Points of Regular Polygon

Randy Hengst iowahengst at mac.com
Tue Nov 29 22:43:45 CET 2016


Well, this was fun. I write a question, go teach class, and come back to a very interesting conversation.

Thanks all.

be well,
randy
www.classroomFocusedSoftware.com



> On Nov 29, 2016, at 1:24 PM, hh <hh at hyperhh.de> wrote:
> 
> I should have better used the wording
>    "graphic of type" than "graphic of style"
> because we can
>     set the style of grc 1 to "polygon"
> for example (the function again, just for the completeness here):
> 
> on mouseUp
>   if there is no grc "poly" then create grc "poly"
>   set style of grc "poly" to "polygon"
>   -- 7 vertices, 1 vertix at 12 o'clock, radius 42, loc (100,100)
>   set points of grc "poly" to regularPoints(7,42,100,100)
>   set foreColor of grc "poly" to "0,128,128" -- teal
>   set lineSize of grc "poly" to 2 
> end mouseUp
> 
> -- N is the number of vertices
> -- x0,y0 is the center of the polygon
> -- r is the radius of the polygon
> -- b is the angle of rotation in degrees
> -- (positive b turns clockwise, negative b turns ccw)
> function regularPoints n,r,x0,y0,b
>   put 2*pi/n into cn
>   -- n vertices --> n+1 points if 'closed' polygon
>   -- usually done by setting last=first
>   -- This is here true as sin(0)=sin(2*pi) and cos(0)=cos(2*pi)
>   put empty into pts
>   if b=0 or b is empty then
>      ## compute unrotated n+1 vertices of the n-sided regular polygon
>      repeat with j=0 to n
>         put CR & (round(r*sin(j*cn)+x0),round(-r*cos(j*cn)+y0)) after pts
>      end repeat
>   else
>      ## compute *rotated* n+1 vertices of the n-sided regular polygon
>      put sin(pi*b/180) into s; put cos(pi*b/180) into c 
>      repeat with j=0 to n
>         put round( r*sin(j*cn)) into sx; put round(-r*cos(j*cn)) into sy
>         put CR & ( (round(x0+c*sx-s*sy),round(y0+c*sy+s*sx)) ) after pts
>      end repeat
>    end if
>    return char 2 to -1 of pts
> end regularPoints
> 
> 
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