Verlet Integration and Cloth Physics Simulation

Summary

Physics simulation in games (or simply game physics) is a vast topic, and in this post we'll cover only a tiny part of it; yet certainly an interesting one! Let's understand what Verlet integration is by implementing a simple 2D cloth simulation with C++. Physics in games is always fun, isn't it? Have you ever ditched the main quest of a level just to blow something up? I know I have. But even more fun than watching objects bounce around the screen is to understand how we can use simple concepts from high-school mathematics to simulate those physics laws with code. This article is divided into the following sections: The basics of physics simulation A quick review of differentiation and integration Numerical integration in the context of motion Euler Integration Verlet Integration JavaScript implementation of Verlet integration C++ implementation of cloth simulation And this is still a tiny subset of what we understand by game physics. Our main goal is to explore something called Verlet integration. We'll look at its motivations, intuition, and how we can use Verlet integration to write a simple 2D cloth simulation with C++. Verlet integration is a very popular method to solve systems of particles (masses) and constraints (springs). Oh, and if you ever asked yourself why your university required you to take Calculus as a CS student, this blog post might help you answer that question as well. Physics Simulation is a Discrete Game Simulating physics with a computer requires us to compute things like forces, acceleration, velocity, and position in discrete time steps. We need a way of predicting the new position of an object on the screen for each time step. Computers run at discrete clock ticks, requiring results to be approximated using numerical methods. As it turns out, there are several methods we can use to find these predictions. Some prediction methods are faster, some are more stable, and some are expensive but give better approximations. Depending on the type...