diff options
| -rw-r--r-- | chickadee/math/matrix.scm | 47 | ||||
| -rw-r--r-- | doc/api.texi | 9 |
2 files changed, 56 insertions, 0 deletions
diff --git a/chickadee/math/matrix.scm b/chickadee/math/matrix.scm index b79c94d..a075176 100644 --- a/chickadee/math/matrix.scm +++ b/chickadee/math/matrix.scm @@ -42,6 +42,8 @@ matrix3-rotate matrix3-transform! matrix3-transform + matrix3-inverse! + matrix3-inverse make-matrix4 make-null-matrix4 make-identity-matrix4 @@ -289,6 +291,51 @@ column-major format." (matrix3-transform! matrix new-v) new-v)) +;; I honestly found this wikihow page very helpful in explaining the +;; process of inverting a 3x3 matrix: +;; +;; https://www.wikihow.com/Find-the-Inverse-of-a-3x3-Matrix +(define (matrix3-inverse! matrix target) + (let* ((bv (matrix3-bv matrix)) + (a (matrix3-ref bv 0 0)) + (b (matrix3-ref bv 0 1)) + (c (matrix3-ref bv 0 2)) + (d (matrix3-ref bv 1 0)) + (e (matrix3-ref bv 1 1)) + (f (matrix3-ref bv 1 2)) + (g (matrix3-ref bv 2 0)) + (h (matrix3-ref bv 2 1)) + (i (matrix3-ref bv 2 2)) + ;; Calculate the determinants of the minor matrices of the + ;; inverse of the original matrix. + (a* (- (* e i) (* f h))) + (b* (- (* b i) (* c h))) + (c* (- (* b f) (* c e))) + (d* (- (* d i) (* f g))) + (e* (- (* a i) (* c g))) + (f* (- (* a f) (* c d))) + (g* (- (* d h) (* e g))) + (h* (- (* a h) (* b g))) + (i* (- (* a e) (* b d))) + ;; Determinant and its inverse. + (det (+ (- (* a a*) (* b d*)) (* c g*))) + (invdet (/ 1.0 det))) + ;; If the matrix cannot be inverted (determinant of 0), then just + ;; bail out by resetting target to the identity matrix. + (if (= det 0.0) + (matrix3-identity! target) + ;; Multiply by the inverse of the determinant to get the final + ;; inverse matrix. Every other value is inverted. + (init-matrix3 target + (* a* invdet) (* (- b*) invdet) (* c* invdet) + (* (- d*) invdet) (* e* invdet) (* (- f*) invdet) + (* g* invdet) (* (- h*) invdet) (* i* invdet))))) + +(define (matrix3-inverse matrix) + (let ((new (make-null-matrix3))) + (matrix3-inverse! matrix new) + new)) + ;;; ;;; 4x4 Matrix diff --git a/doc/api.texi b/doc/api.texi index f6333d6..0a15586 100644 --- a/doc/api.texi +++ b/doc/api.texi @@ -1093,6 +1093,10 @@ Return a new 2D vector that is @var{v} as transformed by the 3x3 matrix @var{matrix}. @end deffn +@deffn {Procedure} matrix3-inverse matrix +Return the inverse of @var{matrix}. +@end deffn + The following procedures perform in-place, destructive updates to 3x3 matrix objects: @@ -1125,6 +1129,11 @@ Modify the 2D vector @var{v} in-place to contain @var{v} as transformed by the 3x3 matrix @var{matrix}. @end deffn +@deffn {Procedure} matrix3-inverse! matrix target +Compute the inverse of @var{matrix} and store the results in +@var{target}. +@end deffn + @subsubsection 4x4 Matrices @deffn {Procedure} make-matrix4 aa ab ac ad @ |