3D – actionsnippet

Many years ago when I had just started programming I found this absolute gem by Andries Odendaal.

modern es6 version

let rotX = 0, rotY = 0,
    perspective = 500, 
    depth,
    currX, currY;
// learned something like this at Andries Odendaal's www.wireframe.co.za 
function point3d(x, y, z) {
    let cosX = Math.cos(rotX),
        cosY = Math.cos(rotY),
        sinX = Math.sin(rotX),
        sinY = Math.sin(rotY),
        posX, posY, posZ;
   
    posZ = z * cosX - x * sinX,
    posX = z * sinX + x * cosX,
    posY = y * cosY - posZ * sinY,
    posZ = y * sinY + posZ * cosY;
    
    depth = 1 / (posZ / perspective + 1);
    currX = posX * depth;
    currY = posY * depth;
 
    return [ currX, currY, depth ];
}

Here’s is an example of it in action:

See the Pen <a href='https://codepen.io/ZevanRosser/pen/zBpbzK/'>Nonsense Clocks w Color</a> by Zevan Rosser (<a href='https://codepen.io/ZevanRosser'>@ZevanRosser</a>) on <a href='https://codepen.io'>CodePen</a>.<br />

See the Pen <a href='https://codepen.io/ZevanRosser/pen/WxdgqE/'>Nonsense Clocks</a> by Zevan Rosser (<a href='https://codepen.io/ZevanRosser'>@ZevanRosser</a>) on <a href='https://codepen.io'>CodePen</a>.<br />

I’ve used this code many many times, it’s just easy to throw into any language and instantly get 3d points rendered in 2d. Here is a short video of a Java applet from 2003 called “Catch Env” that made use of it:

Here is the source code for that ^^
http://www.zevanrosser.com/shape2/j/Catchenv.java

You’ll notice in that source, that I nested the equation to allow for local and global transformations. It was around that time that I learned the ins and outs of real 2D and 3D matrix transformation math… Ken Perlin’s classfiles from NYU were a real help when I was learning that stuff. I don’t think this was the exact file I was working with, but it was definitely on his site somewhere.

Before all that, during my junior year in college I created a 3d engine based off Odendaal’s code in Director (Lingo). Here is a video of some of the demos for it:

…and here is a strange screenshot from my personal website at the time:

Just an example of a powerful snippet and a gateway to learning matrix transformation math. When I first really dug in to html5 canvas – before WebGL was supported so widely – having this trick up my sleeve was great. As you can see in the below link, I used it more than a few times back then:

Daily canvas experiments:

http://zreference.com/projects/all-graphics.php

😀

stage.frameRate = 30;
var centerX:Number = 200, centerY:Number = 200, zpos:Number, xpos:Number, ypos:Number, depth:Number;
var rotX:Number = 0, rotY:Number = 0, px:Number, py:Number, pz:Number;
var cosx:Number, cosy:Number, sinx:Number, siny:Number;

var canvas:BitmapData = new BitmapData(400,400,true,0xFF000000);
addChild(new Bitmap(canvas));
 
addEventListener(Event.ENTER_FRAME, onLoop);
 
function onLoop(evt:Event):void {
	canvas.fillRect(canvas.rect, 0xFF000000);
	 rotX += (mouseX / 50 - rotX)/12;
	 rotY += (mouseY / 50 - rotY)/12;
	 
	 cosx = Math.cos(rotX);
	 cosy = Math.cos(rotY);
	 sinx = Math.sin(rotX);
	 siny = Math.sin(rotY);
	 for (var a:Number =0; a < 6.28; a+=.1){
		  for (var b:Number =0; b < 6.28; b+=.05){
			  px = 100 * Math.cos(a) * Math.cos(b) * Math.cos(b);
			  py = 100 * Math.sin(a) * Math.cos(b) 
			  pz = 100 * Math.sin(b);
			  zpos= pz*cosx - px*sinx  ;
	          xpos= pz*sinx +px*cosx  ;
	          ypos= py*cosy - zpos*siny  ;
	          zpos= py*siny+ zpos*cosy ;
			  depth = 1/((zpos/340)+1);
			  canvas.setPixel((xpos * depth) + centerX, (ypos * depth) + centerY, 0xFFFFFF);
		  }
	 }
}

Renders a rotating 3D shape.

Tag: 3D

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