def test_find_intersection_2(self):
spheres = [data.Sphere(data.Point(1, 1, 1), 1), data.Sphere(data.Point(2, 2, 2), 1),
data.Sphere(data.Point(3, 3, 3), 1)]
ray = data.Ray(data.Point(0, 0, 0), data.Vector(1, 0, 0))
result = []
self.assertEqual(collisions.find_intersection_points(spheres, ray) == result, True)
pass
def cast_ray(ray, sphere_list, color, light, point):
intersections = collisions.find_intersection_points(sphere_list, ray)
if intersections != []:
colors = getcolor(ray, intersections)
sphereR = colors[0]
sphereG = colors[1]
sphereB = colors[2]
diffuse = getDiffuse(ray, intersections, sphere_list, light)
sphereDR = diffuse[0]
sphereDG = diffuse[1]
sphereDB = diffuse[2]
specular = getSpecular(ray, intersections, light, point)
sphereSR = specular[0]
sphereSG = specular[1]
sphereSB = specular[2]
closest = findClosestSphere(ray, intersections)
closestSphere = closest[0]
closestPoint = closest[1]
finalcolorR = color.r * sphereR * closestSphere.finish.ambient + sphereDR + sphereSR
finalcolorG = color.g * sphereG * closestSphere.finish.ambient + sphereDG + sphereSG
finalcolorB = color.b * sphereB * closestSphere.finish.ambient + sphereDB + sphereSB
finalcolorRGB = data.Color(finalcolorR, finalcolorG, finalcolorB)
return finalcolorRGB
else:
return data.Color(1.0, 1.0, 1.0)
def test_find_intersection(self):
sphere_1 = data.Sphere(data.Point(1, 1, 0), 1)
sphere_2 = data.Sphere(data.Point(200, 200, 200), 1)
s_list = [sphere_1, sphere_2]
new_list = [(data.Sphere(data.Point(1, 1, 0), 1), data.Point(0, 1, 0))]
r = data.Ray(data.Point(-1, 1, 0), data.Vector(20, 0, 0))
self.assertEqual(collisions.find_intersection_points(s_list, r),
new_list)
def test_find_intersection_2(self):
sphere_1 = data.Sphere(data.Point(20, 20, 20), 2)
sphere_2 = data.Sphere(data.Point(60, 60, 60), 1)
s_list = [sphere_1, sphere_2]
new_list = []
r = data.Ray(data.Point(0, 0, 0), data.Vector(0, 0, 1))
self.assertEqual(collisions.find_intersection_points(s_list, r),
new_list)
def test_find_intersection_points2(self):
sphere1 = data.Sphere(data.Point(0,0,0), 3, data.Color(1.0, 1.0, 1.0))
sphere2 = data.Sphere(data.Point(40, 50, 60), 2, data.Color(1.0, 1.0, 1.0))
sphere3 = data.Sphere(data.Point(104, 150, 200), 8, data.Color(1.0, 1.0, 1.0))
sphere_list = [sphere1, sphere2, sphere3]
ray2 = data.Ray(data.Point(0,-4, 0), data.Vector(0,15,0))
expected2 = [(data.Point(0,-3,0), sphere1)]
self.assertEqual(collisions.find_intersection_points(sphere_list, ray2), expected2)
def test_find_intersection_points1(self):
sphere1 = data.Sphere(data.Point(0, -1, -2), 3, data.Color(1.0, 1.0, 1.0))
sphere2 = data.Sphere(data.Point(-4, -5, -6), 7, data.Color(1.0, 1.0, 1.0))
sphere3 = data.Sphere(data.Point(-10, -15, -20), 2, data.Color(1.0, 1.0, 1.0))
sphere_list = [sphere1, sphere2, sphere3]
ray1 = data.Ray(data.Point(12, 14, 18), data.Vector(4,6,8))
expected = []
self.assertEqual(collisions.find_intersection_points(sphere_list, ray1), expected)
def test_find_sphere_intersections_0(self):
point_ray = data.Point(-10.0, 0.0, 0.0)
direction = data.Vector(1.0, 0.0, 0.0)
ray = data.Ray(point_ray, direction)
point0_sphere = data.Point(0.0, 2.0, 0.0)
sphere0 = data.Sphere(point0_sphere, 1.0)
collision_points = collisions.find_intersection_points([sphere0], ray)
self.assertListAlmostEqual(collision_points, [])
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 test_find_intersection_points_3(self):
sphere_list = [
data.Sphere(data.Point(-5, 2, 9), 2, data.Color(0.23, 0.12, 0.2), data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(0, 0, -9), 1, data.Color(0.24, 0.14, 0.68), data.Finish(0.5, 0.4, 0.5, 0.05)),
]
ray = data.Ray(data.Point(0, -7, 0), data.Vector(0, 5, 0))
fip = collisions.find_intersection_points(sphere_list, ray)
result_list = []
self.assertEqual(fip, result_list)
def collides_with_spheres(ray, list, pE, light):
l = collisions.find_intersection_points(list, ray)
d = vector_math.distance(pE, light.pt)
s = False
if len(l) > 0:
for x in l:
if vector_math.distance(x[1], pE) < d:
s = True
return s
def collides_with_spheres(ray, list, pE, light):
l = collisions.find_intersection_points(list, ray)
d = vector_math.distance(pE, light.pt)
s = False
if len(l) > 0:
for x in l:
if vector_math.distance(x[1], pE) < d:
s = True
return s
def test_find_intersection_1(self):
t = math.sqrt(2)
spheres = [data.Sphere(data.Point(1, 1, 0), t), data.Sphere(data.Point(2, 2, 0), t),
data.Sphere(data.Point(3, 3, 0), t)]
ray = data.Ray(data.Point(0, 0, 0), data.Vector(1, 1, 0))
result = [(spheres[0], data.Point(0, 0, 0)), (spheres[1], data.Point(1, 1, 0)),
(spheres[2], data.Point(2, 2, 0))]
self.assertEqual(collisions.find_intersection_points(spheres, ray) == result, True)
pass
def test_find_intersection_points_2(self):
sphere_list = [
data.Sphere(data.Point(0, 0, 0), 2, data.Color(0.23, 0.23, 0.23), data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(20.3, 20, -100), 1, data.Color(0.45, 0.45, 0.67), data.Finish(0.5, 0.4, 0.5, 0.05)),
]
ray = data.Ray(data.Point(0, -7, 0), data.Vector(0, 5, 0))
fip = collisions.find_intersection_points(sphere_list, ray)
result_list = [(sphere_list[0], collisions.sphere_intersection_point(ray, sphere_list[0]))]
self.assertEqual(fip, result_list)
def point_unobstructed(point, light, sphere_list):
light_dir = vector_math.normalize_vector(vector_math.difference_point(
light.pt, point))
ray_to_light = data.Ray(point, light_dir)
spheres_intersected = collisions.find_intersection_points(sphere_list,
ray_to_light)
if spheres_intersected == []:
return True
else:
return False
def cast_ray(ray, sphere_list, am_color, light, point):
l = collisions.find_intersection_points(sphere_list, ray)
if len(l) > 0:
tu = smallest_point_distance(ray, l)
s = tu[0]
p = tu[1]
c = s.color
return get_color(c, am_color, tu, light, sphere_list)
else:
return data.Color(1.0, 1.0, 1.0)
def cast_ray(ray, sphere_list, am_color, light, point):
l = collisions.find_intersection_points(sphere_list, ray)
if len(l) > 0:
tu = smallest_point_distance(ray,l)
s = tu[0]
p = tu[1]
c = s.color
return get_color(c, am_color, tu, light, sphere_list)
else:
return data.Color(1.0,1.0,1.0)
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 find_closest_collision(ray, sphere_list):
collision_list = collisions.find_intersection_points(sphere_list, ray)
if collision_list:
closest_sphere_index = 0
for i in range(1, len(collision_list)):
if distance(ray.pt, collision_list[i][1]) < distance(ray.pt, collision_list[closest_sphere_index][1]):
closest_sphere_index = i
return collision_list[closest_sphere_index]
else:
return None
def test_intersection_points_3(self):
s1 = data.Sphere(data.Point(2, 2, 2), math.sqrt(3),
data.Color(0, 1, 0), data.Finish(.2, 1, 0, 0))
s2 = data.Sphere(data.Point(-2, -2, 3), 1, data.Color(0, 1, 0),
data.Finish(0.2, 1, 0, 0))
s3 = data.Sphere(data.Point(0, 3, 0), 3 * math.sqrt(2),
data.Color(0, 1, 0), data.Finish(.2, 1, 0, 0))
ray = data.Ray(data.Point(0, 0, 0), data.Vector(1, 1, 1))
s_list = [s1, s2, s3]
result_list = [(s1, data.Point(1, 1, 1)), (s3, data.Point(3, 3, 3))]
self.assertEqual(collisions.find_intersection_points(s_list, ray),
result_list)
def test_intersection_points_2(self):
s1 = data.Sphere(data.Point(2, 0, 2), 2, data.Color(0, 1, 0),
data.Finish(.2, 1, 0, 0))
s2 = data.Sphere(data.Point(0, 2, 4), 2, data.Color(0, 1, 0),
data.Finish(.2, 1, 0, 0))
s3 = data.Sphere(data.Point(2, 2, 0), 2, data.Color(0, 1, 0),
data.Finish(.2, 1, 0, 0))
ray = data.Ray(data.Point(0, 0, -6), data.Vector(0, 0, 1))
s_list = [s1, s2, s3]
result_list = [(s1, data.Point(0, 0, 2)), (s2, data.Point(0, 0, 4))]
self.assertEqual(collisions.find_intersection_points(s_list, ray),
result_list)
def test_find_intersection_points(self):
sphere_list = [
data.Sphere(data.Point(0, 0, 0), 2, data.Color(1, 0.5, 0.3), data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(0, 20, 0), 1, data.Color(1.0, 0.0, 0.4), data.Finish(0.5, 0.4, 0.5, 0.05)),
]
ray = data.Ray(data.Point(0, -20, 0), data.Vector(0, 1.3, 0))
fip = collisions.find_intersection_points(sphere_list, ray)
result_list = [
(sphere_list[0], collisions.sphere_intersection_point(ray, sphere_list[0])),
(sphere_list[1], collisions.sphere_intersection_point(ray, sphere_list[1])),
]
self.assertEqual(fip, result_list)
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 cast_ray(ray, sphere_list, ambient, light, eye_point):
points= collisions.find_intersection_points(sphere_list, ray)
if len(points) == 0:
return Color(1.0, 1.0, 1.0)
else:
#using helper functions below
closest= closest_sphere(ray, points)
pe=translated_point(closest[0], closest[1])
n=normalize_vector(difference_point(closest[1], closest[0].center))
ldir=normalized_ldir(light.pt, pe)
visable=light_visable(n, ldir)
spheres_finish_color=finish_sphere(closest[0], ambient)
reflection=reflection_vector(ldir, n)
vdir=normalized_vdir(eye_point, pe)
specular=specular_intensity(vdir, reflection)
if not visable:
return spheres_finish_color
newpoints=collisions.find_intersection_points(sphere_list, Ray(pe, ldir))
if newpoints != []:
return spheres_finish_color
#no shine
else:
red=spheres_finish_color.r + (dot_vector(n, ldir) * light.color.r *
closest[0].color.r * closest[0].finish.diffuse)
green=spheres_finish_color.g + (dot_vector(n, ldir) * light.color.g *
closest[0].color.g * closest[0].finish.diffuse)
blue=spheres_finish_color.b + (dot_vector(n, ldir) * light.color.b *
closest[0].color.b * closest[0].finish.diffuse)
if specular<=0:
return Color(red, green, blue)
#white shine
else:
red1= red + (light.color.r * closest[0].finish.specular *
specular**(1.0/closest[0].finish.roughness))
green1= green + (light.color.g * closest[0].finish.specular *
specular**(1.0/closest[0].finish.roughness))
blue1= blue + (light.color.b * closest[0].finish.specular *
specular**(1.0/closest[0].finish.roughness))
return Color(red1, green1, blue1)
def test_find_sphere_intersections_1(self):
point_ray = data.Point(-10.0, 0.0, 0.0)
direction = data.Vector(1.0, 0.0, 0.0)
ray = data.Ray(point_ray, direction)
point0_sphere = data.Point(0.0, 2.0, 0.0)
sphere0 = data.Sphere(point0_sphere, 1.0)
point1_sphere = data.Point(0.0, 1.0, 0.0)
sphere1 = data.Sphere(point1_sphere, 1.0)
point2_sphere = data.Point(0.0, 0.0, 0.0)
sphere2 = data.Sphere(point2_sphere, 1.0)
collision_points = collisions.find_intersection_points(
[sphere0, sphere1, sphere2], ray)
self.assertEqual(collision_points[0][1], data.Point(0.0, 0.0, 0.0))
self.assertEqual(collision_points[1][1], data.Point(-1.0, 0.0, 0.0))
def cast_ray(ray,sphere_list,amb,light,eye_point): white = data.Color(1.0,1.0,1.0) inter = collisions.find_intersection_points(sphere_list,ray) if (inter != []): closest_sphere, closest_int = find_closest(inter,ray) diffuse,spec = comp(sphere_list,inter,light,closest_sphere,closest_int,eye_point) val = closest_sphere.finish.ambient final_red = (closest_sphere.color.r*val*amb.r)+diffuse.r+spec.r final_green = (closest_sphere.color.g*val*amb.g)+diffuse.g+spec.g final_blue = (closest_sphere.color.b*val*amb.b)+diffuse.b+spec.b new_color = data.Color(final_red,final_green,final_blue) return new_color else : return white
def cast_ray(ray: data.Ray, sphere_list: typing.List[data.Sphere],
am_light_color: data.Color, light: data.Light,
eye_point: data.Point) -> data.Color:
color = data.Color(1, 1, 1)
intersected_spheres = collisions.find_intersection_points(sphere_list, ray)
if not intersected_spheres:
return color
else:
sphere_point = auxiliary.closest_sphere(intersected_spheres, ray)
light_components = auxiliary.calculate_light_components(
sphere_point, sphere_list, eye_point, light)
color = auxiliary.calculate_color(sphere_point[0], am_light_color,
light_components[0],
light_components[1], light)
return color
def closest_intersect(ray, sphere_list):
"""Find the nearest intersection point and sphere"""
intersections = find_intersection_points(ray, sphere_list)
if len(intersections) < 1:
# We don't intersect anything
return None
# Find the nearest intersection point and its sphere
nearest = intersections[0]
nearest_dist_sq = length_vector_sq(vector_from_to(ray.pt, nearest[0]))
for tup in intersections[1:]:
dist_sq = length_vector_sq(vector_from_to(ray.pt, tup[0]))
if dist_sq < nearest_dist_sq:
nearest = tup
nearest_dist_sq = dist_sq
return nearest
def test_closestSphere1(self):
spheres = [
data.Sphere(data.Point(0.0, 2.0, 0.0), 1.0, data.Color(1, 0, 0),
data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(0.0, 5.0, 0.0), 1.0, data.Color(0, 0, 1),
data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(0.0, 4.0, 0.0), 1.0, data.Color(0, 1, 0),
data.Finish(0.5, 0.4, 0.5, 0.05)),
data.Sphere(data.Point(0.0, 8.0, 0.0), 1.0, data.Color(0, 0, 0),
data.Finish(0.5, 0.4, 0.5, 0.05))
]
ray = data.Ray(data.Point(0.0, 0.0, 0.0), data.Vector(0.0, 1.0, 0.0))
intersected_spheres = collisions.find_intersection_points(spheres, ray)
result = auxiliary.closest_sphere(intersected_spheres, ray)
check = (data.Sphere(data.Point(0.0, 2.0, 0.0), 1.0,
data.Color(1, 0, 0),
data.Finish(0.5, 0.4, 0.5,
0.05)), data.Point(0, 1, 0))
self.assertEqual(result, check)
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 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 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_find_intersection_points(self):
sphere_list = [data.Sphere(data.Point(1, 1, 1), 1), data.Sphere(data.Point(3, 3, 3), 1)]
ray = data.Ray(data.Point(1, 1, 1), data.Vector(1, 0, 0))
list_of_intersection_pairs = collisions.find_intersection_points(sphere_list, ray)
self.assertTrue(id(list_of_intersection_pairs), (4300121440, 4300122088))
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
def test_find_intersection_points1(self):
sphere_list = [data.Sphere(data.Point(1, 6, 4), 8), data.Sphere(data.Point(3, 2, 1), 1)]
ray = data.Ray(data.Point(2, 1, 4), data.Vector(1, 3, 0))
list_of_intersection_pairs = collisions.find_intersection_points(sphere_list, ray)
self.assertTrue(id(list_of_intersection_pairs), (4379206576, 4379236616))
