| 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667 |
- ;;;; solve-triangle.lisp
- (defpackage #:solve-triangle
- (:use :cl)
- (:export #:solve-asa
- #:solve-ssa))
- (in-package #:solve-triangle)
- ;; SAA, ASA -- Law of Sines
- ;; SSA -- Law of Sines, (or 0 1 2) solutions
- ;; SAS -- Law of Cosines
- ;; SSS -- Law of Cosines
- (defun between-p (lower number upper)
- (and (>= number lower)
- (<= number upper)))
- (defun solve-asa (anglea sidea angleb)
- "Solve a ASA triangle using the method of sines. Angles assumed to be in radians."
- (let* ((anglec (- pi anglea angleb))
- (sideb (/ (* (sin angleb)
- sidea)
- (sin anglea)))
- (sidec (/ (* (sin anglec)
- sidea)
- (sin anglea))))
- (list :angle-a anglea
- :angle-b angleb
- :angle-c anglec
- :side-a sidea
- :side-b sideb
- :side-c sidec)))
- (defun solve-ssa (sidea sideb anglea)
- "Solve an SSA triangle using the method of sines. Angles are assumed to be in degrees."
- (let ((sinb (/ (* sideb (sin anglea))
- sidea)))
- (if (between-p -1 sinb 1)
- (let* ((angleb (asin sinb))
- (anglec (- pi anglea angleb))
- (sidec (asin (/ (* (sin anglec) sidea)
- (sin anglea)))))
- (if (< (+ anglea angleb) pi)
- (let* ((angleb-prime (- pi angleb))
- (anglec-prime (- pi anglea angleb-prime))
- (sidec-prime (/ (* (sin anglec-prime) sidea)
- (sin anglea))))
- (values (list :angle-a anglea
- :angle-b angleb
- :angle-c anglec
- :side-a sidea
- :side-b sideb
- :sidec sidec)
- (list :angle-a anglea
- :angle-b angleb-prime
- :angle-c anglec-prime
- :sidea sidea
- :sideb sideb
- :sidec sidec-prime)))
- (values (list :angle-a anglea
- :angle-b angleb
- :angle-c anglec
- :side-a sidea
- :side-b sideb
- :sidec sidec)
- nil)))
- (values nil nil))))
|
