Ray Tracer [FINAL].nlogo

globals [
  cam-x
  cam-y
  cam-z

  cam-yaw
  cam-pitch

  cam-fov
]

patches-own [
  patch-xcor
  patch-ycor
  patch-zcor

  patch-xvel
  patch-yvel
  patch-zvel

  patch-hits

  patch-is-done
]

turtles-own [
  world-xcor
  world-ycor
  world-zcor
  world-size
]

;;; CAMERA ;;;

to reset-camera
  set cam-x 0
  set cam-y 0
  set cam-z 0
  set cam-yaw 0
  set cam-pitch 0
  reset-patches
end

to move-camera [ dist ]
  set cam-x (cam-x + dist * (sin cam-yaw) * (cos cam-pitch))
  set cam-y (cam-y + dist * (sin cam-pitch))
  set cam-z (cam-z + dist * (cos cam-yaw) * (cos cam-pitch))
  reset-patches
end

to move-camera-up [ dist ]
  set cam-y (cam-y + dist)
  reset-patches
end

to move-camera-sideways [ dist ]
  set cam-x (cam-x + dist * (sin (cam-yaw + 90)))
  set cam-z (cam-z + dist * (cos (cam-yaw + 90)))
  reset-patches
end

to-report loop-angle [ ang ]
  let looped-ang (((ang mod 360) + 3600) mod 360)
  if (looped-ang > 180)
  [ set looped-ang (looped-ang - 360) ]
  report looped-ang
end

to turn-camera-yaw [ ang ]
  set cam-yaw (loop-angle (cam-yaw + ang))
  reset-patches

end

to turn-camera-pitch [ ang ]
  set cam-pitch (loop-angle (cam-pitch + ang))
  reset-patches
end

;;; PATCHES ;;;

to reset-patches
  ; camera must be above ground
  set cam-y (abs cam-y)

  ; direction camera is facing
  let start-xvel ((sin cam-yaw) * (cos cam-pitch))
  let start-yvel (sin cam-pitch)
  let start-zvel ((cos cam-yaw) * (cos cam-pitch))

  ; amount that the camera must turn due to fov
  let delt (tan (cam-fov / 2))

  ; amount that each of the axis
  ; will turn due to change in yaw
  let yaw-xdelt (delt * (sin (90 + cam-yaw)))
  let yaw-ydelt (0)
  let yaw-zdelt (delt * (cos (90 + cam-yaw)))

  ; amount that each of the axis
  ; will turn due to change in pitch
  let pitch-xdelt (delt * (0 - sin cam-yaw) * (sin cam-pitch))
  let pitch-ydelt (delt * (cos cam-pitch))
  let pitch-zdelt (delt * (0 - cos cam-yaw) * (sin cam-pitch))

  ; amount that the patches scale themself too
  let div-cor ((max-pxcor + max-pycor) / 2)

  ask patches [
    ; move ray to camera
    set patch-xcor (cam-x)
    set patch-ycor (cam-y)
    set patch-zcor (cam-z)

    ; add yaw and pitch to ray
    set patch-xvel (start-xvel + (yaw-xdelt * pxcor + pitch-xdelt * pycor) / div-cor)
    set patch-yvel (start-yvel + (yaw-ydelt * pxcor + pitch-ydelt * pycor) / div-cor)
    set patch-zvel (start-zvel + (yaw-zdelt * pxcor + pitch-zdelt * pycor) / div-cor)

    ; reset hits
    set patch-hits (0)

    ; activate-patch
    set patch-is-done false

    ; render really quickly
    move-patch
    update-patch-color
  ]
end

to-report distance-xyz [ x y z ]
  ; report pythagorean theorem
  report sqrt (x * x + y * y + z * z)
end

to-report patch-distancexyz [ x y z ]
  ; take distance of each axis
  let xdist (x - patch-xcor)
  let ydist (y - patch-ycor)
  let zdist (z - patch-zcor)

  ; report relative distance
  report (distance-xyz xdist ydist zdist)
end

to-report turtle-distancexyz [ x y z ]
  ; take distance of each axis
  let xdist (x - world-xcor)
  let ydist (y - world-ycor)
  let zdist (z - world-zcor)

  ; report relative distance
  report (distance-xyz xdist ydist zdist)
end

to-report is-touching-turtle [ x y z ]
  ; take distance of each axis
  let xdist (x - world-xcor)
  let ydist (y - world-ycor)
  let zdist (z - world-zcor)

  ; test if two are touching without sqrt
  report ((xdist * xdist + ydist * ydist + zdist * zdist) <= (world-size * world-size))
end

to-report max-step-size [ x y z xv yv zv ]
  ; take distance of each axis
  let xoc (x - world-xcor)
  let yoc (y - world-ycor)
  let zoc (z - world-zcor)

  ; calculate roots
  let a (xv * xv + yv * yv + zv * zv)
  let b (2 * (xoc * xv + yoc * yv + zoc * zv))
  let c ((xoc * xoc + yoc * yoc + zoc * zoc) - (world-size * world-size))

  ; get square root part of equation
  let step-size (b * b - 4 * a * c)

  ; if root is negative return big number
  if (step-size < 0) [ report 65536 ]

  ; get entire equation
  set step-size ((0 - (b + (sqrt step-size))) / (2 * a))

  ; if answer is negative return really big number
  if (step-size < 0) [ report 65536 ]

  ; return answer
  report step-size
end

to normalize-patch
  ; get distance of velocity
  let mag (distance-xyz patch-xvel patch-yvel patch-zvel)

  ; scale velocity down
  set patch-xvel (patch-xvel / mag)
  set patch-yvel (patch-yvel / mag)
  set patch-zvel (patch-zvel / mag)
end

to move-patch
  if (not patch-is-done) [
    ; normalize the velocitys
    normalize-patch

    ; push data into local memory
    let local-xcor (patch-xcor)
    let local-ycor (patch-ycor)
    let local-zcor (patch-zcor)
    let local-xvel (patch-xvel)
    let local-yvel (patch-yvel)
    let local-zvel (patch-zvel)
    let local-hits (patch-hits)
    let local-is-done (false)

    ; get largest steps size possible
    let floor-distance (65535)

    ; if patch is moving down, limit step size
    if (local-yvel < 0) [
      set patch-is-done false
      let scaled-ycor (abs (local-ycor / local-yvel))
      set floor-distance scaled-ycor
    ]

    ; calculate the closest turtle to the ray
    let closest-turtle (min-one-of turtles [
      max-step-size local-xcor local-ycor local-zcor
                    local-xvel local-yvel local-zvel
    ])

    ; do reflection calculation on closest turtle
    ask closest-turtle [
      ; get the distance from the ray to the turtle
      let dist (max-step-size local-xcor local-ycor local-zcor local-xvel local-yvel local-zvel)

      ; check which is closer, the turtle or floor
      ifelse(dist < floor-distance) [
        ; move the ray to the surface of the circle
        set local-xcor (local-xcor + local-xvel * dist)
        set local-ycor (local-ycor + local-yvel * dist)
        set local-zcor (local-zcor + local-zvel * dist)

        ; calculate dot product of the
        let normal-dist (turtle-distancexyz local-xcor local-ycor local-zcor)
        let normal-x ((local-xcor - world-xcor) / normal-dist)
        let normal-y ((local-ycor - world-ycor) / normal-dist)
        let normal-z ((local-zcor - world-zcor) / normal-dist)
        let dot (normal-x * local-xvel + normal-y * local-yvel + normal-z * local-zvel)

        ; reflect the ray off the turtle
        set local-xvel (local-xvel - 2 * dot * normal-x)
        set local-yvel (local-yvel - 2 * dot * normal-y)
        set local-zvel (local-zvel - 2 * dot * normal-z)

        ; increase the amount of hits
        set local-hits (local-hits + 1)
      ] [
        ; only bounce off floor when moving down
        ifelse (local-yvel < 0) [
          ; move ray to the floor
          set local-xcor (local-xcor + local-xvel * floor-distance)
          set local-ycor (local-ycor + local-yvel * floor-distance)
          set local-zcor (local-zcor + local-zvel * floor-distance)

          ; bounce the ray off the floor
          set local-ycor (abs local-ycor)
          set local-yvel (abs local-yvel)

          ; floor patch settings
          let square-size 20
          let floor-hits 2.5
          let square-diff 0.5

          ; calculate if it is a bright or dark square
          if-else (
            ((local-xcor mod square-size) <= (square-size / 2)) !=
            ((local-zcor mod square-size) <= (square-size / 2)))
          [ set local-hits (local-hits + floor-hits - square-diff) ]
          [ set local-hits (local-hits + floor-hits + square-diff) ]
        ] [
          ; if everything is done, tell ray that it is done
          set local-is-done (true)
        ]
      ]
    ]

    ; push data into patch memory
    set patch-xcor (local-xcor)
    set patch-ycor (local-ycor)
    set patch-zcor (local-zcor)
    set patch-xvel (local-xvel)
    set patch-yvel (local-yvel)
    set patch-zvel (local-zvel)
    set patch-hits (local-hits)
    set patch-is-done (local-is-done)
  ]
end

to-report cap-rgb [ val ]
  ; cap value from 0 - 255
  if (val < 000) [ report 000 ]
  if (val > 255) [ report 255 ]
  report val
end

to update-patch-color
  ; copy amount of hits into local memory
  let local-hits (patch-hits)

  ; if patch is traveling down, simulate hit
  if (patch-yvel < 0) [ set local-hits (local-hits + 3) ]

  ; get angle of the ray for rainbow color
  let angle 270
  if (rainbow and ((patch-xvel != 0) or (patch-zvel != 0)))
  [ set angle ((atan patch-xvel patch-zvel) * (2)) ]

  ; get pitch of the ray
  let xz-mag (sqrt (patch-xvel * patch-xvel + patch-zvel * patch-zvel))
  let hit-scale (0.618 ^ local-hits)
  let sky-scale (0.25 + 1.6 * (cos (atan xz-mag (abs patch-yvel))))

  ; turn angles into rainbow and shadows
  let r (128 + 128 * (sin (angle + 000)))
  let g (128 + 128 * (sin (angle + 120)))
  let b (128 + 128 * (sin (angle + 240)))

  ; darken colors due to sky
  set r (r * sky-scale)
  set g (g * sky-scale)
  set b (b * sky-scale)

  ; average color with hits
  set r (r * hit-scale + circle-r * (1 - hit-scale))
  set g (g * hit-scale + circle-g * (1 - hit-scale))
  set b (b * hit-scale + circle-b * (1 - hit-scale))

  ; set color to the calculated color
  set pcolor (list (cap-rgb r) (cap-rgb g) (cap-rgb b))
end

to update-progress
  set render-progress (round (1000 * (count patches with [ patch-is-done ]) / (count patches)) / 10)
end

to turtle-init [ x y z in-size]
  set hidden? true
  set world-xcor x
  set world-ycor y
  set world-zcor z
  set world-size in-size
end

;;; TEST ;;;

to setup
  ca

  ; create the spheres
  cro 1 [ turtle-init 0   12  10  3 ]
  cro 1 [ turtle-init -48 12  10  3 ]
  cro 1 [ turtle-init -24 40  10  3 ]
  cro 1 [ turtle-init -24 16  16  6 ]
  cro 1 [ turtle-init 0   24  50  25 ]
  cro 1 [ turtle-init -48 24  50  24 ]
  cro 1 [ turtle-init 0   50  150 36 ]
  cro 1 [ turtle-init -72 50  150 36 ]
  reset-camera

  ; setup camera
  set cam-x -30
  set cam-y 42
  set cam-z -40
  set cam-pitch -15
  set cam-yaw 7
  set cam-fov 90
  set fov cam-fov

  reset-patches
end

to go
  ; if fov changes, draw new image
  if (fov != cam-fov) [
    set cam-fov (fov)
    reset-patches
  ]

  ; cycle through update groups
  ask patches [
    move-patch
    update-patch-color
  ]

  ; update progress bar
  update-progress

  display
end
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Reset
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=== Initialization ===
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=== Settings ===
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=== Customization ===
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=== Richard's Progress Bar I Stole === 
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@#$#@#$#@
## WHAT IS IT?

This is a ray tracer that is implemented completely within NetLogo. There is obviously no hardware acceleration in netlogo so the raytracing is done in software. 

## HOW IT WORKS

The ray tracing is done by having the light work its way backwards out of the camera. So you can simulate the reflections off of circles in a really realistic way. Many optimizaitons had to be made when creating this ray tracer.   

## HOW TO USE IT

Click the reset button, then click the render button to start the rendering process. 

It is best that you leave the render button running at all time as everything can be interacted with while it is running.

WASD is used to move the camera forwards and backwards. 
E moves you up
W moves you down
IJKL is used to move the camera around

You can try changing the movement speed if you feel like you are moving too slowly.

The FOV slider will let you change how much you can see, but it can create distortions in size around the edges if set too high.

Also change the rainbow setting to your liking.

If the rendering is too slow, or too pixelated, you can manually change the patch size and the program will scale accordingly.

## THINGS TO TRY

If you would like to try adding in another circle type this command

`cro 1 [ turtle-init (NEW-X) (NEW-Y) (NEW-Z) (NEW-SIZE) ]`

and move around to see it update

## EXTENDING THE MODEL

You can attempt to add new shapes, but circles demonstrate the way ray tracers work quite well.

## CREDITS AND REFERENCES

Richard Lee) for inventing the idea of a progress bar. really helpful
Ray Tracing in a Weekend) formula for reflections and formula for finding point of intersection
@#$#@#$#@
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Polygon -7500403 true true 90 75 75 150 90 150 90 75
Polygon -7500403 true true 210 75 225 150 210 150 210 75
Rectangle -16777216 true false 105 90 195 120
Rectangle -7500403 true true 90 150 120 195
Rectangle -7500403 true true 180 150 210 195
Circle -7500403 true true 84 159 42
Circle -7500403 true true 174 159 42

sheep
false
15
Circle -1 true true 203 65 88
Circle -1 true true 70 65 162
Circle -1 true true 150 105 120
Polygon -7500403 true false 218 120 240 165 255 165 278 120
Circle -7500403 true false 214 72 67
Rectangle -1 true true 164 223 179 298
Polygon -1 true true 45 285 30 285 30 240 15 195 45 210
Circle -1 true true 3 83 150
Rectangle -1 true true 65 221 80 296
Polygon -1 true true 195 285 210 285 210 240 240 210 195 210
Polygon -7500403 true false 276 85 285 105 302 99 294 83
Polygon -7500403 true false 219 85 210 105 193 99 201 83

square
false
0
Rectangle -7500403 true true 30 30 270 270

square 2
false
0
Rectangle -7500403 true true 30 30 270 270
Rectangle -16777216 true false 60 60 240 240

star
false
0
Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108

target
false
0
Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240
Circle -7500403 true true 60 60 180
Circle -16777216 true false 90 90 120
Circle -7500403 true true 120 120 60

tree
false
0
Circle -7500403 true true 118 3 94
Rectangle -6459832 true false 120 195 180 300
Circle -7500403 true true 65 21 108
Circle -7500403 true true 116 41 127
Circle -7500403 true true 45 90 120
Circle -7500403 true true 104 74 152

triangle
false
0
Polygon -7500403 true true 150 30 15 255 285 255

triangle 2
false
0
Polygon -7500403 true true 150 30 15 255 285 255
Polygon -16777216 true false 151 99 225 223 75 224

truck
false
0
Rectangle -7500403 true true 4 45 195 187
Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194
Rectangle -1 true false 195 60 195 105
Polygon -16777216 true false 238 112 252 141 219 141 218 112
Circle -16777216 true false 234 174 42
Rectangle -7500403 true true 181 185 214 194
Circle -16777216 true false 144 174 42
Circle -16777216 true false 24 174 42
Circle -7500403 false true 24 174 42
Circle -7500403 false true 144 174 42
Circle -7500403 false true 234 174 42

turtle
true
0
Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210
Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105
Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105
Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87
Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210
Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99

wheel
false
0
Circle -7500403 true true 3 3 294
Circle -16777216 true false 30 30 240
Line -7500403 true 150 285 150 15
Line -7500403 true 15 150 285 150
Circle -7500403 true true 120 120 60
Line -7500403 true 216 40 79 269
Line -7500403 true 40 84 269 221
Line -7500403 true 40 216 269 79
Line -7500403 true 84 40 221 269

wolf
false
0
Polygon -16777216 true false 253 133 245 131 245 133
Polygon -7500403 true true 2 194 13 197 30 191 38 193 38 205 20 226 20 257 27 265 38 266 40 260 31 253 31 230 60 206 68 198 75 209 66 228 65 243 82 261 84 268 100 267 103 261 77 239 79 231 100 207 98 196 119 201 143 202 160 195 166 210 172 213 173 238 167 251 160 248 154 265 169 264 178 247 186 240 198 260 200 271 217 271 219 262 207 258 195 230 192 198 210 184 227 164 242 144 259 145 284 151 277 141 293 140 299 134 297 127 273 119 270 105
Polygon -7500403 true true -1 195 14 180 36 166 40 153 53 140 82 131 134 133 159 126 188 115 227 108 236 102 238 98 268 86 269 92 281 87 269 103 269 113

x
false
0
Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270
@#$#@#$#@
NetLogo 6.1.1
@#$#@#$#@
@#$#@#$#@
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@#$#@#$#@
default
0.0
-0.2 0 0.0 1.0
0.0 1 1.0 0.0
0.2 0 0.0 1.0
link direction
true
0
Line -7500403 true 150 150 90 180
Line -7500403 true 150 150 210 180
@#$#@#$#@
0
@#$#@#$#@