matrix.lisp

   1
   2 (in-package :cl-tuples)
   3
   4 (def-tuple-type matrix22
   5         :tuple-element-type fast-float
   6         :initial-element 0.0f0
   7         :elements (e00 e01
   8                    e10 e11))
   9
  10 (export-tuple-operations matrix22)
  11
  12 (def-tuple-type matrix33
  13         :tuple-element-type fast-float
  14         :initial-element 0.0f0
  15         :elements (e00 e01 e02
  16                                    e10 e11 e12
  17                                    e20 e21 e22))
  18
  19 (export-tuple-operations matrix33)
  20
  21 (def-tuple-type matrix44
  22         :tuple-element-type fast-float
  23         :initial-element 0.0f0
  24         :elements (e00 e01 e02 e03
  25                                    e10 e11 e12 e13
  26                                    e20 e21 e22 e23
  27                                    e30 e31 e32 e33))
  28
  29 (export-tuple-operations matrix44)
  30
  31 (def-tuple-op matrix33-equal*
  32     ((k matrix33 (k00 k01 k02
  33                   k10 k11 k12
  34                   k20 k21 k22))
  35      (m matrix33 (m00 m01 m02
  36                   m10 m11 m12
  37                   m20 m21 m22)))
  38   (:return boolean
  39            (and
  40             (= k00 m00) (= k01 m01) (= k02 m02)
  41             (= k10 m10) (= k11 m11) (= k12 m12)
  42             (= k20 m20) (= k21 m21) (= k22 m22))))
  43
  44 (def-tuple-op matrix44-equal*
  45     ((k matrix44 (k00 k01 k02 k03
  46                   k10 k11 k12 k13
  47                   k20 k21 k22 k23
  48                   k30 k31 k32 k33))
  49      (m matrix44 (m00 m01 m02 m03
  50                   m10 m11 m12 m13
  51                   m20 m21 m22 m23
  52                   m30 m31 m32 m33)))
  53   (:return boolean
  54            (and
  55             (= k00 m00) (= k01 m01) (= k02 m02) (= k03 m03)
  56             (= k10 m10) (= k11 m11) (= k12 m12) (= k13 m13)
  57             (= k20 m20) (= k21 m21) (= k22 m22) (= k23 m23)
  58             (= k30 m30) (= k31 m31) (= k32 m32) (= k33 m33))))
  59
  60 ;; TODO: this probably needs to check the TRACE as well, since otherwise
  61 ;; it might crash in other functions (e.g. MATRIX33-ANGLE-AXIS*)
  62 (def-tuple-op check-rotation-matrix33*
  63     ((m matrix33 :default))
  64   (:return boolean (matrix33-equal*
  65                     (identity-matrix33*)
  66                     (matrix33-product*
  67                      m (transpose-matrix33* m)))))
  68
  69 ;; TODO: maybe check also whether it is purely a rotation?
  70 (def-tuple-op check-rotation-matrix44*
  71     ((m matrix44 :default))
  72   (:return boolean (check-rotation-matrix33* (matrix44-matrix33* m))))
  73
  74 (def-tuple-op transpose-matrix22*
  75     ((mat22 matrix22
  76                                  (e00 e01
  77                                           e10 e11)))
  78         "Return the transpose of the matrix"
  79         (:return matrix22
  80                          (matrix22-values*
  81                           e00 e10
  82                           e01 e11)))
  83
  84 (defmacro matrix-dot (dimension row col)
  85   "Generate the symbols required for a dot product between the row and column of a matrix, assuming accessor symbol is e<row><col>"
  86   (labels
  87           ((make-matrix-element-symbol (mat row col)
  88                  (intern (string-upcase (format nil "e~A~A~A" mat row col)) :cl-tuples)))
  89         (let
  90                 ((col-sym-names
  91                   (loop for row from 0 below dimension
  92                          collect (make-matrix-element-symbol 0 row col)))
  93                  (row-sym-names
  94                   (loop for col from 0 below dimension
  95                          collect (make-matrix-element-symbol 1 row col))))
  96           `(+
  97                 ,@(loop
  98                          for col-sym in col-sym-names
  99                          for row-sym in row-sym-names
 100                          collect `(* ,col-sym ,row-sym))))))
 101
 102
 103 (def-tuple-op transform-vertex2d*
 104         ((mat matrix33 (e00 e01 e02 e10 e11 e12 e20 e21 e22))
 105          (vert vector2d (x y w)))
 106   (:return vertex2d
 107                    (vertex2d-values*
 108                         (+ (* x e00) (* y e01) (* w e02))
 109                         (+ (* x e10) (* y e11) (* w e12))
 110                         (+ (* x e20) (* y e21) (* w e22)))))
 111
 112
 113 (def-tuple-op transform-vector2d*
 114         ((mat matrix33 (e00 e01 e02 e10 e11 e12 e20 e21 e22))
 115          (vec vector2d (x y)))
 116   (:return vector2d
 117                    (vector2d-values*
 118                         (+ (* x e00) (* y e01))
 119                         (+ (* x e10) (* y e11)))))
 120
 121
 122 (def-tuple-op matrix33-product*
 123         ((m0 matrix33 (e000 e001 e002 e010 e011 e012 e020 e021 e022))
 124          (m1 matrix33 (e100 e101 e102 e110 e111 e112 e120 e121 e122)))
 125   (:return matrix33
 126                    (matrix33-values*
 127                         (matrix-dot 3 0 0)
 128                         (matrix-dot 3 0 1)
 129                         (matrix-dot 3 0 2)
 130
 131                         (matrix-dot 3 1 0)
 132                         (matrix-dot 3 1 1)
 133                         (matrix-dot 3 1 2)
 134
 135                         (matrix-dot 3 2 0)
 136                         (matrix-dot 3 2 1)
 137                         (matrix-dot 3 2 2))))
 138
 139
 140 (def-tuple-op transform-vertex3d*
 141         ((mat matrix44
 142                   (e00 e01 e02 e03
 143                            e10 e11 e12 e13
 144                            e20 e21 e22 e23
 145                            e30 e31 e32 e33))
 146          (vert vertex3d (x y z w)))
 147   (:return vertex3d
 148                    (vertex3d-values*
 149                         (+ (* x e00) (* y e01) (* z e02) (* w e03))
 150                         (+ (* x e10) (* y e11) (* z e12) (* w e13))
 151                         (+ (* x e20) (* y e21) (* z e22) (* w e23))
 152                         (+ (* x e30) (* y e31) (* z e32) (* w e33)))))
 153
 154 (def-tuple-op transform-vector3d*
 155         ((mat matrix33
 156                   (e00 e01 e02
 157                            e10 e11 e12
 158                            e20 e21 e22))
 159          (vect vector3d (x y z)))
 160   (:return vector3d
 161                    (vector3d-values*
 162                         (+ (* x e00) (* y e01) (* z e02) )
 163                         (+ (* x e10) (* y e11) (* z e12) )
 164                         (+ (* x e20) (* y e21) (* z e12) ))))
 165
 166 (def-tuple-op transpose-matrix33*
 167     ((mat33 matrix33 (e00 e01 e02 e10 e11 e12 e20 e21 e22)))
 168         "Return the transpose of the matrix"
 169         (:return matrix33
 170                          (matrix33-values*
 171                           e00 e10 e20
 172                           e01 e11 e21
 173                           e02 e12 e22)))
 174
 175 (def-tuple-op print-matrix33*
 176         ((mat matrix44 (e00 e01 e02 e03
 177                                                 e10 e11 e12 e13
 178                                                 e20 e21 e22 e23
 179                                                 e30 e31 e32 e33)))
 180   "Print a 3x3 matrix in a useful format."
 181   (:return (values)
 182                    (format t "~A ~A ~A ~A ~%" e00 e01 e02)
 183                    (format t "~A ~A ~A ~A ~%" e10 e11 e12)
 184                    (format t "~A ~A ~A ~A ~%" e20 e21 e22)))
 185
 186 (def-tuple-op matrix44-product*
 187         ((m0 matrix44 (e000 e001 e002 e003 e010 e011 e012 e013  e020 e021 e022 e023  e030 e031 e032 e033))
 188          (m1 matrix44 (e100 e101 e102 e103 e110 e111 e112 e113  e120 e121 e122 e123  e130 e131 e132 e133)))
 189   (:return matrix44
 190                    (matrix44-values*
 191                         (matrix-dot 4 0 0)
 192                         (matrix-dot 4 0 1)
 193                         (matrix-dot 4 0 2)
 194                         (matrix-dot 4 0 3)
 195
 196                         (matrix-dot 4 1 0)
 197                         (matrix-dot 4 1 1)
 198                         (matrix-dot 4 1 2)
 199                         (matrix-dot 4 1 3)
 200
 201                         (matrix-dot 4 2 0)
 202                         (matrix-dot 4 2 1)
 203                         (matrix-dot 4 2 2)
 204                         (matrix-dot 4 2 3)
 205
 206                         (matrix-dot 4 3 0)
 207                         (matrix-dot 4 3 1)
 208                         (matrix-dot 4 3 2)
 209                         (matrix-dot 4 3 3))))
 210
 211 (def-tuple-op identity-matrix22*
 212     ()
 213   (:return matrix22
 214            (matrix22-key-values
 215             e00 1.0
 216             e11 1.0)))
 217
 218 (def-tuple-op identity-matrix33*
 219     ()
 220   (:return matrix33
 221            (matrix33-key-values
 222             e00 1.0
 223             e11 1.0
 224             e22 1.0)))
 225
 226 (def-tuple-op identity-matrix44*
 227     ()
 228   (:return matrix44
 229            (matrix44-key-values
 230             e00 1.0
 231             e11 1.0
 232             e22 1.0
 233             e33 1.0)))
 234
 235 (def-tuple-op translation-matrix44*
 236         ((tx fast-float)
 237          (ty fast-float)
 238          (tz fast-float))
 239   "Return a matrix that represents a translation transformation"
 240   (:return matrix44
 241                    (matrix44-values*
 242                         1.0f0 0.0f0 0.0f0 tx
 243                         0.0f0 1.0f0 0.0f0 ty
 244                         0.0f0 0.0f0 1.0f0 tz
 245                         0.0f0 0.0f0 0.0f0 1.0f0)))
 246
 247 (def-tuple-op scaling-matrix44*
 248     ((sx #1=fast-float)
 249      (sy #1#)
 250      (sz #1#))
 251   (:return matrix44
 252            (matrix44-key-values
 253             e00 sx
 254             e11 sy
 255             e22 sz
 256             e33 1.0)))
 257
 258 (def-tuple-op vertex3d-translation-matrix44*
 259         ((vert vertex3d (tx ty tz tw)))
 260   "Return a matrix that represents a translation transformation"
 261   (:return matrix44
 262                    (matrix44-values*
 263                         1.0f0 0.0f0 0.0f0 tx
 264                         0.0f0 1.0f0 0.0f0 ty
 265                         0.0f0 0.0f0 1.0f0 tz
 266                         0.0f0 0.0f0 0.0f0 1.0f0)))
 267
 268 (def-tuple-op rotatex-matrix33*
 269     ((rotation fast-float))
 270   "Return a matrix for rotating around the x axis."
 271   (:return matrix33
 272            (let* ((sin (sin rotation))
 273                   (-sin (- sin))
 274                   (cos (cos rotation)))
 275              (matrix33-values*
 276               1.0 0.0 0.0
 277               0.0 cos -sin
 278               0.0 sin cos))))
 279
 280 (def-tuple-op rotatex-matrix44*
 281     ((rotation fast-float))
 282   "Return a matrix for rotating around the x axis."
 283   (:return matrix44
 284            (matrix33-matrix44*
 285             (rotatex-matrix33* rotation))))
 286
 287
 288 (def-tuple-op rotatey-matrix33*
 289     ((rotation fast-float))
 290   "Return a matrix for rotating around the y axis."
 291   (:return matrix33
 292            (let* ((sin (sin rotation))
 293                   (-sin (- sin))
 294                   (cos (cos rotation)))
 295              (matrix33-values*
 296               cos  0.0 sin
 297               0.0  1.0 0.0
 298               -sin 0.0 cos))))
 299
 300
 301 (def-tuple-op rotatey-matrix44*
 302     ((rotation fast-float))
 303   "Return a matrix for rotating around the y axis."
 304   (:return matrix44
 305            (matrix33-matrix44*
 306             (rotatey-matrix33* rotation))))
 307
 308 (def-tuple-op rotatez-matrix33*
 309     ((rotation fast-float))
 310   "Return a matrix for rotating around the z axis."
 311   (:return matrix33
 312            (let* ((sin (sin rotation))
 313                   (-sin (- sin))
 314                   (cos (cos rotation)))
 315              (matrix33-values*
 316               cos -sin 0.0
 317               sin cos  0.0
 318               0.0 0.0  1.0))))
 319
 320
 321 (def-tuple-op rotatez-matrix44*
 322     ((rotation fast-float))
 323   "Return a matrix for rotating around the z axis."
 324   (:return matrix44
 325            (matrix33-matrix44*
 326             (rotatez-matrix33* rotation))))
 327
 328 (def-tuple-op transpose-matrix44*
 329         ((mat44 matrix44
 330                         (e00 e01 e02 e03
 331                                  e10 e11 e12 e13
 332                                  e20 e21 e22 e23
 333                                  e30 e31 e32 e33)))
 334   "Return the transpose of the matrix"
 335   (:return matrix44
 336                    (matrix44-values*
 337                         e00 e10 e20 e30
 338                         e01 e11 e21 e31
 339                         e02 e12 e22 e32
 340                         e03 e13 e23 e33)))
 341
 342 (def-tuple-op make-test-matrix44*
 343         ()
 344   "Return a matrix for testing purposes"
 345   (:return matrix44
 346                    (matrix44-values*
 347                         1.0f0  2.0f0  3.0f0  4.0f0
 348                         5.0f0  6.0f0  7.0f0  8.0f0
 349                         9.0f0  10.0f0 11.0f0 12.0f0
 350                         13.0f0 14.0f0 15.0f0 16.0f0)))
 351
 352
 353 (def-tuple-op print-matrix44*
 354         ((mat matrix44 (e00 e01 e02 e03
 355                                                 e10 e11 e12 e13
 356                                                 e20 e21 e22 e23
 357                                                 e30 e31 e32 e33)))
 358   "Print a matrix in a useful format."
 359   (:return (values)
 360                    (format t "~A ~A ~A ~A ~%" e00 e01 e02 e03)
 361                    (format t "~A ~A ~A ~A ~%" e10 e11 e12 e13)
 362                    (format t "~A ~A ~A ~A ~%" e20 e21 e22 e23)
 363                    (format t "~A ~A ~A ~A ~%" e30 e31 e32 e33)))
 364
 365
 366 (def-tuple-op matrix44-matrix33*
 367         ((mat44 matrix44
 368                         (e00 e01 e02 e03
 369                                  e10 e11 e12 e13
 370                                  e20 e21 e22 e23
 371                                  e30 e31 e32 e33)))
 372   "Convert a 4x4 matrix to a 3x3 matrix"
 373   (:return matrix33
 374                    (matrix33-values* e00 e01 e02 e10 e11 e12 e20 e21 e22)))
 375
 376 (def-tuple-op matrix33-matrix44*
 377         ((mat3 matrix33
 378                    (e00 e01 e02
 379                                 e10 e11 e12
 380                                 e20 e21 e22)))
 381   "Convert a 3x3 matrix to a 4x4 matrix"
 382   (:return matrix44
 383                    (matrix44-values* e00 e01 e02 0.0f0
 384                                           e10 e11 e12 0.0f0
 385                                           e20 e21 e22 0.0f0
 386                                           0.0f0 0.0f0 0.0f0 1.0f0)))
 387
 388 (def-tuple-op vector3d-matrix3d*
 389         ((zvec vector3d (zx zy zz))
 390          (yvec vector3d (yx yy yz)))
 391   "Construct a rotation matrix from 2 vectors"
 392   (:return matrix33
 393                    (with-vector3d
 394                            (vector3d-cross
 395                                 zvec yvec)
 396                            (xx xy xz)
 397                          (matrix33*
 398                           (xx yx zx
 399                                   xy yy zy
 400                                   xz yz zz)))))
 401
 402
 403 (def-tuple-op matrix22-determinant*
 404     ((mat matrix22 #.(tuple-elements 'matrix22)))
 405   (:return fast-float
 406            (- (* e00 e11)
 407               (* e01 e10))))
 408
 409 (def-tuple-op matrix33-determinant*
 410     ((mat matrix33 #.(tuple-elements 'matrix33)))
 411   (:return fast-float
 412            (- (+ (* e00 e11 e22)
 413                  (* e01 e12 e20)
 414                  (* e02 e10 e21))
 415               (* e02 e11 e20)
 416               (* e01 e10 e22)
 417               (* e00 e12 e21))))
 418
 419 (def-tuple-op matrix44-determinant*
 420     ((mat matrix44 #.(tuple-elements 'matrix44)))
 421   (:return fast-float
 422            (let ((t0 (* e00 e22))
 423                  (t1 (* e11 e33))
 424                  (t2 (* e01 e23))
 425                  (t3 (* e12 e30))
 426                  (t4 (* e03 e21))
 427                  (t5 (* e10 e32))
 428                  (t6 (* e13 e31))
 429                  (t7 (* e02 e20)))
 430              (- (+ (* t0 t1)
 431                    (* t2 t3)
 432                    (* t7 t6)
 433                    (* t4 t5))
 434                 (* t3 t4)
 435                 (* t7 t1)
 436                 (* t2 t5)
 437                 (* t0 t6)))))
 438
 439 (def-tuple-op matrix22-scale*
 440     ((x fast-float)
 441      (mat matrix22 #1=#.(tuple-elements 'matrix22)))
 442   (:return matrix22 (multiply-arguments matrix22-values* x #1#)))
 443
 444 (def-tuple-op matrix33-scale*
 445     ((x fast-float)
 446      (mat matrix33 #1=#.(tuple-elements 'matrix33)))
 447   (:return matrix33 (multiply-arguments matrix33-values* x #1#)))
 448
 449 (def-tuple-op matrix44-scale*
 450     ((x fast-float)
 451      (mat matrix44 #1=#.(tuple-elements 'matrix44)))
 452   (:return matrix44 (multiply-arguments matrix44-values* x #1#)))
 453
 454 (def-tuple-op cofactor-matrix22*
 455     ((mat matrix22 #.(tuple-elements 'matrix22)))
 456   (:return matrix22
 457            (matrix22-values*
 458             e11 e10
 459             e01 e00)))
 460
 461 (def-tuple-op cofactor-matrix33*
 462     ((mat matrix33 #.(tuple-elements 'matrix33)))
 463   (:return matrix33
 464            (macrolet ((cofactors ()
 465                         `(matrix33-values*
 466                           ,@(matrix-cofactors 3))))
 467              (cofactors))))
 468
 469 (def-tuple-op cofactor-matrix44*
 470     ((mat matrix44 #.(tuple-elements 'matrix44)))
 471   (:return matrix44
 472            (macrolet ((cofactors ()
 473                         `(matrix44-values*
 474                           ,@(matrix-cofactors 4))))
 475              (cofactors))))
 476
 477 (def-tuple-op inverted-matrix22*
 478     ((mat matrix22 #.(tuple-elements 'matrix22)))
 479   (:return matrix22
 480            (matrix22-scale*
 481             (matrix22-determinant* mat)
 482             (transpose-matrix22*
 483              (cofactor-matrix22* mat)))))
 484
 485 (def-tuple-op inverted-matrix33*
 486     ((mat matrix33 #.(tuple-elements 'matrix33)))
 487   (:return matrix33
 488            (matrix33-scale*
 489             (matrix33-determinant* mat)
 490             (transpose-matrix33*
 491              (cofactor-matrix33* mat)))))
 492
 493 (def-tuple-op inverted-matrix44*
 494     ((mat matrix44 #.(tuple-elements 'matrix44)))
 495   (:return matrix44
 496            (matrix44-scale*
 497             (matrix44-determinant* mat)
 498             (transpose-matrix44*
 499              (cofactor-matrix44* mat)))))