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;;; Sly
;;; Copyright (C) 2013, 2014 David Thompson <dthompson2@worcester.edu>
;;; Copyright (C) 2014 Jordan Russell <jordan.likes.curry@gmail.com>
;;;
;;; This program is free software: you can redistribute it and/or
;;; modify it under the terms of the GNU General Public License as
;;; published by the Free Software Foundation, either version 3 of the
;;; License, or (at your option) any later version.
;;;
;;; This program is distributed in the hope that it will be useful,
;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
;;; General Public License for more details.
;;;
;;; You should have received a copy of the GNU General Public License
;;; along with this program. If not, see
;;; <http://www.gnu.org/licenses/>.
;;; Commentary:
;;
;; Miscellaneous math procedures. Currently just trigonometry.
;;
;;; Code:
(define-module (sly math)
#:export (pi 2pi pi/2
degrees->radians
radians->degrees
sin-degrees
cos-degrees
tan-degrees
atan-degrees
cotan
clamp
linear-scale
half square
make-lerp lerp
modulo*))
;; Dave was editing this module on Pi Approximation Day.
;;
;; 3.141592653589793238462643383279
;; 5028841971693993751058209749445923
;; 07816406286208998628034825342117067
;; 9821 48086 5132
;; 823 06647 09384
;; 46 09550 58223
;; 17 25359 4081
;; 2848 1117
;; 4502 8410
;; 2701 9385
;; 21105 55964
;; 46229 48954
;; 9303 81964
;; 4288 10975
;; 66593 34461
;; 284756 48233
;; 78678 31652 71
;; 2019091 456485 66
;; 9234603 48610454326648
;; 2133936 0726024914127
;; 3724587 00660631558
;; 817488 152092096
;;
(define pi 3.141592654)
(define 2pi (* pi 2))
(define pi/2 (/ pi 2))
(define (degrees->radians angle)
"Convert ANGLE in degrees to radians."
(* angle (/ pi 180)))
(define (radians->degrees angle)
"Convert ANGLE in radians to degrees."
(* angle (/ 180 pi)))
(define (sin-degrees angle)
"Compute the sin of ANGLE expressed in degrees."
(sin (degrees->radians angle)))
(define (cos-degrees angle)
"Compute the cosine of ANGLE expressed in degrees."
(cos (degrees->radians angle)))
(define (tan-degrees angle)
"Compute the tangent of ANGLE expressed in degrees."
(tan (degrees->radians angle)))
(define (atan-degrees y x)
"Compute the arctangent in degrees of the coordinates Y and X."
(radians->degrees (atan y x)))
(define (cotan z)
"Return the cotangent of Z."
(/ 1 (tan z)))
(define (clamp min max x)
"Restrict X to the range defined by MIN and MAX. Assumes that MIN is
actually less than MAX."
(cond ((< x min) min)
((> x max) max)
(else x)))
(define (linear-scale min max a b n)
"Map a number N in the range [MIN,MAX] to the range [A,B]."
(+ a
(/ (* (- b a) (- n min))
(- max min))))
(define (half x)
(/ x 2))
(define (square x)
(* x x))
(define (make-lerp + *)
"Return a new procedure that accepts three arguments: START, END,
and ALPHA. The returned procedure uses the procedures + and * to
linearly interpolate a value between START and END. ALPHA should
always be in the range [0, 1]."
(lambda (start end alpha)
(+ (* start (- 1 alpha))
(* end alpha))))
(define lerp (make-lerp + *))
(define (modulo* x y)
"Return the remainder of X / Y. X and Y may be exact integers,
rational numbers, or inexact numbers."
(- x (* (floor (/ x y)) y)))
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