Physics for Game Developers, 2nd Edition

Chapter 12. 3D Rigid-Body Simulator

In this chapter we’ll show you how to make the leap from 2D to 3D by implementing a rigid-body simulation of an airplane. Specifically, this is a simulation of the hypothetical airplane model that we’ll discuss extensively in Chapter 15. This airplane is of typical configuration with its large wings forward, its elevators aft, a single vertical tail, and plain flaps fitted on the wings.

As with the 2D simulator in previous chapters, we’ll concentrate on the code that implements the physics part of the simulator and not the platform-specific GUI aspects of the simulations.

As in 2D, there are four main elements to this 3D simulation—the model, integrator, user input, and rendering. Remember, the model refers to your idealization of the thing—an airplane, in this case—that you are trying to simulate, while the integrator refers to the method by which you integrate the differential equations of motion. These two elements take care of most of the physics of the simulation. The user input and rendering elements refer to how you’ll allow the user to interact with and view your simulation.

In this simulation, the world coordinate system has its positive x-axis pointing into the screen, its positive y-axis pointing to the left of your screen, and the positive z-axis pointing up. Also, the local, or body-fixed, coordinate system has its positive x-axis pointing toward the front of the airplane, its positive y-axis pointing to the port side (left side), and ...