From: Oliver Burghard <OliverBurghard@...>
Date: 2008-11-30T05:34:35+09:00
Subject: Re: rmagick and circles

Hey,

I am not sure what you want. If you only want one point it is easy:

x = x_0 + radius * Math.cos(angle * 2.0 * Math::PI / 360.0)
y = y_0 + radius * Math.sin(angle * 2.0 * Math::PI / 360.0)

This is for the angle in degrees. Like this you can get any point on the
circle. Now if you want to get the points of an arc you could just
increase the angle a bit at a time and plot the points. But that would
not be a very nice circle and would be slow.

An option would be to get a starting point with the formula above and
then iterate with x**2 + y**2 = r**2. For example in the first part of
the circle between 0 and 45 degrees y is growing faster than x. 

You would start with an y and increase it once by one. 
( leave away the translation for easiness )

y' <- y + 1
x' <- sqrt( r**2 - (y+1)**2 ) = sqrt( r**2 - y**2 -2*y - 1) 
	= sqrt( x**2 - 2 * y - 1)

Hope it gives some ideas.

Oliver

Am Sonntag, den 30.11.2008, 04:45 +0900 schrieb shawn bright:
> Hey there all,
> 
> I am using RMagick to draw some circles.
> what i need though is a math formula to give me a pair of plot points
> for an angle.
> 
> Say a circle is 40 x 40 on a sheet of graph paper.
> this would put the center of the circle at x=20, y=20
> and it would make the radius = 20.
> 
> now, i need to be able to pass in a number like say, 20 degrees and
> return the x and y plots of this on the circle.
> 
> i know, more a math problem than ruby, but i could use any suggestions.
> 
> thanks,
> shawn
>