Skip to content

Instantly share code, notes, and snippets.

# rossant/raytracing.py Last active Aug 20, 2019

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 * 2) % 2) == (int(M * 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, S, w)): if i % 10 == 0: print i / float(w) * 100, "%" for j, y in enumerate(np.linspace(S, S, 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)

### kunguz commented Sep 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

### 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?

### JTreguer commented Oct 8, 2018

 Very nice intro to raytracing, thank you! I have a question regarding the screen window as it does not seem to be perpendicular to the initial OQ line of sight, is it for simplification purpose? Also it seems to contain an offset of 0.25 along y, is it for rendering a more interesting view?

### 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)
to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.