From: shawn bright <nephish@...>
Date: 2008-11-30T05:48:21+09:00
Subject: Re: rmagick and circles

This is great, thanks Oliver.
One question,

what is meant by x_0 and y_0, are those the plot points for the center
of the graph?
thanks.
shawn

On Sat, Nov 29, 2008 at 2:34 PM, Oliver Burghard <OliverBurghard@web.de> wrote:
> 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
>>
>
>
>