>From 6529e0bc83f0a31b32fd320be50658a423a83e5c Mon Sep 17 00:00:00 2001
From: AwesomeAdam54321 <[email protected]>
Date: Sun, 16 Feb 2025 12:47:18 +0800
Subject: [PATCH v1] src: (math trigonometry): Add it.
* src/math/trigonometry.scm: New file.
* doc/guile-library.scm: Document it in the manual.
* unit-tests/math.trigonometry.scm: New unit test.
* src/Makefile.am: Register module.
* unit-tests/Makefile.am: Register unit test.
---
doc/guile-library.scm | 2 +
src/Makefile.am | 1 +
src/math/trigonometry.scm | 146 +++++++++++++++++++++++++++++++
unit-tests/Makefile.am | 1 +
unit-tests/math.trigonometry.scm | 61 +++++++++++++
5 files changed, 211 insertions(+)
create mode 100644 src/math/trigonometry.scm
create mode 100644 unit-tests/math.trigonometry.scm
diff --git a/doc/guile-library.scm b/doc/guile-library.scm
index 496c283..d9593b7 100644
--- a/doc/guile-library.scm
+++ b/doc/guile-library.scm
@@ -102,6 +102,8 @@ License\".")
"A golden-section minimum finder")
((math primes)
"Functions related to prime numbers and factorization")
+ ((math trigonometry)
+ "Functions related to motion trigonometry")
((os process)
"Spawning processes and capturing their output")
((scheme documentation)
diff --git a/src/Makefile.am b/src/Makefile.am
index 889a575..507bbab 100644
--- a/src/Makefile.am
+++ b/src/Makefile.am
@@ -86,6 +86,7 @@ SOURCES = \
logging/rotating-log.scm \
math/minima.scm \
math/primes.scm \
+ math/trigonometry.scm \
match-bind.scm \
md5.scm \
os/process.scm \
diff --git a/src/math/trigonometry.scm b/src/math/trigonometry.scm
new file mode 100644
index 0000000..57804a6
--- /dev/null
+++ b/src/math/trigonometry.scm
@@ -0,0 +1,146 @@
+;; (math trigonometry) -- More exact trigonometry for motion
+;; Copyright (C) 2025 Adam Faiz <[email protected]>
+
+;; 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:
+;;
+;; @cindex normalise angle
+;; @cindex sine
+;; @cindex cosine
+;; @cindex tangent
+;; @cindex arcsine
+;; @cindex arccosine
+;; @cindex arctan
+;; @cindex arctan2
+;; @cindex angle, normalised
+;; @cindex angle, sine of
+;; @cindex angle, cosine of
+;; @cindex angle, tangent of
+;; @cindex sine, inverse of
+;; @cindex cosine, inverse of
+;; @cindex tangent, inverse of
+;; This module defines trigonometry functions for an angle(given in degrees),
+;; as more flexible versions of the trigonometry functions in Guile.
+;; They return exact values for the special angles, regardless of whether
+;; they're negative or how many rotations occurred.
+;; To maintain precision, these functions take their input in degrees.
+;;
+;;; Code:
+
+(define-module (math trigonometry)
+ #:use-module (scheme documentation)
+ #:export (pi
+ deg->rad
+ rad->deg
+ normalise-angle
+ sine
+ cosine
+ tangent
+ arcsine
+ arccosine
+ arctan
+ arctan2))
+
+(define pi (* 2 (acos 0)))
+
+(define (deg->rad degrees)
+ "Convert an angle in degrees to radians."
+ (* degrees (/ pi 180)))
+
+(define (rad->deg radians)
+ "Convert an angle in radians to degrees."
+ (* radians (/ 180 pi)))
+
+(define (normalise-angle angle)
+ "Return a normalised angle where 0 <= angle < 360."
+ (floor-remainder angle 360))
+
+(define (sine degrees)
+ "Calculate the sine of an angle."
+ (define angle (normalise-angle degrees))
+ (cond ((or (= angle 0) (= angle 180)) 0)
+ ((or (= angle 30) (= angle 150)) 1/2)
+ ((or (= angle 45) (= angle 135)) (/ (sqrt 2) 2))
+ ((or (= angle 60) (= angle 120)) (/ (sqrt 3) 2))
+ ((= angle 90) 1)
+ ((or (= angle 210) (= angle 330)) -1/2)
+ ((or (= angle 225) (= angle 315)) (- (/ (sqrt 2) 2)))
+ ((or (= angle 240) (= angle 300)) (- (/ (sqrt 3) 2)))
+ ((= angle 270) -1)
+ (else (sin (deg->rad angle)))))
+
+(define (cosine degrees)
+ "Calculate the cosine of an angle."
+ (define angle (normalise-angle degrees))
+ (cond ((= angle 0) 1)
+ ((or (= angle 30) (= angle 330)) (/ (sqrt 3) 2))
+ ((or (= angle 45) (= angle 315)) (/ (sqrt 2) 2))
+ ((or (= angle 60) (= angle 300)) 1/2)
+ ((or (= angle 90) (= angle 270)) 0)
+ ((or (= angle 120) (= angle 240)) -1/2)
+ ((or (= angle 135) (= angle 225)) (- (/ (sqrt 2) 2)))
+ ((or (= angle 150) (= angle 210)) (- (/ (sqrt 3) 2)))
+ ((= angle 180) -1)
+ (else (cos (deg->rad angle)))))
+
+(define (tangent angle)
+ "Calculate the tangent of an angle."
+ (/ (sine angle) (cosine angle)))
+
+(define (arcsine value)
+ "Calculate the smallest angle from the given sine value."
+ (cond ((= value 0) 0)
+ ((= value 1/2) 30)
+ ((= value (/ (sqrt 2) 2)) 45)
+ ((= value (/ (sqrt 3) 2)) 60)
+ ((= value 1) 90)
+ ((= value -1/2) 210)
+ ((= value (- (/ (sqrt 2) 2))) 225)
+ ((= value (- (/ (sqrt 3) 2))) 240)
+ ((= value -1) 180)
+ (else (rad->deg (asin value)))))
+
+(define (arccosine value)
+ "Calculate the smallest angle from the given cosine value."
+ (cond ((= value 1) 0)
+ ((= value (/ (sqrt 3) 2)) 30)
+ ((= value (/ (sqrt 2) 2)) 45)
+ ((= value 1/2) 60)
+ ((= value 0) 90)
+ ((= value -1/2) 120)
+ ((= value (- (/ (sqrt 2) 2))) 135)
+ ((= value (- (/ (sqrt 3) 2))) 150)
+ ((= value -1) 180)
+ (else (rad->deg (acos value)))))
+
+(define (arctan value)
+ "Calculate the smallest angle from the given tangent value."
+ (cond ((= value 0) 0)
+ ((= value 1) 45)
+ ((= value -1) 135)
+ (else (rad->deg (atan value)))))
+
+(define (arctan2 y x)
+ "Calculate the arc tangent from 2 coordinate components, y and x."
+ (cond ((zero? x)
+ (let ((sign (if (positive? y) + -)))
+ (sign 90)))
+ (else
+ (let ((arc-shift
+ (cond ((positive? x) 0)
+ ((and (negative? x) (>= y 0)) 180)
+ ((and (negative? x) (negative? y)) -180))))
+ (+ (arctan (/ y x)) arc-shift)))))
diff --git a/unit-tests/Makefile.am b/unit-tests/Makefile.am
index 00530ca..0a7ab37 100644
--- a/unit-tests/Makefile.am
+++ b/unit-tests/Makefile.am
@@ -58,6 +58,7 @@ TESTS= \
match-bind.scm \
math.minima.scm \
math.primes.scm \
+ math.trigonometry.scm \
md5.scm \
os.process.scm \
search.basic.scm \
diff --git a/unit-tests/math.trigonometry.scm b/unit-tests/math.trigonometry.scm
new file mode 100644
index 0000000..d995f74
--- /dev/null
+++ b/unit-tests/math.trigonometry.scm
@@ -0,0 +1,61 @@
+;;; ----------------------------------------------------------------------
+;;; unit test
+;;; Copyright (C) 2025 Adam Faiz <[email protected]>
+;;;
+;;; 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/>.
+;;; ----------------------------------------------------------------------
+
+(use-modules (math trigonometry)
+ (unit-test)
+ (oop goops))
+
+;; **********************************************************************
+;; Test of trigonometry
+;; **********************************************************************
+(define-class <test-trigonometry> (<test-case>)
+ (angles #:accessor test-angles)
+ (x-coords #:accessor test-x-values)
+ (y-coords #:accessor test-y-values))
+
+(define-method (set-up-test (self <test-trigonometry>))
+ (set! (test-angles self)
+ (list -720 -360 -270 -180 -90 -60 -45 -30 -15 -0
+ 0 15 30 45 60 90 180 270 360 720))
+ (set! (test-x-values self)
+ (list 1 -1 -1 0 0 1/2 1/3 1/4 1/3 1/2))
+ (set! (test-y-values self)
+ (list 0 0 -1 1 -1 1/3 1/4 1/3 1/2 1)))
+
+(define (within-margin? value estimate)
+ (define margin 0.001)
+ (< (expt (- value estimate) 2) margin))
+
+(define (assert-estimates results estimates)
+ (not (member #f (map within-margin? results estimates))))
+
+(define-method (test-sine (self <test-trigonometry>))
+ (assert-estimates (map sine (test-angles self))
+ (list 0 0 1 0 -1 -0.866 -0.707 -1/2 -0.259 0
+ 0 0.259 1/2 0.707 0.866 1 0 -1 0 0)))
+
+(define-method (test-cosine (self <test-trigonometry>))
+ (assert-estimates (map cosine (test-angles self))
+ (list 1 1 0 -1 0 1/2 0.707 0.866 0.966 1
+ 1 0.966 0.866 0.707 1/2 0 -1 0 1 1)))
+
+(define-method (test-arctan2 (self <test-trigonometry>))
+ (assert-estimates (map arctan2 (test-x-values self) (test-y-values self))
+ (list 90 -90 -135 0 180 56.31 53.13 36.87 33.69 26.57)))
+
+(exit-with-summary (run-all-defined-test-cases))
--
2.46.0
