omaraflak

light = { 'position': np.array([5, 5, 5]), 'ambient': np.array([1, 1, 1]), 'diffuse': np.array([1, 1, 1]), 'specular': np.array([1, 1, 1]) }

omaraflak

objects = [
    { 'center': np.array([-0.2, 0, -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': 100 },
    { 'center': np.array([0.1, -0.3, 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': 100 },
    { 'center': np.array([-0.3, 0, 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': 100 }
]

omaraflak

# ...
intersection = origin + min_distance * direction

normal_to_surface = normalize(intersection - nearest_object['center'])
shifted_point = intersection + 1e-5 * normal_to_surface
intersection_to_light = normalize(light['position'] - shifted_point)

_, min_distance = nearest_intersected_object(objects, shifted_point, intersection_to_light)
intersection_to_light_distance = np.linalg.norm(light['position'] - intersection)
is_shadowed = min_distance < intersection_to_light_distance

omaraflak

# ...
intersection = origin + min_distance * direction

intersection_to_light = normalize(light['position'] - intersection)

_, min_distance = nearest_intersected_object(objects, intersection, intersection_to_light)
intersection_to_light_distance = np.linalg.norm(light['position'] - intersection)
is_shadowed = min_distance < intersection_to_light_distance

omaraflak

import numpy as np
import matplotlib.pyplot as plt

def normalize(vector):
    return vector / np.linalg.norm(vector)

def sphere_intersect(center, radius, ray_origin, ray_direction):
    b = 2 * np.dot(ray_direction, ray_origin - center)
    c = np.linalg.norm(ray_origin - center) ** 2 - radius ** 2
    delta = b ** 2 - 4 * c

omaraflak

objects = [
    { 'center': np.array([-0.2, 0, -1]), 'radius': 0.7 },
    { 'center': np.array([0.1, -0.3, 0]), 'radius': 0.1 },
    { 'center': np.array([-0.3, 0, 0]), 'radius': 0.15 }
]

omaraflak

def nearest_intersected_object(objects, ray_origin, ray_direction):
    distances = [sphere_intersect(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

omaraflak

def sphere_intersect(center, radius, ray_origin, ray_direction):
    b = 2 * np.dot(ray_direction, ray_origin - center)
    c = np.linalg.norm(ray_origin - center) ** 2 - radius ** 2
    delta = b ** 2 - 4 * c
    if delta > 0:
        t1 = (-b + np.sqrt(delta)) / 2
        t2 = (-b - np.sqrt(delta)) / 2
        if t1 > 0 and t2 > 0:
            return min(t1, t2)
    return None

omaraflak

import numpy as np
import matplotlib.pyplot as plt

def normalize(vector):
    return vector / np.linalg.norm(vector)

width = 300
height = 200

camera = np.array([0, 0, 1])

omaraflak

import numpy as np
import matplotlib.pyplot as plt

width = 300
height = 200

camera = np.array([0, 0, 1])
ratio = float(width) / height
screen = (-1, 1 / ratio, 1, -1 / ratio) # left, top, right, bottom