Updates from January, 2011 Toggle Comment Threads

  • Urban 22:31 on 19 Jan. 2011 Permalink  

    Beyond gravity 

    With Gravity Lab, I’ve built what I think is a decent particle simulation framework. Which brings me to my hidden agenda: something I’ve wanted to do for a long time, but could only do incrementally, since the complexity of the entire task was just too overwhelming. So I present to you another particle simulator, codenamed Charges.

    It was a no-brainer, really. Ok, sure — there’s no money in educational apps. There’s that. But the thing was practically already done. Electric forces are just like gravitational forces: obeying inverse square law (read more here, or here). There’s just a matter of inverting the polarity, i.e., introducing “negative masses”. And change some constants.

    Or so I thought.

    It turns out a charged particle simulator is pretty useless by itself: particles always recombine (i.e., neutralize each other), or fly far away from each other until they get garbage-collected.

    What I needed were solid (metallic) objects, which could trap the particles — so I could observe the forces, make capacitors, simulate cathode ray tubes (CRT), and generally bring the “static” into “electrostatic”. So I decided to implement objects. And this is an epic journey of a developer, struggling with an interesting problem and generating much flow™ in the process. 🙂

    Simple enough, I decided to support rectangles and circles only. Why? Because this way, it can be quite easily checked whether a particle has hit the wall. When you tap the screen, I simply loop through an array of all objects and check if you tapped inside a body. If I find that to be true, I set the parent of the particle to the ID of the body. Then, when calculating the motion of the particle (which is done by summing all the forces of all the other particles), I only need to check if the particle has hit the parent object’s wall. If parent object is a rectangle, it’s really simple, like this:

    if rectangle
        if parent.left_wall.x < particle.x < parent.right_wall.x
            move freely (left or right)
        else 
            dont move along x axis
        end
    
        if parent.bottom_wall.y < particle.y < parent.top_wall.y
            move freely (up or down)
        else
            dont move along y axis
        end
    end
    

    With circles, I’ve already hit the first obstacle. You can’t separate x and y coordinate checking into separate conditions, because they are dependent. I tried many options without real success and particles always got stuck in some kind of deadlocked state. What finally proved to be the most efficient solution, was checking if the particle’s future position is too far away from the circle center (more than circle radius away), and projecting it back onto the circle boundary. Like this:

    if circle
        if (x^2 + y^2 < circle.radius^2)   
            move freely along x and y
        else
            phi = atan2(y,x)
            x = circle.radius * cos(phi)
            y = circle.radius * cos(phi)
        end
    end
    

    It worked like a charm. But I faced a more dire problem, one that could not be solved in my limited particle-has-a-single-parent model. Namely, my particles couldn’t migrate from one parent to the next. Which would, of course, happen in nature: if you bring together a charged metallic object and an uncharged metallic object, some of the charge from the first one will be forced out into the second one.

    I wanted that, and it obviously couldn’t be done. Indeed, the composite objects made of circles and rectangles can become quite complex; how could one force the particles to stay within an object in such simple terms as shown above?

    I slept on it, and slept some more. And for the first time I can remember, the solution suddenly blinded me one morning. Yesterday’s morning, that is. And it goes like this.

    Timesharing.

    Let me explain. If a particle happens to be inside an overlap of two or more metallic objects (i.e, inside two or more objects at the same time), cycle through all of them every n frames of the animation. Let them all be parents, but not at the same time. And let the electrostatic forces that drive the particles away from each other do all the work.

    The bottom right particle in the picture above desperately wants to break away, to the South-East direction (down and to the right). If we bring in another body, the particle now has 2 parents (overlap). We iterate through both of them and let the particle just savor the moment for a while. And the moment it is assigned to object 2 above, it is propelled towards South-East, no longer bound by the first object. When there’s no more overlap, the time-sharing doesn’t happen any more. Voila.

    So hopefully, a new and amazing simulator will soon hit the App store. Stay tuned.

     
    • Bozo 19:44 on 20 Jan. 2011 Permalink

      ne ne ne… nisi še končal z gravitacijo :))) včeri zvečer sem neki vidu v enem dokumentarcu pa moraš to sprogramirat!!!… drugač pa enkrat pridem, pa da mi to vse pokažeš!

    • Urban 23:27 on 20 Jan. 2011 Permalink

      Dej posharej kej na deliciousu :p

  • Urban 21:11 on 18 Jan. 2011 Permalink  

    More Gravity Lab 

    It’s been well over a month since Gravity Lab 1.0 was released. Now it has received a nice update with particle trails and a solar system preset. The solar system is actually just a set of bodies with preset masses and initial velocities1. The resulting setup is quite a faithful representation of the real solar system, down to the orbiting times (i.e., the lengths of planetary years) in correct proportions. And there’s also a satellite preset.

    Now you can test first-hand the effects of a stray sun wandering into our planetary system and ejecting Earth into outer space. 🙂

    There’s also a new and interesting setting — adjustable gravitational constant, which allows you to distort the simulated universe and observe the consequences.

    1. planetary masses courtesy of Wolfram Alpha; initial velocities were determined such that a stable orbit was ensured []
     
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