raytracer.erl

   1 -module(raytracer).
   2 -compile(export_all).
   3
   4 -record(vector, {x, y, z}).
   5 -record(colour, {r, g, b}).
   6 %-record(ray, {origin, direction}).
   7 -record(screen, {width, height}). % screen dimensions in the 3D world
   8 -record(camera, {location, rotation, fov, screen}).
   9 -record(sphere, {radius, center, colour}).
  10 %-record(axis_aligned_cube, {size, location}).
  11
  12 raytraced_pixel_list(0, 0, _) ->
  13     done;
  14 raytraced_pixel_list(Width, Height, Scene) when Width > 0, Height > 0 ->
  15     lists:flatmap(
  16       fun(X) ->
  17               lists:map(
  18                 fun(Y) ->
  19                         % coordinates passed as a percentage
  20                         trace_ray_from_pixel({X/Width, Y/Height}, Scene) end,
  21                 lists:seq(0, Height - 1)) end,
  22       lists:seq(0, Width - 1)).
  23
  24 trace_ray_from_pixel({X, Y}, [Camera|Rest_of_scene]) ->
  25     Ray = ray_through_pixel(X, Y, Camera),
  26     {_Nearest_object, _Distance} = nearest_object_intersecting_ray(Ray, Rest_of_scene),
  27     % return the Nearest_object's colour
  28     {random:uniform(256)-1, random:uniform(256)-1, random:uniform(256)-1}.
  29
  30 nearest_object_intersecting_ray(_Ray, _Scene) ->
  31     none.
  32
  33 focal_length(Angle, Dimension) ->
  34     Dimension/(2*math:tan(Angle*(math:pi()/180)/2)).
  35
  36 point_on_screen(_X, _Y, _Camera) ->
  37     none.
  38
  39 shoot_ray(_From, _Through) ->
  40     none.
  41
  42 % assume that X and Y are percentages of the 3D world screen dimensions
  43 ray_through_pixel(X, Y, Camera) ->
  44     shoot_ray(Camera#camera.location, point_on_screen(X, Y, Camera)).
  45
  46 vectors_equal(V1, V2) ->
  47     (V1#vector.x == V2#vector.x)
  48         and (V1#vector.y == V2#vector.y)
  49         and (V1#vector.z == V2#vector.z).
  50
  51 vector_add(V1, V2) ->
  52     #vector{x = V1#vector.x + V2#vector.x,
  53             y = V1#vector.y + V2#vector.y,
  54             z = V1#vector.z + V2#vector.z}.
  55
  56 vector_sub(V1, V2) ->
  57         #vector{x = V1#vector.x - V2#vector.x,
  58             y = V1#vector.y - V2#vector.y,
  59             z = V1#vector.z - V2#vector.z}.
  60
  61 vector_square_mag(#vector{x=X, y=Y, z=Z}) ->
  62     X*X + Y*Y + Z*Z.
  63
  64 vector_mag(V) ->
  65     math:sqrt(vector_square_mag(V)).
  66
  67 vector_scalar_mult(#vector{x=X, y=Y, z=Z}, Scalar) ->
  68     #vector{x=X*Scalar, y=Y*Scalar, z=Z*Scalar}.
  69
  70 vector_dot_product(#vector{x=A1, y=A2, z=A3}, #vector{x=B1, y=B2, z=B3}) ->
  71     A1*B1 + A2*B2 + A3*B3.
  72
  73 vector_cross_product(#vector{x=A1, y=A2, z=A3}, #vector{x=B1, y=B2, z=B3}) ->
  74     #vector{x = A2*B3 - A3*B2,
  75             y = A3*B1 - A1*B3,
  76             z = A1*B2 - A2*B1}.
  77
  78 vector_normalize(V) ->
  79     Mag = vector_mag(V),
  80     if Mag == 0 ->
  81             #vector{x=0, y=0, z=0};
  82        true ->
  83             vector_scalar_mult(V, 1/vector_mag(V))
  84     end.
  85
  86 vector_neg(#vector{x=X, y=Y, z=Z}) ->
  87     #vector{x=-X, y=-Y, z=-Z}.
  88
  89 % returns a list of objects in the scene
  90 % camera is assumed to be the first element in the scene
  91 scene() ->
  92     [#camera{location=#vector{x=0, y=0, z=0},
  93              rotation=#vector{x=1, y=0, z=0},
  94              fov=90,
  95              screen=#screen{width=1, height=1}},
  96      #sphere{radius=2,
  97              center=#vector{x=5, y=0, z=0},
  98              colour=#colour{r=0, g=128, b=255}}
  99     ].
 100
 101
 102 write_pixels_to_ppm(Width, Height, Pixels, MaxValue, Filename) ->
 103     case file:open(Filename, write) of
 104         {ok, IoDevice} ->
 105             io:format("file opened~n", []),
 106             io:format(IoDevice, "P3~n", []),
 107             io:format(IoDevice, "~p ~p~n", [Width, Height]),
 108             io:format(IoDevice, "~p~n", [MaxValue]),
 109             lists:foreach(
 110               fun({R, G, B}) ->
 111                       io:format(IoDevice, "~p ~p ~p ",
 112                                 [R, G, B]) end,
 113               Pixels),
 114             file:close(IoDevice),
 115             io:format("done~n", []);
 116         error ->
 117             io:format("error opening file~n", [])
 118     end.
 119
 120 go() ->
 121     go(1, 1, "/tmp/traced.ppm").
 122 go(Width, Height, Filename) ->
 123     write_pixels_to_ppm(Width,
 124                         Height,
 125                         255,
 126                         raytraced_pixel_list(Width,
 127                                              Height,
 128                                              scene()),
 129                         Filename).
 130
 131 % testing
 132 scene_test() ->
 133     io:format("testing the scene function", []),
 134     case scene() of
 135         [{camera,
 136           {vector, 0, 0, 0},
 137           {vector, 1, 0, 0},
 138           90,
 139           {screen, 1, 1}},
 140          {sphere,
 141           2,
 142           {vector, 5, 0, 0},
 143           {colour, 0, 128, 255}}] ->
 144             true;
 145 _Else ->
 146             false
 147     end.
 148
 149 failing_test() ->
 150     io:format("this test always fails", []),
 151     false.
 152
 153 passing_test() ->
 154     io:format("this test always passes", []),
 155     true.
 156
 157 run_tests() ->
 158     Tests = [fun scene_test/0,
 159              fun passing_test/0,
 160              fun vector_equality_test/0,
 161              fun vector_addition_test/0,
 162              fun vector_subtraction_test/0,
 163              fun vector_square_mag_test/0,
 164              fun vector_mag_test/0,
 165              fun vector_scalar_multiplication_test/0,
 166              fun vector_dot_product_test/0,
 167              fun vector_cross_product_test/0,
 168              fun vector_normalization_test/0,
 169              fun vector_negation_test/0,
 170              fun ray_through_pixel_test/0,
 171              fun ray_shooting_test/0,
 172              fun point_on_screen_test/0,
 173              fun nearest_object_intersecting_ray_test/0,
 174              fun focal_length_test/0
 175             ],
 176     run_tests(Tests, 1, true).
 177
 178 run_tests([], _Num, Success) ->
 179     case Success of
 180         true ->
 181             io:format("Success!~n", []),
 182             ok;
 183         _Else ->
 184             io:format("some tests failed~n", []),
 185             failed
 186     end;
 187
 188 run_tests([First_test|Rest_of_tests], Num, Success_so_far) ->
 189     io:format("test #~p: ", [Num]),
 190     Current_success = First_test(),
 191     case Current_success of
 192         true ->
 193             io:format(" - OK~n", []);
 194         _Else ->
 195             io:format(" - FAILED~n", [])
 196     end,
 197     run_tests(Rest_of_tests, Num + 1, Current_success and Success_so_far).
 198
 199 vector_equality_test() ->
 200     io:format("vector equality"),
 201     Vector1 = #vector{x=0, y=0, z=0},
 202     Vector2 = #vector{x=1234, y=-234, z=0},
 203
 204     vectors_equal(Vector1, Vector1)
 205         and vectors_equal(Vector2, Vector2)
 206         and not (vectors_equal(Vector1, Vector2))
 207         and not (vectors_equal(Vector2, Vector1)).
 208
 209
 210 vector_addition_test() ->
 211     io:format("vector addition", []),
 212     Vector0 = vector_add(
 213                 #vector{x=3, y=7, z=-3},
 214                 #vector{x=0, y=-24, z=123}),
 215     Subtest1 = (Vector0#vector.x == 3)
 216         and (Vector0#vector.y == -17)
 217         and (Vector0#vector.z == 120),
 218
 219     Vector1 = #vector{x=5, y=0, z=984},
 220     Vector2 = vector_add(Vector1, Vector1),
 221     Subtest2 = (Vector2#vector.x == Vector1#vector.x*2)
 222         and (Vector2#vector.y == Vector1#vector.y*2)
 223         and (Vector2#vector.z == Vector1#vector.z*2),
 224
 225     Vector3 = #vector{x=908, y=-098, z=234},
 226     Vector4 = vector_add(Vector3, #vector{x=0, y=0, z=0}),
 227     Subtest3 = vectors_equal(Vector3, Vector4),
 228
 229     Subtest1 and Subtest2 and Subtest3.
 230
 231 vector_subtraction_test() ->
 232     io:format("vector subtraction", []),
 233     Vector1 = #vector{x=0, y=0, z=0},
 234     Vector2 = #vector{x=8390, y=-2098, z=939},
 235     Vector3 = #vector{x=1, y=1, z=1},
 236     Vector4 = #vector{x=-1, y=-1, z=-1},
 237
 238     Subtest1 = vectors_equal(Vector1, vector_sub(Vector1, Vector1)),
 239     Subtest2 = vectors_equal(Vector3, vector_sub(Vector3, Vector1)),
 240     Subtest3 = not vectors_equal(Vector3, vector_sub(Vector1, Vector3)),
 241     Subtest4 = vectors_equal(Vector4, vector_sub(Vector4, Vector1)),
 242     Subtest5 = not vectors_equal(Vector4, vector_sub(Vector1, Vector4)),
 243     Subtest5 = vectors_equal(vector_add(Vector2, Vector4),
 244                              vector_sub(Vector2, Vector3)),
 245
 246     Subtest1 and Subtest2 and Subtest3 and Subtest4 and Subtest5.
 247
 248 vector_square_mag_test() ->
 249     io:format("vector square magnitude test", []),
 250     Vector1 = #vector{x=0, y=0, z=0},
 251     Vector2 = #vector{x=1, y=1, z=1},
 252     Vector3 = #vector{x=3, y=-4, z=0},
 253
 254     Subtest1 = (0 == vector_square_mag(Vector1)),
 255     Subtest2 = (3 == vector_square_mag(Vector2)),
 256     Subtest3 = (25 == vector_square_mag(Vector3)),
 257
 258     Subtest1 and Subtest2 and Subtest3.
 259
 260 vector_mag_test() ->
 261     io:format("vector magnitude test", []),
 262     Vector1 = #vector{x=0, y=0, z=0},
 263     Vector2 = #vector{x=1, y=1, z=1},
 264     Vector3 = #vector{x=3, y=-4, z=0},
 265
 266     Subtest1 = (0 == vector_mag(Vector1)),
 267     Subtest2 = (math:sqrt(3) == vector_mag(Vector2)),
 268     Subtest3 = (5 == vector_mag(Vector3)),
 269
 270     Subtest1 and Subtest2 and Subtest3.
 271
 272 vector_scalar_multiplication_test() ->
 273     io:format("scalar multiplication test", []),
 274     Vector1 = #vector{x=0, y=0, z=0},
 275     Vector2 = #vector{x=1, y=1, z=1},
 276     Vector3 = #vector{x=3, y=-4, z=0},
 277
 278     Subtest1 = vectors_equal(Vector1, vector_scalar_mult(Vector1, 45)),
 279     Subtest2 = vectors_equal(Vector1, vector_scalar_mult(Vector1, -13)),
 280     Subtest3 = vectors_equal(Vector1, vector_scalar_mult(Vector3, 0)),
 281     Subtest4 = vectors_equal(#vector{x=4, y=4, z=4},
 282                              vector_scalar_mult(Vector2, 4)),
 283     Subtest5 = vectors_equal(Vector3, vector_scalar_mult(Vector3, 1)),
 284     Subtest6 = not vectors_equal(Vector3, vector_scalar_mult(Vector3, -3)),
 285
 286     Subtest1 and Subtest2 and Subtest3 and Subtest4 and Subtest5 and Subtest6.
 287
 288 vector_dot_product_test() ->
 289     io:format("dot product test", []),
 290     Vector1 = #vector{x=1, y=3, z=-5},
 291     Vector2 = #vector{x=4, y=-2, z=-1},
 292     Vector3 = #vector{x=0, y=0, z=0},
 293     Vector4 = #vector{x=1, y=0, z=0},
 294     Vector5 = #vector{x=0, y=1, z=0},
 295
 296     Subtest1 = 3 == vector_dot_product(Vector1, Vector2),
 297     Subtest2 = vector_dot_product(Vector2, Vector2)
 298         == vector_square_mag(Vector2),
 299     Subtest3 = 0 == vector_dot_product(Vector3, Vector1),
 300     Subtest4 = 0 == vector_dot_product(Vector4, Vector5),
 301
 302     Subtest1 and Subtest2 and Subtest3 and Subtest4.
 303
 304 vector_cross_product_test() ->
 305     io:format("cross product test", []),
 306     Vector1 = #vector{x=0, y=0, z=0},
 307     Vector2 = #vector{x=1, y=0, z=0},
 308     Vector3 = #vector{x=0, y=1, z=0},
 309     Vector4 = #vector{x=0, y=0, z=1},
 310     Vector5 = #vector{x=1, y=2, z=3},
 311     Vector6 = #vector{x=4, y=5, z=6},
 312     Vector7 = #vector{x=-3, y=6, z=-3},
 313     Vector8 = #vector{x=-1, y=0, z=0},
 314     Vector9 = #vector{x=-9, y=8, z=433},
 315
 316     Subtest1 = vectors_equal(Vector1, vector_cross_product(Vector2, Vector2)),
 317     Subtest2 = vectors_equal(Vector1, vector_cross_product(Vector2, Vector8)),
 318     Subtest3 = vectors_equal(Vector2, vector_cross_product(Vector3, Vector4)),
 319     Subtest4 = vectors_equal(Vector7, vector_cross_product(Vector5, Vector6)),
 320     Subtest5 = vectors_equal(
 321                  vector_cross_product(Vector7,
 322                                       vector_add(Vector8, Vector9)),
 323                  vector_add(
 324                    vector_cross_product(Vector7, Vector8),
 325                    vector_cross_product(Vector7, Vector9))),
 326     Subtest6 = vectors_equal(Vector1,
 327                              vector_add(
 328                                vector_add(
 329                                  vector_cross_product(
 330                                    Vector7,
 331                                    vector_cross_product(Vector8, Vector9)),
 332                                  vector_cross_product(
 333                                    Vector8,
 334                                    vector_cross_product(Vector9, Vector7))),
 335                                vector_cross_product(
 336                                  Vector9,
 337                                  vector_cross_product(Vector7, Vector8)))),
 338
 339     Subtest1 and Subtest2 and Subtest3 and Subtest4 and Subtest5 and Subtest6.
 340
 341 vector_normalization_test() ->
 342     io:format("normalization test", []),
 343     Vector1 = #vector{x=0, y=0, z=0},
 344     Vector2 = #vector{x=1, y=0, z=0},
 345     Vector3 = #vector{x=5, y=0, z=0},
 346
 347     Subtest1 = vectors_equal(Vector1, vector_normalize(Vector1)),
 348     Subtest2 = vectors_equal(Vector2, vector_normalize(Vector2)),
 349     Subtest3 = vectors_equal(Vector2, vector_normalize(Vector3)),
 350     Subtest4 = vectors_equal(Vector2, vector_normalize(
 351                                         vector_scalar_mult(Vector2, 324))),
 352
 353     Subtest1 and Subtest2 and Subtest3 and Subtest4.
 354
 355 vector_negation_test() ->
 356     io:format("vector negation test", []),
 357     Vector1 = #vector{x=0, y=0, z=0},
 358     Vector2 = #vector{x=4, y=-5, z=6},
 359
 360     Subtest1 = vectors_equal(Vector1, vector_neg(Vector1)),
 361     Subtest2 = vectors_equal(Vector2, vector_neg(vector_neg(Vector2))),
 362
 363     Subtest1 and Subtest2.
 364
 365 ray_through_pixel_test() ->
 366     io:format("ray through pixel test", []),
 367     false.
 368
 369 ray_shooting_test() ->
 370     io:format("ray shooting test", []),
 371     false.
 372
 373 point_on_screen_test() ->
 374     io:format("point on screen test", []),
 375     Camera1 = #camera{location=#vector{x=0, y=0, z=0},
 376                       rotation=#vector{x=0, y=0, z=0},
 377                       fov=90,
 378                       screen=#screen{width=1, height=1}},
 379     false.
 380
 381 nearest_object_intersecting_ray_test() ->
 382     io:format("nearest object intersecting ray test", []),
 383     false.
 384
 385 focal_length_test() ->
 386     Epsilon = 0.1,
 387     Size = 36,
 388     io:format("focal length test", []),
 389     lists:foldl(
 390       fun({Focal_length, Dimension}, Matches) ->
 391               Result = focal_length(Dimension, Size),
 392               %io:format("comparing ~w ~w ~w ~w~n", [Focal_length, Dimension, Result, Matches]),
 393      Matches
 394                   and ((Focal_length + Epsilon >= focal_length(
 395                                                     Dimension, Size))
 396                        and (Focal_length - Epsilon =< focal_length(
 397                                                        Dimension, Size)))
 398       end, true,
 399       [{13, 108}, {15, 100.4}, {18, 90}, {21, 81.2}]).