Many times I’ve set up interfaces where I need to place different objects equidistant around a central object. The solution to this problem is to first calculate the angle of each object by converting Radians to Degrees. This can be expressed by the following formula

So, you simply need to loop through your collection of objects and assign each a different angle. After that you plug that angle into a new Polar Point.

for(var i=0;i<array.length;i++)
{
	var angle:Number = i*( 180/Math.PI )
	var coord:Point = Point.polar( circumference, angle )
}

Here’s the complete source: radians.zip

package
{
	import flash.ui.*;
	import flash.display.*;
	import flash.events.*;
	import flash.geom.*;

	public class Main extends Sprite
	{

		/*
		========================================================
		| Private Variables                         | Data Type
		========================================================
		*/

		private var array:Array = new Array()
		private var circumference:int;

		/*
		========================================================
		| Constructor
		========================================================
		*/

		public function Main ()
		{
			stage.align = StageAlign.TOP_LEFT;

			// make some balls
			addParticle( 100 )

			menu.txtParticles.text = 'Particles: 100';

			stage.addEventListener( Event.ENTER_FRAME, runParticle )

			menu.slideCircumference.addEventListener( Event.CHANGE, changeCircumference );
			menu.particles.addEventListener( Event.CHANGE, changeParticles );

		}

		private function addParticle( num )
		{
			stage.removeEventListener( Event.ENTER_FRAME, runParticle )

			var tot:Number = array.length

			// kill mc's
			for( var t=0;t<tot;t++ )
			{
				removeChild( array[t].mc );
			}

			// kill array
			for( var r=0;r<tot;r++ )
			{
				array.shift();
			}

			trace( 'removed particles '+array.length )

			for( var d=0;d<num;d++ )
			{
				var c:MovieClip = new MovieClip()
				c.name = "particle"
				c.graphics.beginFill( 0xffffff, 1 )
				c.graphics.drawCircle( 0, 0, 1 )
				c.graphics.endFill()
				addChild( c )

				array.push( { mc:c } )
			}

			trace( 'added particles '+array.length )

			changeCirc( circumference )

			stage.addEventListener( Event.ENTER_FRAME, runParticle )
		}

		private function runParticle( e:Event )
		{
			//trace( 'running' )
			graphics.clear()
			graphics.lineStyle( 1, 0xffffff, .1 )

			for(var i=0;i<array.length;i++)
			{
				graphics.moveTo( stage.stageWidth/2, stage.stageHeight/2 )
				graphics.lineTo( array[i].mc.x, array[i].mc.y )
			}

		}

		private function changeCirc( c:int )
		{
			for(var i=0;i<array.length;i++)
			{
				var angle:Number = i*( 180/Math.PI )
				var coord:Point = Point.polar( c, angle )

				array[i].mc.x = ( stage.stageWidth/2 ) + coord.x
				array[i].mc.y = ( stage.stageHeight/2 ) + coord.y
			}

			circumference = c
		}

		private function changeCircumference( e:Event ):void
		{
			menu.txtCircumference.text = 'Circumference: ' + e.target.value;
			changeCirc( e.target.value )
		}

		private function changeParticles( e:Event ):void
		{
			menu.txtParticles.text = 'Particles: ' + e.target.value;
			addParticle( e.target.value )
		}
	}
}

Permalink: http://www.christeso.com/index.php/lab/as3-polar-coordinates-and-radians

You can see the drop down in use on my homepage.

Edit [ 12.16.08 ] : added directional code.

//usage
// array for drop
var dropOtherArray:Array = new Array()
dropOtherArray.push( {title:"iWork", name:"folio"} )
dropOtherArray.push( {title:"iExperiment", name:"lab"} )
dropOtherArray.push( {title:"iWrite", name:"blog"} )
dropOtherArray.push( {title:"iPhotograph", name:"photo"} )
dropOtherArray.push( {title:"iFlickr", name:"flickr"} )
dropOtherArray.push( {title:"iRecord", name:"vimeo"} )
dropOtherArray.push( {title:"contactMe", name:"contact"} )

fmat.color = 0xffffff
fmat.font = font.fontName
fmat.size = 11

addChild( _dropOther = new DropDown( 180, 25, "iLiveElsewhere:", fmat, 0x000033, dropOtherArray, "down", other ) )

package com.teso.ui
{
	import com.gskinner.motion.*
	import flash.display.*;
	import flash.events.*;
	import flash.net.*;
	import flash.utils.*;
	import flash.text.*;
	import fl.transitions.*;
	import fl.transitions.easing.*;

	public class DropDown extends Sprite
	{
		private var _items:Array = new Array()
		private var _overC:uint;
		private var _backC:uint;
		private var _w:Number;
		private var _h:Number;
		private var _timer:Timer;
		private var _open:Boolean = false;
		private var _defaultText:TextField;
		private var _title:String;
		private var _direction:String;
		private var _fmt:TextFormat;

		public function DropDown( w:Number, h:Number, title:String, fmt:TextFormat, colorBack:uint, itemArray:Array, direction:String, callback )
		{
			// timer
			_timer = new Timer( 300 );
			_timer.addEventListener( TimerEvent.TIMER, closeDrop )

			// vars
			_w = w
			_h = h
			_backC = colorBack
			_items = itemArray
			_title = title
			_direction = direction
			_fmt = fmt

			// create a back for the holder
			var holder:MovieClip = new MovieClip();
			holder.name = "holder"
			holder.graphics.beginFill( _backC, 1 );
			holder.graphics.drawRoundRect( 0, 0, _w, _h, 2, 2 )
			holder.graphics.endFill()

			// add the drop
			addChild( holder )

			// set listeners
			holder.buttonMode = true;
			holder.addEventListener( MouseEvent.MOUSE_OVER, openDrop )
			holder.addEventListener( MouseEvent.MOUSE_OVER, cancelClose )
			holder.addEventListener( MouseEvent.MOUSE_OUT, startClose )

			// create a text field
			var t:TextField = new TextField()
			t.name = "holderText"
			t.selectable = false;
			t.autoSize = TextFieldAutoSize.LEFT;
			t.htmlText = title
			t.setTextFormat( fmt )
			t.y = ( holder.height/2 ) - ( t.height/2 )

			_defaultText = t

			// add the text
			holder.addChild( t )

			// create children
			for( var i=0; i<_items.length; i++ )
			{
				// create a back
				var back:MovieClip = new MovieClip()
				back.name = _items[i].name;
				back.graphics.beginFill( _backC, 1 )
				back.graphics.drawRoundRect( 0, 0, _w, _h, 10, 10 )
				back.graphics.endFill()

				// create a text field
				t = new TextField();
				t.name = "t"
				t.x = 5
				t.selectable = false;
				t.autoSize = TextFieldAutoSize.LEFT;
				t.htmlText = _items[i].title;
				t.setTextFormat( fmt )
				t.y = ( back.height/2 ) - ( t.height/2 )

				if( _items[i].d )
				{
					_defaultText.htmlText = _title+" "+_items[i].title
					_defaultText.setTextFormat( _fmt )
				}

				// make them invisible for now
				back.visible = false;

				// set a listener
				back.buttonMode = true;
				back.addEventListener( MouseEvent.CLICK, closeDrop )
				back.addEventListener( MouseEvent.CLICK, setDefaultText )
				back.addEventListener( MouseEvent.CLICK, callback )
				back.addEventListener( MouseEvent.MOUSE_OUT, startClose )
				back.addEventListener( MouseEvent.MOUSE_OVER, cancelClose )

				// add the text
				back.addChild( t )

				// add it to the holder
				addChildAt( back, 0 )

				_items[i].mc = back
			}
		}

		private function openDrop( e:Event )
		{
			if( !_open )
			{

				for( var i=0; i<_items.length; i++ )
				{
					// set a var
					var item:DisplayObject = _items[i].mc

					// set the items alpha to zero
					item.alpha = 0;

					// make the item visible
					item.visible = true

					// fade it in
					var tweenIn:GTween;

					if( _direction == "down" )
					{
						tweenIn = new GTween( item, .3, {y:_h + ( _h * i ),  alpha:1} )
					}
					else
					{
						tweenIn = new GTween( item, .3, {y:-_h - ( _h * i ),  alpha:1} )
					}
					tweenIn.ease = Regular.easeOut
				}
			}
			_open = true;

		}
		private function cancelClose( e:Event )
		{
			if( e.currentTarget.name != "holder" )
			{
				e.currentTarget.alpha = .8
			}
			_timer.stop()
		}
		private function startClose( e:Event )
		{
			e.currentTarget.alpha = 1
			_timer.start()
		}
		private function setDefaultText( e:Event )
		{
			_defaultText.htmlText = _title+" "+e.currentTarget.getChildByName( "t" ).text
			_defaultText.setTextFormat( _fmt )
		}
		private function closeDrop( e:Event )
		{
			closeIt()
		}
		private function closeIt()
		{
			if( _open )
			{
				for( var i=0; i<_items.length; i++ )
				{
					// set a var
					var item:DisplayObject = _items[i].mc

					// make the item visible
					item.visible = true

					// fade it in
					var tweenOut:GTween = new GTween( item, .3, {y:0, alpha:0}, {completeListener:done, data:item} )
					tweenOut.ease = Regular.easeOut
				}
			}

			_timer.stop()

			_open = false;
		}
		private function done( e:Event )
		{
			e.currentTarget.data.visible = false

		}

	}
}
Permalink:
http://www.christeso.com/index.php/lab/as3-drop-down-menu-classas3-drop-down-menu-class/