Browsing the archives for the Math category.


3D Christmas tree (aka the “Merry Christmas” post)

3D, actionscript 3, Math, Particles

Hi there,

lot of time without posting some code. I have been working three months on a Disney project, which will be on-line soon and makes me very proud, but almost drained all of my energies.

Here is my Christmas card/gift for my readers, in less than 80 lines of code. Obviously with source code. The lights are vector graphics in the attached FLA’s library to make it easy to customize or animate.

Nothing too fancy here about the code, just some trigonometric math. You can have a look at the correctOrientations function which can be interesting to avoid lights deformations due to the FP10 native 3D.
Download source code.

I wish you all great winter holidays, and an awesome beginning of 2010!
And make me smile by leaving a greetings comment ;)

Watch the running example:
Click to start (mouseX affects rotation)
xmas2009

10 Comments

Actionscript 3 – as3 Lightning / Thunderbolt / Electric discharge Class

actionscript 3, algorithms, BitmapData, classes, fun, Math, morphing, perlinNoise, simulation

Finally here we come!

Yup, sry for the delay, I’ve had a lot of work recently.

I have prepared three demos and a publishable (but far from perfect and not yet documented) class. The demos are FLA based… you can find the timeline code to assemble the demos at the bottom of the post. I’ll publish some documentation in the next days, so until then just look at the demos’ code to unserstand the basic of the class usage.

Download Lightning classes

Demo N°1:
This demo shows the two different behaviours the class can mimic: Electric discharge/beam or lightning. Drag the ball near or far to the coil to see different behaviors.


Click to start

Demo N°2:
This demos show the maxLength and maxLengthVary properties in action.
Bring the fingers near to the plug to have continuos electricity. Bringing the hand far from the plug lowers the discharge probability. Reaching the max distance simply disables it.


Click to start

Demo N°3:
This demo is a good reason for the publishing delay :P

A nice sandbox to play with (some of) the properties.
The class is recursive to create children so many properties have also a decay twin property which rule how the property is passed to children.
As instance if you set a childrenMaxCount = 6 to the main Lightning instance it will have a maximum of 6 direct children. Its children will have a childrenMaxCount value which depends on the main instance childrenMaxCount and childrenMaxCountDecay.
So if you set childrenMaxCount = 6 and childrenMaxCountDecay = .5 the children of the main instance will have childrenMaxCount = 3.
If you set childrenMaxCount = 6 and childrenMaxCountDecay = 0 the children of the main instance will have childrenMaxCount = 6 (no decay).

This value can be very useful to optimize the speed of execution cause smaller branches don’t need many children or many steps of detail.


Click to start

Ok, I’m too tired to write more. I’ll publish some documentation in the next days.
Feel free to ask everything question you can have in the comments, and as usual if you like this stuff scream it in the comments!

Demos’ code after the break. Waiting for your comments I will surf through the website of fatcow and see if they have any good hosting plans.

Continue Reading »

86 Comments

Actionscript 3 | Speedcoding video – session #1: Black Branches

actionscript 3, algorithms, BitmapData, classes, fun, Math, perlinNoise

Yesterday night I wanted to have some “no-purpose coding session” and thought it was a nice idea to record the session and do a speedcoding video. The original video has been collapsed from 45 minutes to 3 minutes circa.

The main concept is once again based on perlinNoise which (I am sure you already guessed) is something I do like very much. So please start call me “The PerlinNoise Guy” or “Perlinator”. :-D

So this is my first speedcoding video (be sure to look at it in high quality):

Here’s the interactive demo:

400
Click to launch. Move mouse (x position) to change smoothness (my favourite values are around 100)

The code consist on a Branch.as class file (click to download) and some timeline code to assemble the demo:

import com.oaxoa.fx.Branch;

const w:uint=stage.stageWidth;
const h:uint=stage.stageHeight;

var ct:ColorTransform=new ColorTransform(1,1,1,1,1,1,1);
var renderView:BitmapData=new BitmapData(w, h, true);
var bmp:Bitmap=new Bitmap(renderView);
addChild(bmp);

var tf:TextFormat=new TextFormat("_sans", 16, 0, true);
var label:TextField=new TextField();
label.width=400;
label.defaultTextFormat=tf;
addChild(label);

var timer:Timer=new Timer(10);
timer.addEventListener(TimerEvent.TIMER, ontimer);
timer.start();

function ontimer(event:TimerEvent):void {
	addNew();
}
function addNew():void {
	label.text="Smoothness: "+String(mouseX-w/2);
	var tt:Branch=new Branch(mouseX-w/2);
	tt.x=stage.stageWidth/2;
	tt.y=stage.stageHeight/2;
	tt.addEventListener(Event.COMPLETE, oncomplete);
	addChild(tt);
	renderView.colorTransform(renderView.rect, ct);
}
function oncomplete(event:Event):void {
	var t:Branch=event.currentTarget as Branch;
	var matrix:Matrix=new Matrix();
	matrix.translate(t.x, t.y);
	renderView.draw(t, matrix);
	removeChild(t);
	t.removeEventListener(Event.COMPLETE, oncomplete);
	t=null;
}

I didn’t forget about the lightning class part 3 that I will publish soon :)

As usual if you liked this drop a line in the comments.
Ciao

11 Comments

Actionscript 3 Lightning class – step 2

actionscript 3, algorithms, BitmapData, fluids, fun, Math, perlinNoise, simulation

The first rule for the good blogger I read 18 months ago (when I started this blog) was: “Never, ever post on Sunday… people coming back to the office on monday morning will find tons of weekend rss notifications and miss your post among them”.

But… since I am not a good blogger and since this blog is mine… I do post whenever I want :-D

Here we are with the second post dedicated to the lightning class I’m working on. It had to force myself to sit down here and write again about this, I am working on other 3 nice experiments and the fun part of this class for me has already gone, now starts the boring part: optimize/parametrize/explainize. But I think it could be interesting for someone, so here we are.

Still no code, I still have to optimize/parametrize but I can start to “explain-ize”. In the first post we just saw a couple of samples running. Some people asked me for the raw logic behind this.

The key here are two perlinNoise, one for simulate the macro behaviour and one for the micro variations. As often a monodimensional (1px height) perlinNoise is perfect to simulate bidimensional effects, since perlinNoise images contain an additional dimension defined by luminosity variations.

So, if from a 2D perlinNoise image you can easily get a 3D voxelTerrain (X+Y+Height), from a 1D image you can easily get for instance 2D mountains (X+Height).
1px height perlinNoise images are very fast to render so they do not kill your cpu even if many of them are used.

I have prepared two “debug” sample movies. The first is to show how the two perlinNoise bitmapDatas affect the movement of the final shape (children are disabled for clarity purpose).


Debug sample #1

As you can see there are 3 different grey bars under the lightning:

  • The first one is the perlinNoise used to displace the discharge on a micro scale
  • the second one for the macro movements (this is really what makes it feel as real)
  • the third one is the image merged onto the second one to smooth the edges.

Obviously the 3 bitmaps are 1 pixel height, I just stretched them here to 30px to make ‘em visible.

Speaking about perlinNoise edges smoothing this is the fact: without any smoothing the extremities of the perlinNoise have a random value between 0×000000 and 0xffffff which stand for black and white. Black value will displace the beam in a negative direction, white value will displace it in a positive direction. To be sure the edges are sticked to the x/y coords of the graphic that simulates the origin of the discharge, we need no displacement at the beginning and at the end.
No displacement=grey value (0×808080).

The easiest way to do this is to create a vector shape, fill it with a gradient (alphas=[1,0,0,1]), adjust ration accordingly to the smooth percentage and draw it onto the macro variations bitmap (Bitmap.draw(…)). Is off course possible to to this directly using bitmap methods. But I found this being the most natural for me. I like the idea to mix vector and bitmaps using the easiest way for what I need.

Naturally you cannot set the last pixels to medium gray without some smooth transition, and so we use the gradient. Check this sample with code snippet:


perlinNoise edges smoothing

const grey:uint=0x808080;
var smooth:Sprite=new Sprite();
var ratioOffset:uint=smoothPercentage/100*128;
smooth.graphics.beginGradientFill(GradientType.LINEAR, [grey, grey, grey, grey], [1, 0, 0, 1], [0, ratioOffset, 255-ratioOffset, 255], matrix);
smooth.graphics.drawRect(0, 0, w, 1);

I used the smoothing only on the macro bitmap, not one the micro too save some cpu cycle on a barely visible detail and because I like the micro variations on the edges too.

The second one shows the same concept applied also to children with a slider to vary the children birth probability:

[demo removed cause I overwrote the files LOL. Don't ask to get them from backups please, simply refer to part 3 post :) ]

The main beam can create bridges of electricity, or “children”. A child is simply another instance of the class with a “generationNumber” parameter to manage descendant probability and avoid infite recursion. All the rules described until now applies to children too. Children need to be sticked to the parent beam so they always have a non-variable smoothing of 50%.

Coming soon with part 3 and the full class.
As always leave a comment if you find something interesting.

12 Comments

Actionscript 3 Lightning class – First tests

actionscript 3, advanced image editing, algorithms, fun, game, Math, perlinNoise, Physics, simulation

Here again with the first test of a Fx class.

The class can render lightnings with these specs:

- different shapes and aspect
- variable edge-smoothness to keep the extremities sticked to the origin
- runtime children generation (every trunk can generate children)


Sample #1


Sample #2

Perhaps not that useful but could be nice to implement in some game or demo.
Code soon.

13 Comments
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