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 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 test_translate_2(self): p = data.Point(1,2,3) v = data.Vector(4,5,6) newp = vector_math.translate_point(p, v) equals = data.Point(5, 7, 9) self.assertEqual(newp == equals, True) pass
def test_translate_point_2(self):
p = data.Point(0.0, 0.0, 0.0)
v = data.Vector(1.0, 2.0, 3.0)
p_translated = vector_math.translate_point(p, v)
self.assertAlmostEqual(p_translated.x, 1.0)
self.assertAlmostEqual(p_translated.y, 2.0)
self.assertAlmostEqual(p_translated.z, 3.0)
def test_translate_point_1(self):
p = data.Point(0.0, 0.0, 0.0)
v = data.Vector(0.0, 0.0, 0.0)
p_translated = vector_math.translate_point(p, v)
self.assertEqual(p_translated, data.Point(0.0, 0.0, 0.0))
self.assertAlmostEqual(p_translated.x, 0.0)
self.assertAlmostEqual(p_translated.y, 0.0)
self.assertAlmostEqual(p_translated.z, 0.0)
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 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 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 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 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 find_pt_off_sphere(inter_point,normal): vect = vector_math.scale_vector(normal, 0.01) return vector_math.translate_point(inter_point,vect)
def test_translate_point_1(self):
point = data.Point(1, 2, 3)
vector = data.Vector(1, 2, 3)
newpoint = vector_math.translate_point(point, vector)
self.assertEqual(newpoint, data.Point(2, 4, 6))
def test_translate_point_2(self):
p = data.Point(1, 1, 1)
vect = data.Vector(1, 1, 1)
new_p = data.Point(2, 2, 2)
self.assertAlmostEqual(vector_math.translate_point(p, vect), new_p)
def test_translate_point(self):
p = data.Point(1, 1, 1)
vect = data.Vector(0.5, 0.5, 0.5)
new_p = data.Point(1.5, 1.5, 1.5)
self.assertAlmostEqual(vector_math.translate_point(p, vect), new_p)
def point_t(t):
return vector_math.translate_point(
ray.pt, vector_math.scale_vector(ray.dir, t))
def find_pt_off_sphere(inter_point, normal):
vect = vector_math.scale_vector(normal, 0.01)
return vector_math.translate_point(inter_point, vect)
def test_translate_point_1(self):
point1 = data.Point(0, 1, 2)
vector1 = data.Vector(3, 4, 5)
translation = data.Point(3, 5, 7)
self.assertEqual(vector_math.translate_point(point1, vector1), translation)
def test_translate_point_2(self):
point = data.Point(3, -2, 6)
vector = data.Vector(-2.5, 3.3, -2)
newpoint = vector_math.translate_point(point, vector)
self.assertEqual(newpoint, data.Point(0.5, 1.3, 4))
def get_pe(tu): vector = collisions.sphere_normal_at_point(tu[0], tu[1]) sVector = vector_math.scale_vector(vector, .01) scaledPoint = vector_math.translate_point(tu[1], sVector) return scaledPoint
def get_pe(tu):
vector = collisions.sphere_normal_at_point(tu[0], tu[1])
sVector = vector_math.scale_vector(vector, .01)
scaledPoint = vector_math.translate_point(tu[1], sVector)
return scaledPoint
def test_translate_1(self): p = data.Point(1,2,3) v = data.Vector(0,0,0) newp = vector_math.translate_point(p, v) self.assertEqual(p == newp, True) pass
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_translate_point_2(self):
point2 = data.Point(-8, 9, -4)
vector2 = data.Vector(-3, 5, -9)
translation = data.Point(-11, 14, -13)
self.assertEqual(vector_math.translate_point(point2, vector2), translation)
def test_translate_point(self):
tp = vector_math.translate_point(data.Point(9, 0, 1), data.Vector(1, 2, 3))
self.assertEqual(tp, data.Point(10, 2, 4))
def test_translate_point_again(self):
tp = vector_math.translate_point(data.Point(10, -4, 7.4), data.Vector(3.1, -7, 0.6))
self.assertEqual(tp, data.Point(13.1, -11, 8))
def point_t(t):
return vector_math.translate_point(ray.pt,
vector_math.scale_vector(ray.dir,t))
def find_point_near_sphere(sphere, point): normal_vector = collisions.sphere_normal_at_point(sphere, point) translate_vec = vector_math.scale_vector(normal_vector, 0.01) return vector_math.translate_point(point, translate_vec)