Very simple ray tracing engine in (almost) pure Python. Depends on NumPy and Matplotlib. Diffuse and specular lighting, simple shadows, reflections, no refraction. Purely sequential algorithm, slow execution.
""" | |
MIT License | |
Copyright (c) 2017 Cyrille Rossant | |
Permission is hereby granted, free of charge, to any person obtaining a copy | |
of this software and associated documentation files (the "Software"), to deal | |
in the Software without restriction, including without limitation the rights | |
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell | |
copies of the Software, and to permit persons to whom the Software is | |
furnished to do so, subject to the following conditions: | |
The above copyright notice and this permission notice shall be included in all | |
copies or substantial portions of the Software. | |
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR | |
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, | |
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE | |
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER | |
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, | |
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE | |
SOFTWARE. | |
""" | |
import numpy as np | |
import matplotlib.pyplot as plt | |
w = 400 | |
h = 300 | |
def normalize(x): | |
x /= np.linalg.norm(x) | |
return x | |
def intersect_plane(O, D, P, N): | |
# Return the distance from O to the intersection of the ray (O, D) with the | |
# plane (P, N), or +inf if there is no intersection. | |
# O and P are 3D points, D and N (normal) are normalized vectors. | |
denom = np.dot(D, N) | |
if np.abs(denom) < 1e-6: | |
return np.inf | |
d = np.dot(P - O, N) / denom | |
if d < 0: | |
return np.inf | |
return d | |
def intersect_sphere(O, D, S, R): | |
# Return the distance from O to the intersection of the ray (O, D) with the | |
# sphere (S, R), or +inf if there is no intersection. | |
# O and S are 3D points, D (direction) is a normalized vector, R is a scalar. | |
a = np.dot(D, D) | |
OS = O - S | |
b = 2 * np.dot(D, OS) | |
c = np.dot(OS, OS) - R * R | |
disc = b * b - 4 * a * c | |
if disc > 0: | |
distSqrt = np.sqrt(disc) | |
q = (-b - distSqrt) / 2.0 if b < 0 else (-b + distSqrt) / 2.0 | |
t0 = q / a | |
t1 = c / q | |
t0, t1 = min(t0, t1), max(t0, t1) | |
if t1 >= 0: | |
return t1 if t0 < 0 else t0 | |
return np.inf | |
def intersect(O, D, obj): | |
if obj['type'] == 'plane': | |
return intersect_plane(O, D, obj['position'], obj['normal']) | |
elif obj['type'] == 'sphere': | |
return intersect_sphere(O, D, obj['position'], obj['radius']) | |
def get_normal(obj, M): | |
# Find normal. | |
if obj['type'] == 'sphere': | |
N = normalize(M - obj['position']) | |
elif obj['type'] == 'plane': | |
N = obj['normal'] | |
return N | |
def get_color(obj, M): | |
color = obj['color'] | |
if not hasattr(color, '__len__'): | |
color = color(M) | |
return color | |
def trace_ray(rayO, rayD): | |
# Find first point of intersection with the scene. | |
t = np.inf | |
for i, obj in enumerate(scene): | |
t_obj = intersect(rayO, rayD, obj) | |
if t_obj < t: | |
t, obj_idx = t_obj, i | |
# Return None if the ray does not intersect any object. | |
if t == np.inf: | |
return | |
# Find the object. | |
obj = scene[obj_idx] | |
# Find the point of intersection on the object. | |
M = rayO + rayD * t | |
# Find properties of the object. | |
N = get_normal(obj, M) | |
color = get_color(obj, M) | |
toL = normalize(L - M) | |
toO = normalize(O - M) | |
# Shadow: find if the point is shadowed or not. | |
l = [intersect(M + N * .0001, toL, obj_sh) | |
for k, obj_sh in enumerate(scene) if k != obj_idx] | |
if l and min(l) < np.inf: | |
return | |
# Start computing the color. | |
col_ray = ambient | |
# Lambert shading (diffuse). | |
col_ray += obj.get('diffuse_c', diffuse_c) * max(np.dot(N, toL), 0) * color | |
# Blinn-Phong shading (specular). | |
col_ray += obj.get('specular_c', specular_c) * max(np.dot(N, normalize(toL + toO)), 0) ** specular_k * color_light | |
return obj, M, N, col_ray | |
def add_sphere(position, radius, color): | |
return dict(type='sphere', position=np.array(position), | |
radius=np.array(radius), color=np.array(color), reflection=.5) | |
def add_plane(position, normal): | |
return dict(type='plane', position=np.array(position), | |
normal=np.array(normal), | |
color=lambda M: (color_plane0 | |
if (int(M[0] * 2) % 2) == (int(M[2] * 2) % 2) else color_plane1), | |
diffuse_c=.75, specular_c=.5, reflection=.25) | |
# List of objects. | |
color_plane0 = 1. * np.ones(3) | |
color_plane1 = 0. * np.ones(3) | |
scene = [add_sphere([.75, .1, 1.], .6, [0., 0., 1.]), | |
add_sphere([-.75, .1, 2.25], .6, [.5, .223, .5]), | |
add_sphere([-2.75, .1, 3.5], .6, [1., .572, .184]), | |
add_plane([0., -.5, 0.], [0., 1., 0.]), | |
] | |
# Light position and color. | |
L = np.array([5., 5., -10.]) | |
color_light = np.ones(3) | |
# Default light and material parameters. | |
ambient = .05 | |
diffuse_c = 1. | |
specular_c = 1. | |
specular_k = 50 | |
depth_max = 5 # Maximum number of light reflections. | |
col = np.zeros(3) # Current color. | |
O = np.array([0., 0.35, -1.]) # Camera. | |
Q = np.array([0., 0., 0.]) # Camera pointing to. | |
img = np.zeros((h, w, 3)) | |
r = float(w) / h | |
# Screen coordinates: x0, y0, x1, y1. | |
S = (-1., -1. / r + .25, 1., 1. / r + .25) | |
# Loop through all pixels. | |
for i, x in enumerate(np.linspace(S[0], S[2], w)): | |
if i % 10 == 0: | |
print i / float(w) * 100, "%" | |
for j, y in enumerate(np.linspace(S[1], S[3], h)): | |
col[:] = 0 | |
Q[:2] = (x, y) | |
D = normalize(Q - O) | |
depth = 0 | |
rayO, rayD = O, D | |
reflection = 1. | |
# Loop through initial and secondary rays. | |
while depth < depth_max: | |
traced = trace_ray(rayO, rayD) | |
if not traced: | |
break | |
obj, M, N, col_ray = traced | |
# Reflection: create a new ray. | |
rayO, rayD = M + N * .0001, normalize(rayD - 2 * np.dot(rayD, N) * N) | |
depth += 1 | |
col += reflection * col_ray | |
reflection *= obj.get('reflection', 1.) | |
img[h - j - 1, i, :] = np.clip(col, 0, 1) | |
plt.imsave('fig.png', img) |
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aflaxman
commented
Dec 22, 2016
I've been playing around with this and Google Cardboard. Can you put an open-source license of some sort on it? |
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JTreguer
commented
Oct 8, 2018
Very nice intro to raytracing, thank you! |
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DelSquared
commented
Nov 19, 2018
I wonder if it will gain any performance improvements if the normalise function was implemented with Quake III's bitshifting hack for 1/sqrt(x) |
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cryptid11
commented
Oct 15, 2019
is there a similar compact version in C? |
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kunguz commentedSep 27, 2014
This is pretty cool, you may want to check for my previous work under https://github.com/kunguz/odak/blob/master/source/lib/odak.py#L83