corgano

aTan always positive (Bug or intended?)

5 posts in this topic

This thread is about something odd i noticed with AutoIt's aTan function, that caused me a lot of time to track down.

Recently i was writing a program to change GPX files, splitting each set of points into smaller directions. It works by taking the current and next point in the gpx file, calculating the angle between them, and then adding points between them every x meters until it's near enough to the second point. Lather, rinse, repeat.

The problem is sometimes the angle the new points would make would go completely the wrong direction, approximately half the time. Hurm...

Anyways I eventually discovered that aTan would always return a positive result. This is fine for calculating SLOPE, but for calculating ANGLE this was very annoying. I eventually came up with a work-around that works, but i was wondering if this behavior was intended or not. Example script here, will show the buggy behavior by default. Uncomment line 28 to see the expected behavior

#include <GUIConstantsEx.au3>

$Form1 = GUICreate("Form1", 318, 288, 192, 124)
$Radio1 = GUICtrlCreateRadio("", 160, 120, 17, 17)
$Label1 = GUICtrlCreateLabel("Label1", 16, 232, 316, 77)
GUISetState(@SW_SHOW)

Local $s, $olds, $hwnd=WinGetHandle(ControlGetHandle($Form1,"",$Radio1))

While 1
    $nMsg = GUIGetMsg()
    Switch $nMsg
        Case $GUI_EVENT_CLOSE
            Exit

    EndSwitch

    $pos = WinGetPos($hwnd)
    If @error then ContinueLoop
    $pos2 = MouseGetPos()

    $dx = $pos2[0] - $pos[0]
    $dy = $pos2[1] - $pos[1]

    $angle = ATan($dy/$dx)

    ;this is the fix, uncomment to see expected (desired) behavior
;~  If $dx < 0 Then $angle -= 3.14159265359

    $s = "Pos 1 = "&$pos[0]&" , "&$pos[0]&"       Angle= "&($angle*57.295779513)+90&@CRLF&"Pos 2 = "&$pos2[0]&" , "&$pos2[1]&@CRLF&"DX = "&$dx&"         DY = "&$dy
    If $s <> $olds Then
        $olds = $s
        GUICtrlSetData($Label1, $s)
    EndIf
WEnd

 


0x616e2069646561206973206c696b652061206d616e20776974686f7574206120626f64792c20746f206669676874206f6e6520697320746f206e657665722077696e2e2e2e2e

Share this post


Link to post
Share on other sites



I don't believe Arctangent can ever return a negative number.


If I posted any code, assume that code was written using the latest release version unless stated otherwise. Also, if it doesn't work on XP I can't help with that because I don't have access to XP, and I'm not going to.
Give a programmer the correct code and he can do his work for a day. Teach a programmer to debug and he can do his work for a lifetime - by Chirag Gude
How to ask questions the smart way!

I hereby grant any person the right to use any code I post, that I am the original author of, on the autoitscript.com forums, unless I've specifically stated otherwise in the code or the thread post. If you do use my code all I ask, as a courtesy, is to make note of where you got it from.

Back up and restore Windows user files _Array.au3 - Modified array functions that include support for 2D arrays.  -  ColorChooser - An add-on for SciTE that pops up a color dialog so you can select and paste a color code into a script.  -  Customizable Splashscreen GUI w/Progress Bar - Create a custom "splash screen" GUI with a progress bar and custom label.  -  _FileGetProperty - Retrieve the properties of a file  -  SciTE Toolbar - A toolbar demo for use with the SciTE editor  -  GUIRegisterMsg demo - Demo script to show how to use the Windows messages to interact with controls and your GUI.  -   Latin Square password generator

Share this post


Link to post
Share on other sites

It is common to see inverse trig functions return result in [0, 2π[. Some softwares use the range ]-π/2, π/2[ for result of ArcTan but these ranges are only conventions. Angles in radian are always Mod(2π).

Yes of course ArcTan can return something in ]-π/2, π/2[ or even [-π/2, π/2] if the underlying library deals with infinities.


This wonderful site allows debugging and testing regular expressions (many flavors available). An absolute must have in your bookmarks.
Another excellent RegExp tutorial. Don't forget downloading your copy of up-to-date pcretest.exe and pcregrep.exe here
RegExp tutorial: enough to get started
PCRE v8.33 regexp documentation latest available release and currently implemented in AutoIt beta.

SQLitespeed is another feature-rich premier SQLite manager (includes import/export). Well worth a try.
SQLite Expert (freeware Personal Edition or payware Pro version) is a very useful SQLite database manager.
An excellent eBook covering almost every aspect of SQLite3: a must-read for anyone doing serious work.
SQL tutorial (covers "generic" SQL, but most of it applies to SQLite as well)
A work-in-progress SQLite3 tutorial. Don't miss other LxyzTHW pages!
SQLite official website with full documentation (may be newer than the SQLite library that comes standard with AutoIt)

Share this post


Link to post
Share on other sites

That made it even less clear than before.


If I posted any code, assume that code was written using the latest release version unless stated otherwise. Also, if it doesn't work on XP I can't help with that because I don't have access to XP, and I'm not going to.
Give a programmer the correct code and he can do his work for a day. Teach a programmer to debug and he can do his work for a lifetime - by Chirag Gude
How to ask questions the smart way!

I hereby grant any person the right to use any code I post, that I am the original author of, on the autoitscript.com forums, unless I've specifically stated otherwise in the code or the thread post. If you do use my code all I ask, as a courtesy, is to make note of where you got it from.

Back up and restore Windows user files _Array.au3 - Modified array functions that include support for 2D arrays.  -  ColorChooser - An add-on for SciTE that pops up a color dialog so you can select and paste a color code into a script.  -  Customizable Splashscreen GUI w/Progress Bar - Create a custom "splash screen" GUI with a progress bar and custom label.  -  _FileGetProperty - Retrieve the properties of a file  -  SciTE Toolbar - A toolbar demo for use with the SciTE editor  -  GUIRegisterMsg demo - Demo script to show how to use the Windows messages to interact with controls and your GUI.  -   Latin Square password generator

Share this post


Link to post
Share on other sites

#5 ·  Posted (edited)

If you consider the complex plane (or the affine plane) instead of the traditionnal trigonometric circle and conventions, you can define the arctangent of a complex number (or a pair of points in the affine plane). Then the arctangent can be mapped to any range of span 2π, the origin of the interval being your choice. That's what the OP seems to expect: angles of vectors u, v, w and t wrt the x axis to be resp. > 0, > 0, < 0, < 0 by using the range [-π, π].

Trig C.pdf

Trig trad.pdf

In the picture above the traditionnal trigonometric (real) arctangent of points A and C are drawn, resp. angles β and α. (Excuse the weird naming sequence).

β and α can be anywhere in ]-π/2, π/2[ if the line (t) maps to ℝ or even in [-π/2, π/2] if the map is to ℝ ∪ {-∞, +∞}.

 

Edited by jchd
Images didn't make it

This wonderful site allows debugging and testing regular expressions (many flavors available). An absolute must have in your bookmarks.
Another excellent RegExp tutorial. Don't forget downloading your copy of up-to-date pcretest.exe and pcregrep.exe here
RegExp tutorial: enough to get started
PCRE v8.33 regexp documentation latest available release and currently implemented in AutoIt beta.

SQLitespeed is another feature-rich premier SQLite manager (includes import/export). Well worth a try.
SQLite Expert (freeware Personal Edition or payware Pro version) is a very useful SQLite database manager.
An excellent eBook covering almost every aspect of SQLite3: a must-read for anyone doing serious work.
SQL tutorial (covers "generic" SQL, but most of it applies to SQLite as well)
A work-in-progress SQLite3 tutorial. Don't miss other LxyzTHW pages!
SQLite official website with full documentation (may be newer than the SQLite library that comes standard with AutoIt)

Share this post


Link to post
Share on other sites

Create an account or sign in to comment

You need to be a member in order to leave a comment

Create an account

Sign up for a new account in our community. It's easy!


Register a new account

Sign in

Already have an account? Sign in here.


Sign In Now