Physics for Games

Part 1: Linear Forces

The first - and perhaps easiest - part of implementing any rigid body physics system is getting the entities in your scene to move in response to linear forces. With this implementation alone, you can achieve an interesting level of realism in your 2D (and even 3D) scene.

Let's begin by recalling the relationships between acceleration, velocity, and position.

Knowing all this, you should be able to understand the following source code fairly easily;

                        
function update(dtSeconds) {
    // Add up the forces acting on the circle
    const GRAVITY = 9.8;
    const lGravityForce = vec2(0, -1.0 * (lCircle.mass * GRAVITY));
    lCircle.force = addVec2(lCircle.force, lGravityForce);

    // Figure out acceleration (a = F / m)
    const lCurrentAcceleration = scaleVec2(lCircle.force, 1.0 / lCircle.mass);

    // Calculate the new velocity: v = v0 + a * t
    lCircle.velocity = addVec2(lCircle.velocity, scaleVec2(lCurrentAcceleration, dtSeconds));

    // Update the position based on velocity: x = x0 + v * t
    lCircle.position = addVec2(lCircle.position, scaleVec2(lCircle.velocity, dtSeconds));

    // Update the model matrix accordingly
    lCircle.model = translateMatrix(mat4(), lCircle.position.x, lCircle.position.y, 0);

    // Reset the force vector for the next update
    lCircle.force = vec2()
}