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