distance(off_pt, light.pt)
nearest_point = find_nearest(inter_list, ray)
if distance(off_pt, nearest_point) < dist_pt_to_light:
return [0, 0, 0]
else:
return [r_comp, g_comp, b_comp]
else:
return [0, 0, 0]
def point_light_same_side(point, sphere, light):
normal = collisions.sphere_normal_at_point(sphere, point)
pt_light_vec = vector_math.normalize_vector(
vector_math.difference_point(light.pt, point))
dot_product = vector_math.dot_vector(normal, pt_light_vec)
if dot_product <= 0:
return False
else:
return True
def cast_ray(ray, sphere_list, ambient, light, point):
a = collisions.find_intersection_points(sphere_list, ray)
if a == []:
return data.Color(1.0, 1.0, 1.0)
sphere_look = a[0]
for x in a:
if distance(ray.pt, x[1]) < distance(ray.pt, sphere_look[1]):
sphere_look = x
red = sphere_look[0].color.r * sphere_look[0].finish.ambient * ambient.r
green = sphere_look[0].color.g * sphere_look[0].finish.ambient * ambient.g
blue = sphere_look[0].color.b * sphere_look[0].finish.ambient * ambient.b
n = collisions.sphere_normal_at_point(sphere_look[0], sphere_look[1])
pe = vector_math.translate_point(sphere_look[1],
vector_math.scale_vector(n, .01))
visible_ray = data.Ray(pe, vector_math.vector_from_to(pe, light.point))
ldir = vector_math.normalize_vector(visible_ray.dir)
visible = vector_math.dot_vector(ldir, n)
n = collisions.sphere_normal_at_point(sphere_look[0], sphere_look[1])
ldir_dot_n = vector_math.dot_vector(ldir, n)
reflection_vector = vector_math.difference_vector(
vector_math.scale_vector(n, ldir_dot_n * 2), ldir)
vdir = vector_math.normalize_vector(vector_math.vector_from_to(point, pe))
specular_intensity = vector_math.dot_vector(reflection_vector, vdir)
if visible > 0:
if collisions.find_intersection_points(sphere_list, visible_ray) == []:
red += (visible * light.color.r * sphere_look[0].color.r *
sphere_look[0].finish.diffuse)
green += (visible * light.color.g * sphere_look[0].color.g *
sphere_look[0].finish.diffuse)
blue += (visible * light.color.b * sphere_look[0].color.b *
sphere_look[0].finish.diffuse)
if specular_intensity > 0:
spec_intensity_calc = specular_intensity**(
1 / sphere_look[0].finish.roughness)
red += light.color.r * sphere_look[
0].finish.specular * spec_intensity_calc
green += light.color.g * sphere_look[
0].finish.specular * spec_intensity_calc
blue += light.color.b * sphere_look[
0].finish.specular * spec_intensity_calc
return data.Color(red, green, blue)
def sphere_intersection_point(ray, sphere):
a = vm.dot_vector(ray.dir, ray.dir)
b = vm.dot_vector(vm.scale_vector(vm.vector_from_to(sphere.center, ray.pt), 2), ray.dir)
c = vm.dot_vector(vm.vector_from_to(sphere.center, ray.pt), vm.vector_from_to(sphere.center, ray.pt)) - sphere.radius ** 2
x = vm.quadForm(a, b, c)
def point_along_ray(ray, t):
if t >= 0:
x = ray.pt.x + ray.dir.x * t
y = ray.pt.y + ray.dir.y * t
z = ray.pt.z + ray.dir.z * t
return data.Point(x, y, z)
else:
return None
if x is None:
return None
if isinstance(x, list):
intersections = []
for i in x:
intersections.append(point_along_ray(ray, i))
distances = []
for i in intersections:
if i is not None:
distances.append(vm.distForm(i, ray.pt))
else:
distances.append(None)
if distances[0] is None:
return intersections[1]
if distances[1] is None:
return intersections[0]
if distances[0] < distances[1]:
return intersections[0]
else:
return intersections[1]
else:
intersection = point_along_ray(ray, x)
return intersection
def sphere_intersection_point(ray, sphere):
#define variables
A = vector_math.dot_vector(ray.dir, ray.dir)
B = vector_math.dot_vector(
vector_math.scale_vector(
(vector_math.difference_point(ray.pt, sphere.center)), 2), ray.dir)
C = vector_math.dot_vector(
vector_math.difference_point(ray.pt, sphere.center),
vector_math.difference_point(ray.pt, sphere.center)) - sphere.radius**2
discriminant = B**2 - 4 * A * C
if discriminant < 0:
return None
#define t
t = (-B + math.sqrt(discriminant)) / (2.0 * A)
t_2 = (-B - math.sqrt(discriminant)) / (2.0 * A)
point_t = vector_math.translate_point(ray.pt,
vector_math.scale_vector(ray.dir, t))
point_t2 = vector_math.translate_point(
ray.pt, vector_math.scale_vector(ray.dir, t_2))
#Cases
if t >= 0 and t_2 >= 0:
if t_2 > t:
return point_t
else:
return point_t2
elif t < 0 and t_2 < 0:
return None
elif (t < 0 and t_2 >= 0) or (t >= 0 and t_2 < 0):
if t >= 0:
return point_t
else:
return point_t2
else:
return None
def get_diffuse_color(tu, light, s_list):
pE = get_pe(tu)
N = collisions.sphere_normal_at_point(tu[0], tu[1])
lDir = vector_math.vector_from_to(pE, light.pt)
lDir = vector_math.normalize_vector(lDir)
lDirection = vector_math.dot_vector(N, lDir)
sI = get_specular_intensity(lDir, lDirection, N, pE, light, tu[0])
ray = data.Ray(pE, lDir)
if lDirection <= 0 or collides_with_spheres(ray, s_list, pE, light):
return data.Color(0,0,0)
dif = get_diffuse(lDirection, light, tu[0], tu[0].finish.diffuse)
finalColor = data.Color(sI.r + dif.r, sI.g + dif.g, sI.b + dif.b)
return finalColor
def comp(sphere_list,inter,light,sphere,int,eye_point): n = collisions.sphere_normal_at_point(sphere,int) scaled_normal = vector_math.scale_vector(n,.01) Pe = vector_math.translate_point(inter[0][1],scaled_normal) vr_light = vector_math.vector_from_to(Pe,light.pt) L_dir = vector_math.normalize_vector(vr_light) dot_product = vector_math.dot_vector(n,L_dir) reflection_vr = vector_math.difference_vector(L_dir,vector_math.scale_vector(n,(2 * dot_product))) V_dir = vector_math.normalize_vector(vector_math.vector_from_to(eye_point,Pe)) intensity = vector_math.dot_vector(reflection_vr,V_dir) ray = data.Ray(Pe,L_dir) inter2 = collisions.find_intersection_points(sphere_list,ray) if dot_product>0 and inter2 == []: diff_r = sphere.color.r*sphere.finish.diffuse*dot_product*light.color.r diff_g = sphere.color.g*sphere.finish.diffuse*dot_product*light.color.g diff_b = sphere.color.b*sphere.finish.diffuse*dot_product*light.color.b spec_r = light.color.r*sphere.finish.specular*math.pow(intensity,(1/sphere.finish.roughness)) spec_g = light.color.g*sphere.finish.specular*math.pow(intensity,(1/sphere.finish.roughness)) spec_b = light.color.b*sphere.finish.specular*math.pow(intensity,(1/sphere.finish.roughness)) return data.Color(diff_r,diff_g,diff_b),data.Color(spec_r,spec_g,spec_b) else : return data.Color(0,0,0), data.Color(0,0,0)
def get_diffuse_color(tu, light, s_list):
pE = get_pe(tu)
N = collisions.sphere_normal_at_point(tu[0], tu[1])
lDir = vector_math.vector_from_to(pE, light.pt)
lDir = vector_math.normalize_vector(lDir)
lDirection = vector_math.dot_vector(N, lDir)
sI = get_specular_intensity(lDir, lDirection, N, pE, light, tu[0])
ray = data.Ray(pE, lDir)
if lDirection <= 0 or collides_with_spheres(ray, s_list, pE, light):
return data.Color(0, 0, 0)
dif = get_diffuse(lDirection, light, tu[0], tu[0].finish.diffuse)
finalColor = data.Color(sI.r + dif.r, sI.g + dif.g, sI.b + dif.b)
return finalColor
def find_specular_intensity(spherepair, light, eye_point, l_dot_n):
light_dir = vector_math.normalize_vector(vector_math.difference_point(
light.pt, spherepair[1]))
sphere_normal = collisions.sphere_normal_at_point(spherepair[0], spherepair[1])
reflection_vector = vector_math.difference_vector(light_dir,
vector_math.scale_vector(sphere_normal, 2 * l_dot_n))
view_dir = vector_math.normalize_vector(vector_math.difference_point(
spherepair[1], eye_point))
specular_intensity = vector_math.dot_vector(view_dir, reflection_vector)
return specular_intensity
def get_specular_intensity(lDir, lDirection, N, pE, light, sphere):
reflection_vector = vector_math.difference_vector(lDir, vector_math.scale_vector(N, lDirection * 2))
vDir = vector_math.vector_from_to(data.Point(0.0,0.0,-14.0), pE)
vDir = vector_math.normalize_vector(vDir)
intensity = vector_math.dot_vector(reflection_vector, vDir)
if intensity > 0:
r = light.color.r * sphere.finish.specular * intensity**(1 / sphere.finish.roughness)
g = light.color.g * sphere.finish.specular * intensity**(1 / sphere.finish.roughness)
b = light.color.b * sphere.finish.specular * intensity**(1 / sphere.finish.roughness)
color = data.Color(r,g,b)
else:
color = data.Color(0,0,0)
return color
def sphere_intersection_point(ray, sphere):
a = vector_math.dot_vector(ray.dir, ray.dir)
b = (2 * (vector_math.dot_vector(
vector_math.difference_point(ray.pt, sphere.center), ray.dir)))
c = vector_math.dot_vector(
vector_math.difference_point(ray.pt, sphere.center),
(vector_math.difference_point(ray.pt,
sphere.center))) - sphere.radius**2
d = b**2 - 4 * a * c
if d < 0:
return None
if d == 0:
t1 = (-b + math.sqrt(b**2 - 4 * a * c)) / (2 * a)
if t1 > 0:
x = (t1 * ray.dir.x) + ray.pt.x
y = (t1 * ray.dir.y) + ray.pt.y
z = (t1 * ray.dir.z) + ray.pt.z
return data.Point(x, y, z)
else:
return None
if d > 0:
t1 = (-b + math.sqrt(b**2 - 4 * a * c)) / (2 * a)
t2 = (-b - math.sqrt(b**2 - 4 * a * c)) / (2 * a)
if t2 < 0 and t1 < 0:
return None
elif t2 < 0:
x = (t1 * ray.dir.x) + ray.pt.x
y = (t1 * ray.dir.y) + ray.pt.y
z = (t1 * ray.dir.z) + ray.pt.z
return data.Point(x, y, z)
else:
x = (t2 * ray.dir.x) + ray.pt.x
y = (t2 * ray.dir.y) + ray.pt.y
z = (t2 * ray.dir.z) + ray.pt.z
return data.Point(x, y, z)
def cast_ray(ray,sphere_list,ambient_color,light,eye_position):
inter_list = collisions.find_intersection_points(sphere_list,
ray)
if inter_list != []:
mindex = 0
for i in range(1,len(inter_list)):
if (distance(ray.pt,inter_list[i][1]) <
distance(ray.pt,inter_list[mindex][1])):
mindex = i
result_sphere = inter_list[mindex][0]
inter_point = inter_list[mindex][1]
sphere_color = result_sphere.color
sphere_finish = result_sphere.finish
sphere_normal = collisions.sphere_normal_at_point(result_sphere,
inter_point)
pt_off_sphere = find_pt_off_sphere(inter_point,sphere_normal)
l_dir = vector_math.normalize_vector(
vector_math.vector_from_to(pt_off_sphere,
light.pt))
l_dot_n = vector_math.dot_vector(sphere_normal,l_dir)
ray_off_to_l = data.Ray(pt_off_sphere,l_dir)
inter_list = collisions.find_intersection_points(sphere_list,ray_off_to_l)
diffuse_list = determine_diffuse_contribution(result_sphere,
pt_off_sphere,
light,sphere_normal,
sphere_list,l_dir,
l_dot_n,ray_off_to_l,
inter_list)
spec_intensity = determine_specular_contribution(l_dir,l_dot_n,
sphere_normal,
eye_position,
pt_off_sphere,
light,
result_sphere.finish,
ray_off_to_l,inter_list)
result_r = ((sphere_color.r * sphere_finish.ambient *
ambient_color.r) + diffuse_list[0] + spec_intensity[0])
result_g = ((sphere_color.g * sphere_finish.ambient *
ambient_color.g) + diffuse_list[1] + spec_intensity[1])
result_b = ((sphere_color.b * sphere_finish.ambient *
ambient_color.b) + diffuse_list[2] + spec_intensity[2])
return data.Color(result_r,result_g,result_b)
else:
return ambient_color
def get_specular_intensity(lDir, lDirection, N, pE, light, sphere):
reflection_vector = vector_math.difference_vector(
lDir, vector_math.scale_vector(N, lDirection * 2))
vDir = vector_math.vector_from_to(data.Point(0.0, 0.0, -14.0), pE)
vDir = vector_math.normalize_vector(vDir)
intensity = vector_math.dot_vector(reflection_vector, vDir)
if intensity > 0:
r = light.color.r * sphere.finish.specular * intensity**(
1 / sphere.finish.roughness)
g = light.color.g * sphere.finish.specular * intensity**(
1 / sphere.finish.roughness)
b = light.color.b * sphere.finish.specular * intensity**(
1 / sphere.finish.roughness)
color = data.Color(r, g, b)
else:
color = data.Color(0, 0, 0)
return color
def get_diffuse_contribution(sphere,light,ray,inter_list,normal,
l_dir,off_pt):
dot = vector_math.dot_vector(normal,l_dir)
diffuse = sphere.finish.diffuse
def calculate_contribution(light_color_component,
sphere_color_component):
return (dot*light_color_component*sphere_color_component*diffuse)
if inter_list == []:
return [calculate_contribution(light.color.r,sphere.color.r),
calculate_contribution(light.color.g,sphere.color.g),
calculate_contribution(light.color.b,sphere.color.b)]
else:
dist_pt_to_light = distance(off_pt,light.pt)
nearest_point = find_nearest(inter_list,ray)
if distance(off_pt,nearest_point) < dist_pt_to_light:
return [0,0,0]
return [calculate_contribution(light.color.r,sphere.color.r),
calculate_contribution(light.color.g,sphere.color.g),
calculate_contribution(light.color.b,sphere.color.b)]
def cast_ray(ray, sphere_list, ambient_color, light, eye_position):
inter_list = collisions.find_intersection_points(sphere_list, ray)
if inter_list != []:
mindex = 0
for i in range(1, len(inter_list)):
if (distance(ray.pt, inter_list[i][1]) < distance(
ray.pt, inter_list[mindex][1])):
mindex = i
result_sphere = inter_list[mindex][0]
inter_point = inter_list[mindex][1]
sphere_color = result_sphere.color
sphere_finish = result_sphere.finish
sphere_normal = collisions.sphere_normal_at_point(
result_sphere, inter_point)
pt_off_sphere = find_pt_off_sphere(inter_point, sphere_normal)
l_dir = vector_math.normalize_vector(
vector_math.vector_from_to(pt_off_sphere, light.pt))
l_dot_n = vector_math.dot_vector(sphere_normal, l_dir)
ray_off_to_l = data.Ray(pt_off_sphere, l_dir)
inter_list = collisions.find_intersection_points(
sphere_list, ray_off_to_l)
diffuse_list = determine_diffuse_contribution(
result_sphere, pt_off_sphere, light, sphere_normal, sphere_list,
l_dir, l_dot_n, ray_off_to_l, inter_list)
spec_intensity = determine_specular_contribution(
l_dir, l_dot_n, sphere_normal, eye_position, pt_off_sphere, light,
result_sphere.finish, ray_off_to_l, inter_list)
result_r = (
(sphere_color.r * sphere_finish.ambient * ambient_color.r) +
diffuse_list[0] + spec_intensity[0])
result_g = (
(sphere_color.g * sphere_finish.ambient * ambient_color.g) +
diffuse_list[1] + spec_intensity[1])
result_b = (
(sphere_color.b * sphere_finish.ambient * ambient_color.b) +
diffuse_list[2] + spec_intensity[2])
return data.Color(result_r, result_g, result_b)
else:
return ambient_color
def getDiffuse(ray, intersection_list, sphere_list, light):
closest = findClosestSphere(ray, intersection_list)
csphere = closest[0]
cpoint = closest[1]
normalVec = collisions.sphere_normal_at_point(csphere, cpoint)
scaled_vector = vector_math.scale_vector(normalVec, 0.01)
p_e = vector_math.translate_point(cpoint, scaled_vector)
light_vector = vector_math.vector_from_to(p_e, light.pt)
L_dir = vector_math.normalize_vector(light_vector)
ldotProduct = vector_math.dot_vector(normalVec, L_dir)
light_ray = data.Ray(p_e, L_dir)
light_intersections = collisions.find_intersection_points(
sphere_list, light_ray)
light_distance = vector_math.length_vector(light_vector)
if_diffuse = True
if ldotProduct > 0:
if light_intersections != []:
for spheres_and_points in light_intersections:
point = spheres_and_points[1]
difference_lengths = vector_math.length_vector(
vector_math.difference_point(point, p_e))
if difference_lengths < light_distance:
if_diffuse = False
else:
if_diffuse = False
if if_diffuse:
lClr_r = light.color.r
lClr_g = light.color.g
lClr_b = light.color.b
sp_r = csphere.color.r
sp_g = csphere.color.g
sp_b = csphere.color.b
diff_r = ldotProduct * lClr_r * sp_r * csphere.finish.diffuse
diff_g = ldotProduct * lClr_g * sp_g * csphere.finish.diffuse
diff_b = ldotProduct * lClr_b * sp_b * csphere.finish.diffuse
else:
diff_r = 0
diff_g = 0
diff_b = 0
return (diff_r, diff_g, diff_b)
def get_diffuse_contribution(sphere, light, ray, inter_list, normal, l_dir,
off_pt):
dot = vector_math.dot_vector(normal, l_dir)
diffuse = sphere.finish.diffuse
def calculate_contribution(light_color_component, sphere_color_component):
return (dot * light_color_component * sphere_color_component * diffuse)
if inter_list == []:
return [
calculate_contribution(light.color.r, sphere.color.r),
calculate_contribution(light.color.g, sphere.color.g),
calculate_contribution(light.color.b, sphere.color.b)
]
else:
dist_pt_to_light = distance(off_pt, light.pt)
nearest_point = find_nearest(inter_list, ray)
if distance(off_pt, nearest_point) < dist_pt_to_light:
return [0, 0, 0]
return [
calculate_contribution(light.color.r, sphere.color.r),
calculate_contribution(light.color.g, sphere.color.g),
calculate_contribution(light.color.b, sphere.color.b)
]
def test_light_direction_2(self):
v1 = data.Vector(1,2,3)
v2 = data.Vector(5,6,7)
product = vector_math.dot_vector(v1,v2)
self.assertEqual(product, 38)
import unittest
import data
import cast
import collisions
import vector_math
a = data.Sphere(data.Point(0.0, 0.0, 0.0), 2.0, data.Color(0.0, 0.0, 1.0),
data.Finish(.2, .4, .5, .05))
t = (a, data.Point(0, 2, 0))
pe = cast.get_pe(t)
sphere = data.Sphere(data.Point(0, 0, 0), 2.0, data.Color(0, 0, 0),
data.Finish(.2, .4, .5, .05))
N = data.Vector(0, 0, 0)
V = data.Vector(5, 5, 5)
s = vector_math.dot_vector(N, V)
print s
print "%f %f %f" % (pe.x, pe.y, pe.z)
def test_light_direction_1(self):
v1 = data.Vector(33,-2,1)
v2 = data.Vector(1,3,38)
product = vector_math.dot_vector(v1,v2)
self.assertEqual(product, 65)
def test_dot_vector_1(self):
v1 = data.Vector(1, 2, 3)
v2 = data.Vector(2, 3, 4)
self.assertAlmostEqual(vector_math.dot_vector(v1, v2), 20)
def point_on_sphere(point, sphere):
v = vector_math.vector_from_to(sphere.center, point)
return vector_math.dot_vector(v, v) == sphere.radius**2
def test_dot_vector_2(self):
v1 = data.Vector(0.0, 0.0, 0.0)
v2 = data.Vector(1.0, 2.0, 3.0)
dot_product = vector_math.dot_vector(v1, v2)
self.assertAlmostEqual(dot_product, 0.0)
def test_dot_vector_1(self):
vector1 = data.Vector(1, 20, 15)
vector2 = data.Vector(2, 5, 3)
product = 147
self.assertEqual(vector_math.dot_vector(vector1, vector2), product)
def light_direction(N, lDir): return vector_math.dot_vector(N, lDir)
def test_dot_vector_2(self):
v1 = data.Vector(0, -5, 2)
v2 = data.Vector(2, 2, 5)
self.assertAlmostEqual(vector_math.dot_vector(v1, v2), 0)
def test_dot_2(self): v1 = data.Vector(0, .5, 1.5) v2 = data.Vector(4, 6, 8) dot = vector_math.dot_vector(v1, v2) self.assertAlmostEqual(dot, 15) pass
def test_dot_vector(self):
v_1 = data.Vector(1, 2, 3)
v_2 = data.Vector(2, 3, 4)
n_v = 20
self.assertEqual(vector_math.dot_vector(v_1, v_2), n_v)
def test_dot_vector_2(self):
vector3 = data.Vector(-15, 21, -9)
vector4 = data.Vector(1, -6, -8)
product = -69
self.assertEqual(vector_math.dot_vector(vector3, vector4), product)
def test_dot_vector(self):
dv = vector_math.dot_vector(data.Vector(1, 2, 3), data.Vector(1.5, 2.5, -2))
self.assertAlmostEqual(dv, 0.5)
def test_dot_vector_again(self):
dv = vector_math.dot_vector(data.Vector(-1, 2.2, 4), data.Vector(-3, 5.5, 4.4))
self.assertAlmostEqual(dv, 32.7)
import unittest import data import cast import collisions import vector_math a = data.Sphere(data.Point(0.0,0.0,0.0), 2.0, data.Color(0.0,0.0,1.0), data.Finish(.2, .4, .5, .05)) t = (a, data.Point(0,2,0)) pe = cast.get_pe(t) sphere = data.Sphere(data.Point(0,0,0), 2.0, data.Color(0,0,0), data.Finish(.2,.4,.5,.05)) N = data.Vector(0,0,0) V = data.Vector(5,5,5) s = vector_math.dot_vector(N,V) print s print "%f %f %f" % (pe.x,pe.y,pe.z)
def cast_ray(ray, sphere_list, light = light_obj, ambient = data.Color(), eye_point = data.Point(0, 0, -14)):
# intersections contains a list of tuples of spheres and points, ex: [(Sphere_1, Point_1), (Sphere_2, Point_2), ...]
intersections = collisions.find_intersection_points(sphere_list, ray)
if len(intersections) == 0:
return data.Color(1.0, 1.0, 1.0)
else:
# initializing variable that stores the index and the distance of the tuple with the smallest distance
index_of_nearest_sphere = 0
distance_of_nearest_sphere = vector_math.distance_between(intersections[0][1], ray.pt)
# loop through all_intersection_point and find the index of the tuple that contains the sphere & intersection with the smallest distance from ray's point
for index in range(0, len(intersections)):
distance_between_points = vector_math.distance_between(intersections[index][1], ray.pt)
if distance_between_points < distance_of_nearest_sphere:
index_of_nearest_sphere = index
distance_of_nearest_sphere = distance_between_points
# storing the sphere and intersection point in to variables for later usage
nearest_sphere = intersections[index_of_nearest_sphere][0]
nearest_intersection = intersections[index_of_nearest_sphere][1]
# ==== color calculation based on ambient light, diffusion, light color and location ====
# Impricision of floats can create collision issues with the sphere where the point lies when using the computed intersection
# A point "pe" that is 0.01 above te intersection point will be used instead
sphere_normal_vector = collisions.sphere_normal_at_point(nearest_sphere, nearest_intersection)
pe_translate_direction_vector = vector_math.scale_vector(sphere_normal_vector, 0.01)
# new point PE is now found
pe = vector_math.translate_point(nearest_intersection, pe_translate_direction_vector)
# === determine whether diffusivity is applicable -- determine if there are any obstruction of light vectors ===
# comput vector from pe to light point then compute normalized vector from pe to to light point
l_dir = vector_math.normalize_vector(vector_math.vector_from_to(pe, light.pt))
n_dot_l_dir = vector_math.dot_vector(sphere_normal_vector, l_dir)
# === computing the specular_intensity ===
reflection_vector = vector_math.difference_vector(l_dir ,vector_math.scale_vector(sphere_normal_vector, 2 * n_dot_l_dir))
#creating the direction vector that points from eye_point to pe
v_dir = vector_math.normalize_vector(vector_math.vector_from_to(eye_point, pe)) #Vdir
# specular_intensity is defined to be the dot product of reflection_vector and the direction vector from eye_point to pe
specular_intensity = vector_math.dot_vector(v_dir, reflection_vector)
ambient_color = compute_ambient_color(nearest_sphere, ambient)
if n_dot_l_dir > 0:
ray_to_point = data.Ray(pe,l_dir)
inter = collisions.find_intersection_points(sphere_list, ray_to_point)
if len(inter) == 0:
diffuse_color = compute_diffuse_color(n_dot_l_dir, light, intersections[index_of_nearest_sphere][0])
if specular_intensity > 0:
specular_color = compute_specular_color(light, nearest_sphere, specular_intensity)
return add_color(add_color(specular_color, diffuse_color), ambient_color)
else:
return add_color(diffuse_color, ambient_color)
else:
return ambient_color
elif specular_intensity > 0:
specular_color = compute_specular_color(light, nearest_sphere, specular_intensity)
return add_color(specular_color, ambient_color)
else:
return ambient_color
def test_light_direction_1(self):
v1 = data.Vector(33, -2, 1)
v2 = data.Vector(1, 3, 38)
product = vector_math.dot_vector(v1, v2)
self.assertEqual(product, 65)
def light_direction(N, lDir):
return vector_math.dot_vector(N, lDir)
def test_light_direction_2(self):
v1 = data.Vector(1, 2, 3)
v2 = data.Vector(5, 6, 7)
product = vector_math.dot_vector(v1, v2)
self.assertEqual(product, 38)
def cast_ray(ray, sphere_list, ambient_color, light, eye_point):
reslist = collisions.find_intersection_points(sphere_list, ray)
if reslist == []:
return data.Color(1, 1, 1)
closest_sphere_pair = find_closest_sphere(ray.pt, reslist)
sphere_color = closest_sphere_pair[0].color
l_dot_n = vector_math.dot_vector(
collisions.sphere_normal_at_point(closest_sphere_pair[0],
closest_sphere_pair[1]),
vector_math.normalize_vector(vector_math.difference_point(light.pt,
closest_sphere_pair[1])))
specular_intensity = find_specular_intensity(closest_sphere_pair, light,
eye_point, l_dot_n)
ambient_component = find_ambient_component(closest_sphere_pair[0], ambient_color)
if specular_intensity > 0 and light_hits_point(closest_sphere_pair, sphere_list, light):
diffuse_component = find_diffuse_component(l_dot_n, light,
closest_sphere_pair[0])
specular_component = find_specular_component(light, closest_sphere_pair[0],
specular_intensity)
newr = specular_component.r + diffuse_component.r + ambient_component.r
newg = specular_component.g + diffuse_component.g + ambient_component.g
newb = specular_component.b + diffuse_component.b + ambient_component.b
pixelcolor = data.Color(newr, newg, newb)
pixelcolor = fix_specular_color(pixelcolor, ambient_component, diffuse_component)
elif light_hits_point(closest_sphere_pair, sphere_list, light):
diffuse_component = find_diffuse_component(l_dot_n, light,
closest_sphere_pair[0])
newr = diffuse_component.r + ambient_component.r
newg = diffuse_component.g + ambient_component.g
newb = diffuse_component.b + ambient_component.b
pixelcolor = data.Color(newr, newg, newb)
pixelcolor = fix_color_issues(pixelcolor, ambient_component)
# if color is past max/min, sets it to the max/min
else: # light doesn't hit ray
newr = ambient_component.r
newg = ambient_component.g
newb = ambient_component.b
pixelcolor = data.Color(newr, newg, newb)
pixelcolor = fix_color_issues(pixelcolor, ambient_component)
return pixelcolor
