Last lecture, we talked about animation, and the techniques used to tell a story. Today, we'll talk about how to simulate physical things (e.g. clothes) using physics.
Newton's Law states that $F = ma$, where the force on an object is equal to the mass of the object times the acceleration of the object.
To calculate the position of an object provided the velocity and acceleration:
$x(t) = x_0 + v_{0x}t + \frac{1}{2}at^2$
We can simulate a piece of cloth as a collection of particles (a collection of point masses). We can also simulate other, more complicated things (e.g. waves & water).
Single particles are very simple to render. Large groups of particles can produce interesting effects, and these particles supplement basic ballistic rules:
In mass-spring systems, we have point masses (the blue dots, in the video below) and springs connecting those point masses (the white lines). We join external forces (e.g. gravity) and internal forces (e.g. between particles, due to the parameters of the spring) that dictate the motion of the particles.
In this video, we see a mass-spring system, where a mass (the top mass) is pinned to the scene.
In this video, we see a mass-spring system, where a mass (the top mass) is pinned to the scene.
We can also model hair using this spring-mass system, with an additional constraint: we can't have hair strands intersecting with one another, so we need to account for the collision forces between them.
For an idealized spring, a spring force is a force that pulls each endpoint towards each other. $a$ and $b$ are vectors, and $f$ is the force between the two particles. Hooke's law dictates the force between particles; it states that the amount of force is linearly proportional to the distance between the particles, scaled by a constant $k_s$ (spring coefficient).