Tech's Obsession with Big
medium.com1 pointsby t3hprogrammer0 comments
ball.y += ball.vy;
ball.vy += gravity;
It looks okay and seems to match the constant acceleration kinematics formulas, but what we're really doing is Euler integration, a first-order numerical integration method. It's pretty bad even for numerical integration, so we should use fourth-order Runge-Kutta (RK4) instead [1]. ball.y = platform.y - ball.radius;
It works in the given situation, of course, but wait a minute - if the ball is moving at 5 cm/frame and, at that particular frame, happens to be 1 cm above the platform, then the ball will move only 1 cm/frame! This means that the velocity has apparently dropped to some nonsensical value! But we can't move it anywhere else, because we haven't checked for collisions yet, and this example also assumes that there is only one other platform the ball could collide with - if it was an acute corner of two platforms, then we're in a bit of a rough situation. ball.vy *= -0.4;
The value, 0.4, is called the coefficient of restitution. In his particular case, where the platform is immovable, it's fairly reasonable (if we had immovable objects in reality!) but obviously a more sophisticated collision will need to consider energy factors.
I tried to embed the "scripting" language as a texture in WebGL to keep the implementation very fast (note that every pixel is a cell), but I think I worked myself into a corner.
Source code here: https://github.com/ericleong/sand.js