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ray_tracing.py
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ray_tracing.py
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import numpy as np
import matplotlib.pyplot as plt
import sys
from surface_defs import *
import random
##################### CONSTANTS/SETUP #####################
width = 1200 # Width of screen
height = 800 # Height of screen
ratio = width / height # Aspect Ratio
max_reflections = 3 # Max number of reflections
camera = np.array([0.6, 0.65, 5]) # Position of Camera
screen = (-camera[1] + -1, camera[1] + 1 / ratio, camera[1] + 1, -camera[1] - 1 / ratio) # Screen: left, top, right, bottom
image = np.zeros([height, width, 3]) # Image, initially black
light = { 'position': np.array([10, 10, 7]), 'ambient': np.array([0.75, 0.75, 0.75]), 'diffuse': np.array([0.75, 0.75, 0.75]), 'specular': np.array([0.75, 0.75, 0.75]) } # Light Info
num_random_objects = 75
##################### ############### #####################
#################### INITIAL OBJECTS ####################
objects = [
{ "object_type": "sphere", 'center': np.array([1.35, 0.7, -1]), 'radius': 0.7, 'ambient': np.array([0.1, 0.1, 0.1]), 'diffuse': np.array([0.7, 0.7, 0]), 'specular': np.array([1, 1, 1]), 'shininess': 300 , 'reflection': 1 },
{ "object_type": "sphere", 'center': np.array([-1.75, 0.7, -1]), 'radius': 0.7, 'ambient': np.array([0, 0, 0.1]), 'diffuse': np.array([0.7, 0, 0.7]), 'specular': np.array([1, 1, 1]), 'shininess': 300 , 'reflection': 1 },
{ "object_type": "sphere", 'center': np.array([-0.2, 0.7, -1]), 'radius': 0.7, 'ambient': np.array([0.1, 0, 0]), 'diffuse': np.array([0.7, 0, 0]), 'specular': np.array([1, 1, 1]), 'shininess': 1800 , 'reflection': 1 },
{ "object_type": "sphere", 'center': np.array([0.1, 0.1, 0]), 'radius': 0.1, 'ambient': np.array([0.1, 0, 0.1]), 'diffuse': np.array([0.7, 0, 0.7]), 'specular': np.array([1, 1, 1]), 'shininess': 300 , 'reflection': 1 },
{ "object_type": "sphere", 'center': np.array([-0.3, 0.15, 0]), 'radius': 0.15, 'ambient': np.array([0, 0.1, 0]), 'diffuse': np.array([0, 0.6, 0]), 'specular': np.array([1, 1, 1]), 'shininess': 150, 'reflection': 1 },
{ "object_type": "sphere", 'center': np.array([0, -9000, 0]), 'radius': 9000, 'ambient': np.array([0.4, 0.4, 0.4]), 'diffuse': np.array([0.7, 0.7, 0.7]), 'specular': np.array([1, 1, 1]), 'shininess': 150, 'reflection': 1 }
]
#################### ############### ####################
################### RANDOMIZE OBJECTS ###################
def is_conflict(surface):
for obj in objects:
min_distance = object_largest_rad[surface["object_type"]](surface) + object_largest_rad[obj["object_type"]](obj)
if np.linalg.norm(surface["center"] - obj["center"]) <= min_distance:
return True
return False
rand = random.random
for i in range(num_random_objects):
rad = 0.1 + rand() * 0.1
sur = {
"object_type": "sphere",
'center': np.array([-2 + rand() * 4, rad + rand() * 0.1, -1 + rand() * 4]),
'radius': rad,
'ambient': np.array([rand() * 0.7, rand() * 0.7, rand() * 0.7]),
'diffuse': np.array([rand() * 0.7, rand() * 0.7, rand() * 0.7]),
'specular': np.array([rand() * 0.7, rand() * 0.7, rand() * 0.7]),
'shininess': 150 + 100 * rand(),
'reflection': rand()
}
while is_conflict(sur):
sur['center'] = np.array([-2 + rand() * 4, rad + rand() * 0.2, -1 + rand() * 4])
objects.append(sur)
#################### ############### ####################
####################### FUNCTIONS #######################
def normalize(vec):
return vec / np.linalg.norm(vec)
def reflected(vector, axis):
return vector - 2 * np.dot(vector, axis) * axis
def nearest_intersected_object(objects, ray_origin, ray_direction):
distances = [object_intersects[obj["object_type"]](obj['center'], obj['radius'], ray_origin, ray_direction) for obj in objects]
nearest_object = None
min_distance = np.inf
for index, distance in enumerate(distances):
if distance and distance < min_distance:
min_distance = distance
nearest_object = objects[index]
return nearest_object, min_distance
####################### ######### #######################
for i, y in enumerate(np.linspace(screen[1], screen[3], height)):
for j, x in enumerate(np.linspace(screen[0], screen[2], width)):
pixel = np.array([x, y, 0])
origin = camera
direction = normalize(pixel - origin) # Unit vector from camera to pixel on screen
color = np.zeros((3)) # Initially black
total_reflection = 1
for _ in range(max_reflections):
nearest_object, min_distance = nearest_intersected_object(objects, origin, direction)
if nearest_object is None:
break
intersection = origin + min_distance * direction # Origin + Distance(time)
normal_to_surface = object_normals[nearest_object["object_type"]](nearest_object, intersection) # Normal of object toward intersection point
shifted_point = intersection + 0.00001 * normal_to_surface # Shift point out, as to not mistake the object we are at, for another
intersection_to_light = normalize(light['position'] - shifted_point) # Vector from light to intersection
_, min_distance = nearest_intersected_object(objects, shifted_point, intersection_to_light) # Distance from intersection to object in between light
intersection_to_light_distance = np.linalg.norm(light['position'] - intersection) # Distance from light to intersection
is_shadowed = min_distance < intersection_to_light_distance # Wether the intersected object is between the light, or not
if is_shadowed:
break # Leave color as black
illumination = np.zeros((3))
################### PHONG MODEL ###################
### Used to compute the illumination of a point ###
illumination += nearest_object['ambient'] * light['ambient'] # Ka * Ia
illumination += nearest_object['diffuse'] * light['diffuse'] * np.dot(intersection_to_light, normal_to_surface) # Ka * Ia * dot(L, N)
intersection_to_camera = normalize(camera - intersection)
H = normalize(intersection_to_light + intersection_to_camera) # ||L + V||
illumination += nearest_object['specular'] * light['specular'] * np.dot(normal_to_surface, H) ** (nearest_object['shininess'] / 4) # Ks * Is * dot(N , (L + V) / ||L + V||) ^ ()α / 4)
################### ########### ###################
################### REFLECTION COLOR ###################
### Formula Used: Color = I0 + (R0)(I1) + (R0)(R1)(I2) + .... ###
color += total_reflection * illumination
total_reflection *= nearest_object['reflection']
################### ################ ###################
origin = shifted_point # Reflection originates at intersection(shifted to avoid any issues)
direction = reflected(direction, normal_to_surface) # Get direction of reflected ray, which then becomes our new ray
image[i, j] = np.clip(color, 0, 1)
sys.stdout.write(f"########### Rendering Image [{round(float(i) * 100 / height)}%] ###########\r")
sys.stdout.flush()
print("########### Rendering Image [100%] ###########")
print("Rendering 'image.png' complete.")
plt.imsave('image.png', image)