Drawing an honeycomb with as3 - actionscript-3

Question

I'm trying to create an honeycomb with as3 but I have some problem on cells positioning.
I've already created the cells (not with code) and for cycled them to a funcion and send to it the parameters which what I thought was need (the honeycomb cell is allready on a sprite container in the center of the stage).
to see the structure of the cycle and which parameters passes, please see the example below, the only thing i calculate in placeCell is the angle which I should obtain directly inside tha called function
alt text http://img293.imageshack.us/img293/1064/honeycomb.png
Note: the angle is reversed but it isn't important, and the color are useful in example only for visually divide cases.
My for cycle calls placeCell and passes cell, current_case, counter (index) and the honeycomb cell_lv (cell level).
I thought it was what i needed but I'm not skilled in geometry and trigonometry, so I don't know how to position cells correctly:
import flash.display.Sprite;
stage.align = StageAlign.TOP_LEFT;
stage.scaleMode = StageScaleMode.NO_SCALE;
function createHoneycomb (cells:int):void {
var honeycomb:Sprite = new Sprite ();
addChild (honeycomb);
var cell_lv:int = 1;
var increment:int = 6;
var tot_cur_cells:int = 1;
var current_case:int = 0;
var case_counter:int = 1;
var case_length:int = 1;
var max_cases:int = 6;
var nucleus:Sprite = new cell (); // hexagon from library
honeycomb.addChild (nucleus);
for (var i:int = 1; i <= cells; i ++) {
if (case_counter < case_length) {
case_counter ++;
} else {
current_case ++;
if (current_case > max_cases) current_case = 1;
case_counter = 1;
}
if (i == tot_cur_cells) { // if i reach the current level
if (i > 1) cell_lv ++;
case_length = cell_lv;
tot_cur_cells += (increment * cell_lv);
}
var current_cell:Sprite = new cell (); // hexagon from library
honeycomb.addChild (current_cell);
placeCell (current_cell, case_counter, current_case, cell_lv);
}
function centerHoneycomb (e:Event):void {
honeycomb.x = stage.stageWidth / 2
honeycomb.y = Math.round (stage.stageHeight / 2);
}
stage.addEventListener (Event.RESIZE, centerHoneycomb)
stage.dispatchEvent (new Event (Event.RESIZE));
}
function placeCell (cell:Sprite, counter:int, current_case:int, cell_lv:int):void {
var margin:int = 2;
// THIS IS MY PROBLEM
var start_degree:Number = (360 / (cell_lv * 6));
var angle:Number = (start_degree * ((current_case - 1) + counter) - start_degree);
var radius:Number = (cell.width + margin) * cell_lv;
cell.x = radius * Math.cos (angle);
cell.y = radius * Math.sin (angle);
// end of the problem
if (angle != 0) trace ("LV " + cell_lv + " current_case " + current_case + " counter " + counter + " angle " + angle + " radius " + radius);
else trace ("LV " + cell_lv + " current_case " + current_case + " counter " + counter + " angle " + angle + " radius " + radius);
}
createHoneycomb (64);
if you copy and paste this code, it works but you need to create an hexagon and call it in the actionscript library as cell
how can I do to solve it?
I've also thought to use a switch with the cases to align it, but i think is a little bit buggy doing this

Answer 1

Okay, I really loved this question. It was interesting, and challenging, and I got a working result. I didn’t use any of your code as the base though, but started from scratch, so depending on your final use, you might need to change a bit.
I did however created similar variables to those inside of your cells (in the picture). For each cell you have the following properties:
the iterating variable i is equally to your cell number
the radius r equals your level, and expresses the distance from the center (with 0 being the center)
the position p expresses the position in the current radius
the sector s equals your case, but starts with zero
p % r equals your index
I don’t have an angle, simply because I don’t position the individual hexagons using an angle. Instead I base the position of the (fixed) positions of the hexagons at radius 1 and calculate the missing ones in between.
The following code shows my implementation with 61 (60 + the center; but it’s configurable). You can also see the code in action on Wonderfl.
package
{
import flash.display.Sprite;
public class Comb extends Sprite
{
public function Comb ()
{
Hexagon.scale = 0.5;
this.x = stage.stageWidth / 2;
this.y = stage.stageHeight / 2;
// draw honeycomb with 60 cells
drawComb( 60 );
}
private function drawComb ( n:uint ):void
{
var colors:Array = new Array( 0x33CC33, 0x006699, 0xCC3300, 0x663399, 0xFF9900, 0x336666 );
var sectors:Array = new Array(
new Array( 2, 0 ),
new Array( 1, 1 ),
new Array( -1, 1 ),
new Array( -2, 0 ),
new Array( -1, -1 ),
new Array( 1, -1 ) );
var w:Number = 0.50 * Hexagon.hxWidth;
var h:Number = 0.75 * Hexagon.hxHeight;
var r:uint, p:uint, s:uint;
var hx:Hexagon;
for ( var i:uint = 0; i <= n; i++ )
{
r = getRadius( i );
p = getPosition( i, r );
s = getSector( i, r, p );
// create hexagon
if ( r == 0 )
hx = new Hexagon( 0xCCCCCC );
else
hx = new Hexagon( colors[s] );
hx.x = w * ( r * sectors[s][0] - ( p % r ) * ( sectors[s][0] - sectors[ ( s + 1 ) % 6 ][0] ) );
hx.y = h * ( r * sectors[s][1] - ( p % r ) * ( sectors[s][1] - sectors[ ( s + 1 ) % 6 ][1] ) );
addChild( hx );
}
}
private function getRadius ( i:uint ):uint
{
var r:uint = 0;
while ( i > r * 6 )
i -= r++ * 6;
return r;
}
private function getPosition ( i:uint, r:uint ):uint
{
if ( r == 0 )
return i;
while ( r-- > 0 )
i -= r * 6;
return i - 1;
}
private function getSector ( i:uint, r:uint, s:uint ):uint
{
return Math.floor( s / r );
}
}
}
import flash.display.Shape;
class Hexagon extends Shape
{
public static var hxWidth:Number = 90;
public static var hxHeight:Number = 100;
private static var _scale:Number = 1;
public function Hexagon ( color:uint )
{
graphics.beginFill( color );
graphics.lineStyle( 3, 0xFFFFFF );
graphics.moveTo( 0, -50 );
graphics.lineTo( 45, -25 );
graphics.lineTo( 45, 25 );
graphics.lineTo( 0, 50 ),
graphics.lineTo( -45, 25 );
graphics.lineTo( -45, -25 );
graphics.lineTo( 0, -50 );
this.scaleX = this.scaleY = _scale;
}
public static function set scale ( value:Number ):void
{
_scale = value;
hxWidth = value * 90;
hxHeight = value * 100;
}
public static function get scale ():Number
{
return _scale;
}
}