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The standard ray tracing algorithm seems unnatural to me because everytime a ray reflects/refracts all (primitive) objects in the scene must be tested for intersection; no matter where they located!

In this method there is no such thing. It just moves each ray voxel by voxel until it hits an opaque/reflective(/refractive) voxel.

I made many simplifications so the image is crude.

Python, 190 lines
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190``` ```# Voxel-based Ray Tracing # No refraction for simplicity! # Single point light source for simplicity! # FB36 - 20130829 import math from PIL import Image imgx = 400; imgy = 400 ; imgz = 400 # voxel-box size image = Image.new("RGB", (imgx, imgy)) pixels = image.load() print "Creating voxels..." # each voxel can have RGB color voxelRGB = [[[(0, 0, 0) for x in range(imgx)] for y in range(imgy)] for z in range(imgz)] # each voxel can have an opacity coefficient 0 or 1 (for simplicity) opacity = [[[0 for x in range(imgx)] for y in range(imgy)] for z in range(imgz)] # each voxel can have a 3d normal unit vector (for reflections/refractions) normal = [[[(0.0, 0.0, 0.0) for x in range(imgx)] for y in range(imgy)] for z in range(imgz)] # each voxel can have a reflectivity coefficient between 0 and 1 reflectivity = [[[0.0 for x in range(imgx)] for y in range(imgy)] for z in range(imgz)] eye = (imgx / 2.0, 250.0, -100.0) light = (- 10.0, -10.0, -10.0) ambientBrightness = 0.3 # between 0 and 1 # cx, cy, cz: center; r: radius (in voxels) # rc: reflectivity coefficient between 0 and 1 def CreateMirrorSphere(cx, cy, cz, r, colorRGB, rc): print "Creating mirror sphere..." # sphere is set of voxels which have distance = r to center for z in range(imgz): for y in range(imgy): for x in range(imgx): dx = x - cx dy = y - cy dz = z - cz d = math.sqrt(dx * dx + dy * dy + dz * dz) if abs(d - r) < 1.0: voxelRGB[z][y][x] = colorRGB opacity[z][y][x] = 1 normal[z][y][x] = (dx / d, dy / d, dz / d) reflectivity[z][y][x] = rc def CreateCheckerboardFloor(sqrX, sqrZ, colorRGB0, colorRGB1): print "Creating checkerboard floor..." for z in range(imgz): for x in range(imgx): if int(x / sqrX) % 2 != int(z / sqrZ) % 2: # xor voxelRGB[z][imgy - 1][x] = colorRGB0 else: voxelRGB[z][imgy - 1][x] = colorRGB1 opacity[z][imgy - 1][x] = 1 normal[z][imgy - 1][x] = (0.0, -1.0, 0.0) def CombineColors(c0, c1, w): return (int(round(c0[0] + (c1[0] - c0[0]) * w)), int(round(c0[1] + (c1[1] - c0[1]) * w)), int(round(c0[2] + (c1[2] - c0[2]) * w))) # 3D Reflection (all vectors are unit vectors) def Reflection(normalVector, incidentRayVector): (nx, ny, nz) = normalVector (ix, iy, iz) = incidentRayVector dotProduct = nx * ix + ny * iy + nz * iz rx = ix - 2 * dotProduct * nx ry = iy - 2 * dotProduct * ny rz = iz - 2 * dotProduct * nz return (rx, ry, rz) def LightIntensity(surfaceVoxelCoordinates, surfaceNormalVector): (svx, svy, svz) = surfaceVoxelCoordinates (nx, ny, nz) = surfaceNormalVector (Lx, Ly, Lz) = light dx = Lx - svx dy = Ly - svy dz = Lz - svz d = math.sqrt(dx * dx + dy * dy + dz * dz) dx = dx / d; dy = dy / d; dz = dz / d # unit vector towards light cosT = nx * dx + ny * dy + nz * dz if cosT < 0.0: cosT = 0.0 # the surface faces away from the light source return cosT def ShadowIntensity(rayX, rayY, rayZ): (Lx, Ly, Lz) = light dx = Lx - rayX dy = Ly - rayY dz = Lz - rayZ d = math.sqrt(dx * dx + dy * dy + dz * dz) dx = dx / d; dy = dy / d; dz = dz / d # unit vector towards light while True: # shadow ray tracing rayX += dx; rayY += dy; rayZ += dz # move the ray by 1 voxel rayXint = int(round(rayX)) rayYint = int(round(rayY)) rayZint = int(round(rayZ)) # if ray goes outside of the voxel-box if rayXint < 0 or rayXint > imgx - 1 \ or rayYint < 0 or rayYint > imgy - 1 \ or rayZint < 0 or rayZint > imgz - 1: return 1.0 # if ray hits an object if opacity[rayZint][rayYint][rayXint] == 1: # stop tracing here for simplicity return 0.0 # if ray hits the light source vx = Lx - rayX vy = Ly - rayY vz = Lz - rayZ d = math.sqrt(vx * vx + vy * vy + vz * vz) if d < 1.0: return 1.0 # Ray Tracer (traces the ray and returns an RGB color) def RayTrace(rayX, rayY, rayZ, dx, dy, dz): brightness = 1.0 # the ray has full brightness at the beginning color = (0, 0, 0) while True: rayX += dx; rayY += dy; rayZ += dz # move the ray by 1 voxel rayXint = int(round(rayX)) rayYint = int(round(rayY)) rayZint = int(round(rayZ)) # if ray goes outside of the voxel-box if rayXint < 0 or rayXint > imgx - 1 \ or rayYint < 0 or rayYint > imgy - 1 \ or rayZint < 0 or rayZint > imgz - 1: return color # if ray hits an object if opacity[rayZint][rayYint][rayXint] == 1: # if ray hits a non-reflective object if reflectivity[rayZint][rayYint][rayXint] == 0.0: brightness *= ShadowIntensity(rayX, rayY, rayZ) brightness *= LightIntensity((rayX, rayY, rayZ), \ normal[rayZint][rayYint][rayXint]) brightness = brightness * (1.0 - ambientBrightness) + ambientBrightness color = CombineColors(color, voxelRGB[rayZint][rayYint][rayXint], brightness) return color # if ray hits a reflective object if reflectivity[rayZint][rayYint][rayXint] > 0.0: brightness *= reflectivity[rayZint][rayYint][rayXint] brightnessTemp = ShadowIntensity(rayX, rayY, rayZ) brightnessTemp *= LightIntensity((rayX, rayY, rayZ), \ normal[rayZint][rayYint][rayXint]) brightnessTemp = brightnessTemp * (1.0 - ambientBrightness) + ambientBrightness colorTemp = voxelRGB[rayZint][rayYint][rayXint] colorTemp = (int(colorTemp[0] * brightnessTemp), \ int(colorTemp[1] * brightnessTemp), \ int(colorTemp[2] * brightnessTemp)) color = CombineColors(color, colorTemp, \ 1.0 - reflectivity[rayZint][rayYint][rayXint]) (dx, dy, dz) = Reflection(normal[rayZint][rayYint][rayXint], (dx, dy, dz)) def CreateScene(): print "Creating scene..." CreateCheckerboardFloor(20, 20, (255, 255, 0), (0, 0, 255)) CreateMirrorSphere(imgx / 2.0, imgy / 2.0, imgz / 2, 150.0, (0, 255, 0), 0.8) def RenderScene(): print "Rendering scene..." for ky in range(imgy): print str(100 * ky / (imgy - 1)).zfill(3) + "%" for kx in range(imgx): dx = kx - eye[0] dy = ky - eye[1] dz = 0.0 - eye[2] d = math.sqrt(dx * dx + dy * dy + dz * dz) dx = dx / d; dy = dy / d; dz = dz / d # ray unit vector pixels[kx, ky] = RayTrace(kx, ky, 0, dx, dy, dz) # MAIN CreateScene() RenderScene() image.save("Voxel_Based_Ray_Tracing.png", "PNG") ```
 Created by FB36 on Thu, 29 Aug 2013 (MIT)