# Tag Archives: isometric

## Isometric to Cartesian

Actionscript:
1. var centerX:Number=stage.stageWidth/2;
2. var centerY:Number=stage.stageHeight/2;
3. // 1 to 2 ratio
4. // try others 1 / 1.5 etc...
5. var theta:Number = Math.atan(1 / 2);
6.
7. var cosX:Number=Math.cos(theta);
8. var sinX:Number=Math.sin(theta);
9. var pnt:Point = new Point();
10.
11. function iso3D(x:Number, y:Number, z:Number):Point {
12.     pnt.x = centerX + (x-z) *  cosX;
13.     pnt.y = centerY -  (x+z) * sinX - y;
14.     return pnt;
15. }
16.
17. var p:Point = iso3D(0,0,0);
18.
19. graphics.beginFill(0x000000);
20. graphics.drawCircle(p.x, p.y, 2);
21.
22. // x axis positive
23. trace("x = red");
24. for (var i:int = 1; i<10; i++){
25.     graphics.beginFill(0xFF0000);
26.     p = iso3D(i*10, 0, 0);
27.     graphics.drawCircle(p.x, p.y, 2);
28. }
29.
30. // y axis positive
31. trace("y = green");
32. for (i= 1; i<10; i++){
33.     graphics.beginFill(0x00FF00);
34.     p = iso3D(0, i * 10, 0);
35.     graphics.drawCircle(p.x, p.y, 2);
36. }
37.
38. // z axis positive
39. trace("z = blue");
40. for (i= 1; i<10; i++){
41.     graphics.beginFill(0x0000FF);
42.     p = iso3D(0, 0, i * 10);
43.     graphics.drawCircle(p.x, p.y, 2);
44. }

The above code demos a conversion from isometric coordinates to cartesian coordinates. It draws out part of the x, y and z axis using the iso3D() function.

I've always faked isometric conversion by just tweaking numbers. A few years ago I created some strange isometric engines (here's another example). The other day when I wrote the isometric voxels snippet I just created the iso3D() function with a little trial and error. As you'll see it's not exactly the same as the one here. This new conversion is the result of some googling. The updated conversion is pretty close to the one that I wrote for the voxel post, but has one less multiplication... and a clearer place to control the scale ratio ...

## Isometric Voxels

Actionscript:
1. // isometric conversion
2. var centerX:Number=stage.stageWidth/2;
3. var centerY:Number=stage.stageHeight/2;
4. var theta:Number=Math.PI/4;// 45 degrees;
5. var cosX:Number=Math.cos(theta);
6. var sinX:Number=Math.sin(theta);
7. var pnt:Point = new Point();
8. function iso3D(x:Number, y:Number, z:Number):Point {
9.     pnt.x = centerX + (x-z) *  cosX
10.     pnt.y = centerY -  (x+z) * 0.5 * sinX - y;
11.     return pnt;
12. }
13. // example:
14. var canvas:BitmapData=new BitmapData(stage.stageWidth,stage.stageHeight,true,0xFF000000);
16. var size:int=100;
17. var hs:int=size / 2;
18. var pen:Point = new Point();
19. var vect:Vector3D = new Vector3D();
20. // draw a few shapes with offset:
21. for (var dist:int = 10; dist <= 80; dist *= 2) {
22.     // voxel space:
23.     for (var i:int = 0; i<size; i++) {
24.         for (var j:int = 0; j<size; j++) {
25.             for (var k:int = 0; k<size; k++) {
26.                 vect.x=j-hs;
27.                 vect.y=i-hs;
28.                 vect.z=k-hs;
29.                 pen = iso3D(vect.x,vect.y,vect.z);
30.                 if (Math.sqrt((vect.x * vect.x) + (vect.y * vect.y) + (vect.z * vect.z)) <dist) {
31.                     // using Vector3D.distance() is very slow compared to above
32.                     // a few types of coloring:
33.                     var xp:Number = pen.x + (dist <<2) - 200;
34.                     canvas.setPixel(xp, pen.y-100, (i <<16 | j <<8 | k) <<1);
35.                     canvas.setPixel(xp, pen.y+100, (k <<16 | k <<8 | k+j)  );
36.                 }
37.             }
38.         }
39.     }
40. }

The above will draw this: This isn't the speediest way to do voxels (especially if you want to animate). This was just the first thing that came to mind.

Posted in 3D, BitmapData, color, pixel manipulation, setPixel | Also tagged , , | 3 Comments

## Isometric Box

Actionscript:
1. stage.frameRate = 30;
2.
3. for (var i:int = 0; i<100; i++){
4.     makeBoxSegment(200, 200 - i, i * 2);
5. }
6.
7. function makeBoxSegment(xp:Number, yp:Number, col:uint):Sprite {
8.     var isoBox:Sprite = Sprite(addChild(new Sprite()));
9.     with (isoBox) scaleY = .5, y = yp, x = xp;
10.     var box:Shape = Shape(isoBox.addChild(new Shape()));
11.     box.rotation = 45;
12.     with (box.graphics) beginFill(col), drawRect(-50,-50,100,100);
14.     return isoBox;
15. }
16.
17. function onRotate(evt:Event):void {
18.     evt.currentTarget.getChildAt(0).rotation = mouseX;
19. }

An isometric box that rotates with the mouseX.

Posted in DisplayObject, Graphics | Also tagged , , | 2 Comments