2D Video Game physics

2D physics for particle

Base equations for movement:
dt = t(i+1) - ti
v(ti+1) = v(ti) + (f(ti)/m)dt
p(ti+1) = p(ti) + v(ti+1)dt

2D Physics for Rigid Body

Position and Mass properties

Center of Mass: $\frac{m_i*r_i}{M}$

If the density of the figure is uniform, then the center of mass is the same as the geometric center also known as centroid.

Since rigid body are continues through the particles, we should not use a discrete equation, but use an integral to calculate the Center of mass of a Rigid Body:
$\frac{1}{M} \int_v p(r)r, dv$

Where r is the position of each point ,p is a function that gives the density at each point within the body (there's the [v]olume part).

Collisions

For sake of simplicity, we will not be using any advanced methods, like SAT or DBVT.

The method we are using is the Axis Aligned Bounding Boxes that can be calculated using AABBvsAABB function.

We simply check if one Axis-Aligned box is inside another Axis-Aligned Box: