Imprecision in the trig functions Topic is solved

[Awesome Quest]

Hi everyone,
I'm writing a tool to draw shapes in OneNote 2016 and having trouble with the sin and cos functions.

I'm using this code to draw a right angle triangle and a rotated square.

Code: Select all

!q::{
	pi := 3.14159265358979323846
	MouseGetPos(x, y)
	; Draw a square rotated by 120 degrees from mouse position
	Scale := 150
	rad:=120*pi/180
	cosRad := cos(rad)
	sinRad := sin(rad)
	; This is set up so that when rad = 0 the mouse is in the top left corner
	; rad then rotates it counter clockwise
	MouseClickDrag("LButton",x,y,x+Scale*cosRad,y-Scale*sinRad,1)
	MouseClickDrag("LButton",0,0, Scale*sinRad, Scale*cosRad,1,"R")
	MouseClickDrag("LButton",0,0,-Scale*cosRad, Scale*sinRad,1,"R")
	MouseClickDrag("LButton",0,0,-Scale*sinRad,-Scale*cosRad,1,"R")

	; Draw a right angle triangle with 30 degree angle and mouse position
	Scale := 500
	rad:=30*pi/180
	MouseClickDrag("LButton",x,y,x+scale,y,1)
	MouseClickDrag("LButton",x+scale,y,x+scale,y-scale*sin(rad),1)
	MouseClickDrag("LButton",x+scale,y-scale*sin(rad),x,y,1)
}

And it produces this when put into OneNote 2016

Screenshot 2021-11-29 143749.png (23.69 KiB) Viewed 916 times

As we can see, they are not parallel. And if you look really close at the square we can see

Screenshot 2021-11-29 142627.png (3.38 KiB) Viewed 916 times

The corners don't line up.

I'm wondering if there's a simple solution to this or if there is just a more precise sin function I could use?

What method does autohotkey use for sin?

[Awesome Quest]

Update:
I tried rewriting the square code so that it no longer uses relative mode.

Code: Select all

!q::{
	pi := 3.14159265358979323846
	MouseGetPos(x, y)
	; Draw a square rotated by 120 degrees from mouse position
	Scale := 150
	rad:=120*pi/180
	cosRad := cos(rad)
	sinRad := sin(rad)
	; This is set up so that when rad = 0 the mouse is in the top left corner
	; rad then rotates it counter clockwise
	; MouseClickDrag("LButton",x,y,x+Scale*cosRad,y-Scale*sinRad,1)
	; MouseClickDrag("LButton",0,0, Scale*sinRad, Scale*cosRad,1,"R")
	; MouseClickDrag("LButton",0,0,-Scale*cosRad, Scale*sinRad,1,"R")
	; MouseClickDrag("LButton",0,0,-Scale*sinRad,-Scale*cosRad,1,"R")
	
	MouseClickDrag("LButton",x,y,x+Scale*cosRad,y-Scale*sinRad,1)
	x:=x+Scale*cosRad
	y:=y-Scale*sinRad
	MouseClickDrag("LButton",x,y,x+Scale*sinRad,y+Scale*cosRad,1)
	x:=x+Scale*sinRad
	y:=y+Scale*cosRad
	MouseClickDrag("LButton",x,y,x-Scale*cosRad,y+Scale*sinRad,1)
	x:=x-Scale*cosRad
	y:=y+Scale*sinRad
	MouseClickDrag("LButton",x,y,x-Scale*sinRad,y-Scale*cosRad,1)


	MouseGetPos(x, y)
	; Draw a right angle triangle with 30 degree angle and mouse position
	Scale := 500
	rad:=30*pi/180
	MouseClickDrag("LButton",x,y,x+scale,y,1)
	MouseClickDrag("LButton",x+scale,y,x+scale,y-scale*sin(rad),1)
	MouseClickDrag("LButton",x+scale,y-scale*sin(rad),x,y,1)
}

And it seems to have fixed the miss aligned kroners of the square

fixedsquare.png (53.21 KiB) Viewed 839 times

not fixed paralell.png (49.91 KiB) Viewed 839 times

but it has not fixed the two shapes alignment.

[joedf]

It could also be OneNote being part of the imprecision, no?
I suggest you print out all the values and disprove that either ahk is imprecise or oneNote is.

[Rohwedder]

Hallo,
Error: Call to nonexistent function.
Specifically: MouseGetPos(x, y)

[joedf]

Hallo,
Error: Call to nonexistent function.
Specifically: MouseGetPos(x, y)

I think this is AHK v2 beta maybe? or some command-as-functions kind of thing?

[iPhilip]

@Awesome Quest, I am not a geometer by any means but it's fairly easy to prove that the bottom edge of the square you drew is not parallel to the hypotenuse of the triangle. The slopes differ by 15%. See my additional lines in the code below:

Code: Select all

!q::{
   pi := 3.14159265358979323846
   MouseGetPos(x, y)
   ; Draw a square rotated by 120 degrees from mouse position
   Scale := 150
   rad:=120*pi/180
   cosRad := cos(rad)
   sinRad := sin(rad)
   ; This is set up so that when rad = 0 the mouse is in the top left corner
   ; rad then rotates it counter clockwise
   ; MouseClickDrag("LButton",x,y,x+Scale*cosRad,y-Scale*sinRad,1)
   ; MouseClickDrag("LButton",0,0, Scale*sinRad, Scale*cosRad,1,"R")
   ; MouseClickDrag("LButton",0,0,-Scale*cosRad, Scale*sinRad,1,"R")
   ; MouseClickDrag("LButton",0,0,-Scale*sinRad,-Scale*cosRad,1,"R")
   
   MouseClickDrag("LButton",x,y,x+Scale*cosRad,y-Scale*sinRad,1)  ; Left edge (bottom to top)
   x:=x+Scale*cosRad
   y:=y-Scale*sinRad
   MouseClickDrag("LButton",x,y,x+Scale*sinRad,y+Scale*cosRad,1)  ; Top edge (left to right)
   x:=x+Scale*sinRad
   y:=y+Scale*cosRad
   MouseClickDrag("LButton",x,y,x-Scale*cosRad,y+Scale*sinRad,1)  ; Right edge (top to bottom)
   x:=x-Scale*cosRad
   y:=y+Scale*sinRad
   MouseClickDrag("LButton",x,y,x-Scale*sinRad,y-Scale*cosRad,1)  ; Bottom edge (right to left)
   SlopeOfSquareBottomEdge := -(y - (y-Scale*cosRad)) / (x - (x-Scale*sinRad))
   SlopeOfSquareBottomEdge := -cosRad / sinRad
   ; SlopeOfSquareBottomEdge := -cos(120) / sin(120)
   ; SlopeOfSquareBottomEdge := sin(30) / cos(30)
   ; SlopeOfSquareBottomEdge := tan(30)  ; 0.577


   MouseGetPos(x, y)
   ; Draw a right angle triangle with 30 degree angle and mouse position
   Scale := 500
   rad:=30*pi/180
   MouseClickDrag("LButton",x,y,x+scale,y,1)  ; Horizontal edge (left to right)
   MouseClickDrag("LButton",x+scale,y,x+scale,y-scale*sin(rad),1)  ; Vertical edge (bottom to top)
   MouseClickDrag("LButton",x+scale,y-scale*sin(rad),x,y,1)  ; Hypotenuse (top-right to bottom-left)
   SlopeOfHypotenuse := -(y-scale*sin(rad) - y) / (x+scale - x)
   SlopeOfHypotenuse := (scale*sin(rad)) / (scale)
   SlopeOfHypotenuse := sin(rad)
   ; SlopeOfHypotenuse := sin(30)  ; 0.5
}

My intuition is that your calculation of the coordinates of the right edge of the square is incorrect.

I hope this helps.

- iPhilip